actually has a probe of unconventional superconductors and I illustrated this on cuprates and iron-based superconductors. So concerning iron-based superconductors, I didn't have time to talk about the superconduting state. So if somebody has questions, I can answer them later on. But for the second part of the lecture, I want to switch a little bit of subject. I want to talk about the Higgs mode in superconductors and essentially how to detect it. So this is going to involve some Raman measurements. But I'm going also to dwell a bit on how we can couple to terroits light in time domain measurements. OK, so first, an introduction to the Higgs mode in superconductors. So as you have seen in the first lectures, you can describe your superconductor in terms of a lambda functional. And this is very general, right? So you have this Mexican hat potential. And once you look at this Mexican hat potential, the ground state is sitting at the bottom here. And you can have, from a very general point of view, two kinds of collective excitations, one that will involve the phase of the superconduting order parameter, and the other one that will involve its amplitude. Now, this has been worked out actually in the 60s by various people. And what you can show is that if the superfluid is neutral, let's say, for example, like helium superfluid, the phase mode is linearly dispersing the function of momentum. And the amplitude mode is gapped. And it's gapped by an amount which is twice the superconduting gap. Now, if you are in a charge system, actually the phase mode couples to the Coulomb interaction, and it's pushed to the plasma energy. This is the so-called Anderson-Higgs mechanism. So it's essentially irrelevant in superconductors. It's just a plasma frequency. Now, the amplitude mode stays. And actually, in that case, you can show that this amplitude mode, in the case of a superconductor, has a strong analogy with the Higgs mode of a standard model. And essentially, to make a long story short, the idea is that in Lorentz-Nevian system, so in our case, the Lorentz-Nevian in the superconductors is associated to the fact that there is some inherent particle whole symmetry in the superconductor state, the Higgs is a true collective mode in the sense that it's decoupled from the phase mode. Now, of course, what you see here is that in this simple cartoon picture, the Higgs mode is sitting right at 2 delta. And as you know from the previous lecture, at 2 delta, it's also the boundary of the electric of the Cooper player braking continuum. So it's sitting right at the threshold of a continuum. So it's expected to be damped. Now, there has been just briefly to mention that apart from superconductors, there has been observation of such an amplitude mode, or at least fingerprint of it, in other systems. The idea is that in order to observe really this excitation, you must have some approximate Lorentz-Nevian. And this can be achieved, for example, in a cold atom gas, where you can show that in some limit of the Coulomb interaction potential, you can go through a quantum critical point from a mud phase to a super-free phase. And close to this quantum critical point, there is such a symmetry. And near this quantum critical point, you can see excitations that look like this Higgs mode. Now, what I want to briefly comment is how to actually probe this mode. So this mode is actually not trivial to probe, because it doesn't carry any charge nor any spin. So it actually, relatively, it weakly couples to external probe. So I'm going to illustrate this using the formalism of BCS theory and introducing Anderson-Suelospin. So the Anderson-Suelospin sigma is written this way. So it's essentially the polymatrices contracted by the superconducting wave function written in non-boo space, so in a C dagger up C down. Now, you can write down, actually, your BCS Hamiltonian just in terms of this Anderson-Suelospin. And this form of the BCS Hamiltonian takes a relatively remarkably compact form, where you have this Anderson-Suelospin here, sigma k, that couples to an effective field. And this effective field is a three-component vector. The first two components are essentially the imaginary and real part of the superconducting gap. So if you take, for example, the superconducting gap, we rear, one of them would be zero. And the third component will include the dispersion. And if you introduce the coupling between light and the superconductor using the pyro substitution, this will be the sum of psi k minus ea plus psi k plus ea. So this is how in this formalism, if you want a light couple to this Suelospin. Now, how do you interpret this Suelospin? So if you look, for example, at the z component of the Suelospin, you can write it this way. And what you can see is that the z component of this Anderson-Suelospin is either minus 1 half or plus 1 half, depending whether the plus k and minus k states are occupied or not. So if you want, maybe the simplest is to start with a normal metal at t equals zero. When you are below kf, they are occupied. So you have spin 1 half. And when you are above kf, those are unoccupied. So you have spin minus 1 half.  So if you want to rethink of the BCF wave function in terms of this Anderson-Suelospin, the BCF wave function will be a linear combination of the up and down spin with uk's and vk's as the prefactors. OK, so right now this is just a rewriting of the BCS Hamiltonian. Now, what is sort of nice in this picture is now you can have sort of an intuitive picture of how this of the BCS gradient state is going to evolve once you couple it to light. So you can think of it as a Blush equations where the dynamic of this pseudo-spin is going to follow this Blush equation where the Anderson-Suelospins are going to be coupled to this effective field, bk. The orientation of the effective field will be given by the superconducting gap here, but also by the value of the vector potential of light. So that you will have a complex dynamic where essentially the pseudo-spins are going to rotate around this effective field. And the orientation of this effective field is going to depend on k. And the resulting gap dynamics is going to be the sum over all the k of the x and y component of this pseudo-spin. And this is, of course, has to be solved self-consistently because both sigma k and bk depend on the superconducting gap. Now, what is interesting in this picture is that if you look at this effective field, and in particular the z component, which represents the coupling to light, you can expand it. And what you see is that once you write down explicitly what this term gives you, you can see that there is actually no coupling to linear order in A and that the next order comes with A squared. So what this shows you is that when you couple light to this pseudo-spin, there is actually no term that couples linearly to it, to the gap dynamics. And the only term that comes goes to A squared. So light enters the z component of the effective magnetic field only up to order A squared. So this is another way of saying that actually there is actually very weak coupling between light and the motion of this Anderson pseudo-spin, so to speak, and so to the Higgs mode. OK, so now I'm going to show you an attempt to probe these Higgs dynamics, essentially using two lines of reasoning. One is, so I'm going to go in historical order. First, I'm going to show you that in a situation where superconductivity coexist with a charge-on-CD wave state, there is actually an indirect coupling between the Higgs mode and the charge-on-CD wave state that is going to make this mode active in a Raman measurement. And in the second part, I'm going to show you another way of probing these Higgs dynamics directly, not necessarily in cases where superconductivity coexist with charge-on-CD wave order. So first, let me start with the case where super, yes. So I think if there is disorder, yes. So the question was, if there is disorder, what happens to this coupling? So I think if there is disorder, the phase and amplitude start to mix. And then you can couple here. So I think this has been studied, for example, by Lara Ben-Fato in some systems. OK, so let me first start with niobium dysenium. So this is a charge-on-CD wave superconductor. The charge-on-CD wave transition happens at around 40 Kelvin. It's barely visible here on this resistivity curve. And then it undergoes a superconducting transition at about 7 Kelvin. Now the charge-on-CD wave is a slightly incommensurate and orders along three different directions, oriented by 120 degrees. So it's still an argument in this system about the respective importance of Fermi surface testing and electron phonon coupling as to the main driver of the charge-on-CD wave state. And there is still a debate about the exact interplay between charge-on-CD wave and CDW gap. But what I'm going to focus on is, of course, this is a simple picture of the charge-on-CD wave gap opening. So this is exactly the same picture as the one I showed you for the spin-on-CD wave gap. You have a new periodicity and back-folding and opening of gaps at a specific point of the Brinoise zone. But now I'm not going to focus on this. If you're on single-particle excitation, I'm going to focus on collective excitation. So just like I showed you in the case of a superconductor, you can define an order parameter of the charge-on-CD wave. In that case, it will be the modulation of the charge-on-CD that I showed here. And you can have both. So the other parameter would have, in general, a phase and an amplitude. And you can have excitation that will involve the amplitude and the phase of this parameter. So the amplitude is going to be called the amplitude-on, or the charge-on-CD wave amplitude mode. And this is essentially a modulation of the charge-on-CD wave. So if electrons are coupled to the lattice, to this modulation of the electron density will correspond to an atomic displacement. So this will be essentially a hybrid excitation between electrons and phonons. It will be a phonon-like excitation. And while if you tune the phase, here you will have the phase mode. And this phase mode is gapless. So the amplitude-on has a gap, and the phase mode is gapless. In the case of a clean charge-on-CD wave system. So you may say, well, this is the Higgs mode also. Now, this is an amplitude mode of another parameter. But the analogy with the Higgs mode is less direct than the case of a superconductor. Because in the charge-on-CD wave state, there is no guarantee that particle-hole symmetry is preserved. In fact, in general, it's not. So the analogy with the Higgs mode does not really exist in that case. But the key point is that this amplitude mode here can be Raman-active. So it can be directly seen in the Raman measurements. So here I show you Raman-spectra as a function of temperature. And what you see is that when you cool down below the charge-on-CD wave transition, there is a new mode that appears. It's a relatively sharp mode. And this new mode corresponds to a phonon-like excitation. Yes. I think in general, they do not mix. Probably in the presence of disorder, again, they would mix. But in the clean system, they do not mix. Yes. Yeah. Yeah, it's a good question. So in the case of niobium diselenide, the CDW gap is not clearly observed in this niobium diselenide. But there is another compound, thallium diselenide, where we can really nicely see the CDW gap and the amplitude mode is inside it. So from that point of view, it would be not damped. But of course, nesting is never perfect. So you will always have a residual Fermi surface. So you expect, in general, some damping of it. It's not the gap, yeah. Yeah, so I think that's a good question. So the problem is there are two other measurements of the gap. You have photoemission measurements and you have STM measurements. And they give vastly different energy scales for these gaps. So the STM measurements give gaps of several tens of millivolts, so much higher than this energy. But they're also from photoemission measurements which show smaller gaps, which are on the order of this. Now I would, yeah. Now if I go now, we have recent measurements on a 2H thallium diselenide where we actually see the gap. And the gap is at much higher energy. And the gap is very broad. So we believe that, and we see the amplitude mode, it's well inside the gap. So we believe that by comparing with nethermthallium diselenide, we believe this is the amplitude. OK, so what happens? And historically, this was the first time the coupling to the Higgs mode in a superconductor was evoked, was that when you cool down below Tc, and this is sort of the first measurements where we could actually see the signal, the Raman signal from a superconducting phase. This was on nethermthallium diselenide, so 1990 by Suryakumar and Klein. When you cool down below Tc, so this is the amplitude mode of the CDW phase that I showed you previously. And you have right below in energy this amplitude mode of the Charzon CDW phase. You have the emergence of a sharp peak, which could be interpreted as a superconducting gap energy to delta. Now what is striking about this superconducting mode is the way it interplays with the Charzon CDW mode. And this is most easily seen by doing a careful temperature dependent measurement across the superconducting transition temperature. And what you see is that essentially when you cool down below Tc, it looks as if this mode here at low energy, the superconducting induced mode, is stealing spectral weight from the amplitude mode of the Charzon CDW phase. So there seem to be an intimate link between these two excitations. And this is actually also seen, and this was first seen actually as a function of magnetic field. So the same thing happens as a function of magnetic field. So this, yes. So that's one scenario. So one scenario, so if you were to follow the idea that this mode here probably is the CDW gap, that could be a sign that could be interpreted as a sign of competition, yes. Now we believe, based on the comparison with the sister compound tally of the SNN, that this is actually the amplitude mode and not the gap. But that could in principle be a possible scenario. But at that time, this was not the scenario that was put forward. The scenario that was put forward was the one that there is actually a coupling between the amplitude mode of the Charzon CDW phase and the amplitude mode of the superconducting phase in other words, the Higgs mode. And this was the scenario proposed by Littlewood and Varma. So this is a PRB paper of 1982. So quite right after the first experimental measurements. And what they proposed here, so I'm extracting an excerpt from this paper. So keeping in mind that U0, so U0 is the lattice distortion associated to the Charzon CDW mode, coupled to the BCS gap. So the way it is coupled was presumably thought that this distortion, by distorting the lattice, modulate the Fermi, the density of state of the Fermi energy. And by modifying the density of state of the Fermi energy, it's also modifying the gap. But at that time in this paper, it was really a phenomenological coupling between the two. We produce a time-dependent modulation of delta. There's the electron phonon coupling for this mode. We build the form. And you see they propose this coupling. So G is really a phenomenological coupling between here, this operator, which are the bosonic operator of this Charzon CDW phonon, and the BCS gap function. So this was proposed. And they could actually, so this is sort of the picture. So you modulate your Charzon CDW wave. And by modulating your Charzon CDW wave, you are modulating the gap. And this is the way these two other parameter oscillations are coupled. So in this scenario, yes. Yeah, you can think of it as an optical phonon. No, so there is a related effect. So there are some constraints to this coupling. First, you need to have a coupling that is strong enough. And this is usually achieved when the two mod energy are close enough in energy. And then the other thing is you need to have a phonon that strongly modulates your gap. And this was presumed to be the case in this Charzon CDW superconductor. But you're right that in fact, you have a very similar coupling between the phonon and the superconducting state. But instead of having tau 1 here, you would have tau 3. And this would be a more regular electron phonon coupling effect. In fact, this is a very special electron phonon coupling effect. And the question is how to derive this coupling constant. And this was done actually one year after by Brown and Levine who derived a microscopic mechanism, a microscopic picture of this coupling constant. But in the paper of Littlewood and Varma, this was taken as phenomenological. OK, so the idea in this scenario is that the Higgs mode would appear as a sort of a side band of the amplitude mode of the Charzon CDW phonon, essentially. So this is the calculation in that paper. So they calculate the phonon spectral function. And by coupling it to the Higgs mode of the superconductor, the phonon spectral function acquires a new pole. And this new pole will generically appear below to delta. So that is good because that is going to render it more long-lived. And those are calculations for varying coupling constant. You can see here this feature is the amplitude mode of the Charzon CDW state. And once you cool down below Tc, there is a very sharp mode, which in this theory is a delta function. And when you crank up the coupling constant, this goes more and more below to delta. So they actually derived an energy for these coupled excitations. And it's always sitting below to delta. So the fact that it's below to delta is good. It means it's going to be less damped than the conventional Higgs mode. It's unaffected by screening. So this is also an important aspect because the Higgs mode does not carry any charge. So Coulomb screening is not going to affect it. And this naturally explains the spectral rate transfer between the two. So you can actually do a more microscopic calculation, not just of the phonon spectral function, but actually on the total Raman response. This was done by Chehan Ben-Fato. So this is really calculating this kind of diagrams, where you have the, this would be the Raman, the regular electronic Raman bubble that I showed you in the first lecture. And that would couple to the CDW phonon. And this CDW phonon will in turn couple to the Higgs mode. And if you do that, what you see is that indeed, once you cross Tc, there is a spectral rate transfer between the CDW phonon and the Higgs mode below Tc. And this matches quite well the experiment that is observed in IEM, I said. Now, I should say that, and this is something that was sort of overlooked, since quite recently, and that goes back to the coupling, to the non-linear coupling I explained you in one of the first slide. So I showed you that actually there is a coupling that is possible to a square term. And you may say, well, Raman, after all, is a two-photon process. So why don't we see it directly?  Actually, you can ask yourself, well, what if I just get rid of the charge on CDW mode and I try to couple it directly? Then I would have this kind of diagrams. And then I can show that my Raman response will involve the first term here, which I labeled k, k is zero. This is the regular pair breaking term. So this is the one that is giving me sharp peak at two delta and the continuum. And if I do, if I insert the Higgs mode here, I will have an additional term. So if you want, this term will be in the density channel, so tau three in terms of polymetrices. And this one will be in the pairing channel, tau one. And what you can see that here in the numerator, this has this form. And usually, so gamma k is the Raman vertex essentially, this coupling between light and electrons. And in the literature, and in particular, if you look at Varmas paper, he would take this essentially as a constant, k independent. And because of particle whole symmetry, actually, because there is only epsilon k here, this vanishes. But you can really clearly see that as soon as you put some k dependence in the Raman vertex, there is no reason for this to vanish. Actually, and this is, I think, that was something that was overlooked. Actually, this direct coupling, not even thinking about 1000 city waveform is actually finite. Now, the question is how big it is. Now, actually, it's a little bit, in the case of a niobium dissonant, it's a little bit smaller, but not that small. So that actually, what you can see is that in the dotted lines here, this is the discontinuation here. And this can be enhanced, actually. If you gap out part of the Fermi surface, this can become more long-lived, and this can gain a lot in strength.  Now, of course, in the case of niobium dissonant, I such a direct coupling mechanism would not explain the spectrary transfer between the 1000 city waveform and the superconductive peak, at least not as easily as in the Varma model. But still, it's not completely out of the question that we can see this Higgs mode in just a regular superconductor, yes. So in this picture, it's at two delta. So the way it becomes more long-lived is because you have CDW gap. That gaps out part of the Fermi surface and that gives it more long. But it's still at two delta, no, no. For this, you need to have the CDW phase. Okay, so let me, so let's say that the spectrary transfer favor the phononic scenario and I'm going to show you experiment and the hydrostatic pressure, which also, I think, lay credit also to this phononic scenario. So the idea is that actually the phase diagram of this compound, 2-H niobium dissonant, is interesting under pressure. What you have when you apply hydrostatic pressure is that you have essentially a suppression of your charge on city wave state. But the superconducting transition temperature is actually very weakly pressure dependent. So by applying pressure, you can actually heal your CDW state and preserve essentially your superconducting state. So this is a key test if you want for this scenario in a way that let's see if really CDW state is crucial or not for the observation of this peak. So this is Raman measurement as a function of pressure. First, showing the data above Tc. So essentially here doing a horizontal line above Tc and this is tracking the pressure evolution of this amplitude mode of the charge on city wave phase. And here I'm showing you experiment in two different polarization configuration and in both polarization configuration, you can see that the peak of the amplitude mode of the city wave state indeed vanishes and that by the time you reach for GPA, it's essentially absent. So you have killed really the charge on city wave state. Now, what happens when you cool down through Tc? So this is above and below Tc at selected pressures. So what you see is that up to 3.2 GPA, you still have the emergence of this relatively sharp peak at low frequency in the superconducting state. There is still a transfer spectral rate and what you can see is that once you move out of the coexistence between superconductivity and charge on city wave, so at 4.4 GPA, instead of a relatively sharp peak, you have a broader signal and importantly, and I'm going to show you that in the next slide, this signal here which I reproduce here is located at a higher energy. Yes, as a function of magnetic field, pressure. Okay, so of course you would need an independent measurement of the superconducting gap for that, but the Higgs mode, if you look at this sharp mode here, it softens as a function of pressure. Much, yeah. Tc is flat, so presumably, yeah, doesn't change much by 10% at most. Well, this can be explained by the fact that, okay, so there is one way of explaining it, which cannot be unique, is as you kill the charge on city wave state, the amplitude mode of the charge on city wave state becomes closer and closer to the gap, and this pushes down, and this pushes down the gap to lower frequency, and this pushes down the gap to lower frequency. If they are exactly degenerate, actually, it's often completely to zero, I think in Barma theory. Yes, yes. No, at first, actually, it's not monotonic. At first, it moves closer, so see, it's a balance between the energy of the amplitude mode and to delta, and I think once they get closer, actually, it gets pushed to lower and lower frequency, and it gets to higher frequency only when it goes on the other side. I think that would be the picture of the Barma theory. Okay, but the key, I think the key observation here is a summarize in this spectrum, yes. So here, so in this scenario, the per-breaking peak is this one, right? In the red, the red spectra here, the spectra taken outside the coexistence region, right? So at high pressure, so this is above Tc and below Tc, this is this small thing, and once you enter the coexistence region, what you see is that you have a sharp peak, and this sharp peak is below to delta, and it's much sharper, and it's clearly not, we are not clearly not talking about the same feature as here, and remember, the Tc is almost equivalent in both states. Yes, yes, yes. Well, to delta, apparently, is what's remaining here. So it's essentially hidden on the high energy side of the Higgs mode. It's overwhelmed by the spectra wave of the Higgs mode, at least in this picture, yeah. And you have a good question. Again, there is another compound, okay, I could show you the data where we can actually both to delta and the Higgs mode. But in the case of Neobium disainite, we only see sharply one mode, and it's located below to delta. So there is a simultaneous collapse of the Higgs mode and CDW order. So if we identify the Higgs mode here as a sharp picture, clearly it has collapsed, while there is little change in Tc. So this is, again, in relatively good agreement with the fact that CDW phase is crucial in bringing this very sharp peak in the coexistence region. Now this can be actually compared with theoretical calculations. So these are theoretical calculations performed by Lara Benfato and coworkers, essentially taking the little VARMA theory. And what they can see is that once you are in the coexistence phase, you have a transfer of spectral weight from the amplitude mode of the Scharzen-CZF state to the Higgs mode. And once you enter the pure superconducting phase, what is remaining is just a weak to delta per breaking feature. So this, at least qualitatively, matches the data. Okay, so now let me move on to something that is somewhat different, but the motivation is, okay, so we see that, okay, we have at least some good evidence that the Higgs mode can be visible via Raman scattering in compounds where you have superconductivity and Scharzen-CZW order. I have already told you that there is some kind of warning sign that you could actually get direct coupling. It's not completely out of the question. So the question is whether you can use other techniques to couple to the Higgs mode via this A-square term, right? So that is going to be a nonlinear technique. And now I'm going to show you some experiment that we are done in the group of Riyoshi Mano. So I had the chance to spend one year in this group and I'm going to show you a bit of kind of another approach to see the Higgs mode using Terahertz light. So to see that, it's interesting to go back a bit back in time and look at some Siri paper that we're addressing sort of a different setting in which you would have a superconducting condensate or a superfluid state and where you would quench the interaction. So for example, suddenly increase the interaction and then follow the dynamic of the superconducting order parameter. So this was done, for example, by these people. So they essentially, non-adiabactically changed the pairing interaction. And what they see is that they see an oscillation. The system oscillates between the superfluid and the normal state is what they say. They see an oscillation of the order parameter. And this oscillation, this inverse of its period, is exactly two delta is the gap. So it's kind of, if you want the analog of the Higgs mode I just described, but this time, not in the frequency domain, but in the time domain. So in the non-adiabatic regime, you can have access actually to these dynamics. In principle, if you want to follow the receipt of the Siri paper, you would need to find a way to quench your pairing interaction. So of course, this is something that can be done theoretically, relatively easily, experimentally, this is another challenge. And if you do that, and in a non-adiabatic way, you would expect actually your gap oscillation. So these people could actually write down an analytical formula for the oscillation of the gap within the BCS framework. And what you can see is that indeed, you have a cosine two delta T over H bar oscillation. And there is a square root of T decay that is essentially due to the lambda damping to the fact that two delta is sitting right at the border of the electron hole continuum. What is giving this one over square root of T decay. Yeah, so there are different settings. So this is actually, this is a, okay, I won't go to the details, I'm not an expert of this kind of calculation, but actually the dynamics depends very much on how you actually prepare your state, whether you quench it down or you quench it up. And the dynamics are quite different. So here in that case, I think what they started is by reducing by half the pairing interaction. So the initial time was reducing by half the pairing interaction. And then let's see and see how the system evolves. So now you can actually try to compute something that may be a little bit more realistic in terms of condensed matter systems. You can try to compute the response of a BCS supercomputer after an optical quench. So you shine a very short pulse on the superconductor. And then you see how it evolves. So this was calculated by these people. And what you see is that two delta, so initially the superconducting gap decreases. So this can be explained by the fact that you are creating particle hole excitations in a non-diabetic way. So this is reducing a little bit your superconducting amplitude. And what you see is that for sufficiently short pulses, so in that case, three picoseconds, you have oscillations. But if you take a very long pulse, so if you don't satisfy the non-diabetic condition, so in that case, the non-diabetic condition would have to have a pulse whose duration is shorter than the inverse of two delta, essentially. You see nothing. So how to do that? So this is another way of looking at the same physics. So if you take your Mexican hat potential, you are essentially sending an optical pulse, you are reducing the widths of your Mexican hat potential, and then the system starts to evolve around the minimum. This is your new example. So you reduce here your other parameter, and then the system is going to oscillate around, around. So this kind of settings has been actually discussed even in the 70s in the context of microwave measurements in superconductors. So one way of seeing how you can quench your superconducting gap using terrorist light or infrared light near the gap frequency is by looking at the gap equation. So if you modify the temperature of your, if you create quasi-particles out of equilibrium according to the gap equation, this is going to change your gap amplitude, and this could provide a way of quenching your superconducting. So essentially creating particle hole excitation, boguluboff excitation in another diabetic way. But for that, there is a condition is that the widths of the optical pulse has to be shorter than h bar over delta. So this can be done, for example, here by shining light that is below the gap. And so with an energy that is slightly below to delta, but the widths in time that is shorter than h bar over delta. So this requires for typical low DC superconductors, this requires a pulse which are in the mid-evolved energy range. So those are terrorist regions and which have picoseconduration. So this experiment was actually done. So here I'm showing you an experiment done on liobium nitride. So it's a terrorist pump, terrorist probe measurements.  So this is the spectrum of this terrorist pulse. So it's roughly centered about one terrorist. So one terrorist is roughly a three mevolved. And this is essentially a single cycle pulse in the time domain. So typical width is about one picosecond. And what you're going to do is you are going to pump your system with this. And then you are going to see its evolution with time by sending another probe pulse that is going to be also in the terrorist range to probe the dynamics of your superconducting. So this is the measurements that was performed. So this is the transmitted electric field in the terrorist range. So remember that in a BCS superconductor, if you are shining light at an energy that is below two delta, there is no transmission. So if you have a reduction of superfluid density or a reduction of two delta, you're going to have a modulation of your transmission. And this is what is observed here. So right immediately after the pump, there is an increase of the transmission. So this increase of the transmission can be interpreted as a reduction of the gap.  And then you can see oscillations. The oscillations are particularly visible here at low fluence when you exert a pump that is not too intense. If you exert a pump, a pump pulse that is too intense, they are essentially damped. And you can extract the frequency of these oscillations. And the frequency of these oscillations at low pump intensity matches very well twice the gap energy that is measured independently by equilibrium transmission measurements. So you have time domain oscillations of your transmitted electric field that have a frequency of exactly two delta. Now it's interesting to compare. Yes. Okay, I'm going to come back to that later. So right now, if you think about this quench, this theoretical ideas about quench measurement superconductors, this really looks like you have realized this quench measurement, right? You quench and you see oscillations at two delta. This really matches. But I'm going to come back to a possible other alternative explanations. Okay, so just to show you, it's interesting to compare the same measurements, but now you don't pump with low energy pulses or close to delta, but you pump at a much higher frequency. So you use visible pulse for example. Now if you do that, so this is the measurements here on the left, what you see is a large signal, but there are absolutely no oscillations. And the reason is presumably relatively simple. When you shine 1.5 electron volt light, you are creating a bunch of electron hole excitation of very high energy. When they cascade, they break completely your coherence. So there is no hope of finding these two delta oscillations. And for that, you really need to use low frequency light. But there is a loss of coherence when you pump with too high energy. Now there is something that is interesting is, so up to now I have focused to a regime here where you see oscillations that persist when the pump is off. So if you want free oscillations. Now you can be interested also, is what is going on actually when both pump and probe overlap. And here this is kind of a zoom, you can zoom in this region here. So this is the waveform of the pump and this is the signal of the probe. And what you can see actually is that the probe seemed to follow not the electric field of the pump, the square of it. So if you look this minima here correspond to this maxima here, this maxima correspond to this maxima. So it looks like when both pump and probe overlap, there is a signal in the probe that is following E square. So you can actually see that more nicely if instead of using essentially a single cycle terrarium waveform, but now you shine a multi-cycle waveform. So now you use for example a narrow bandpass filter. You narrow down in frequency opals. Of course you broaden it in the time domain and this time you have many oscillations. And if you do that you see that you see really clearly these oscillations in the probe signal and these oscillations are really nicely following the square of the pump. So people who do nonlinear optics, they know that. They immediately say, ah, this is a third order signal. So this kind of response that follows E square in the language of nonlinear optics is considered as a third order nonlinearity. And by the way, this is also how these people in nonlinear optics describe Raman also as a third order susceptibility tensor. So I'm going to come back a little bit because this is not the way we in the condensed matter community are used to think about it. But for now let's say that there is a signal that follows E square. So this actually is interesting. You can do a much simpler measurements and these guys did the simpler measurements. You can say, okay, so there is an E square signal. So I am shining E and I collect some E square signal. And actually there is another third order nonlinearity that is much simpler. Third order generation. I shine omega and I look at a signal at three omega. This is also a third order nonlinear susceptibility. So you can do that. You can do not a pump probe signal but read just a very simple nonlinear optic measurement. You shine a tear out slide and you look at its frequency domain composition upon passing through the sample. And what you see is that indeed, so the key curve I think is here, is that you have the fundamental here located right below one terahertz. And when you cool down below TC, there is indeed an harmonic of this fundamental here at three omega that is only seen below two delta. And this, the intensity of this harmonics follow the six power of the pump which is also what is expected for a third order nonlinearity. Yes, yeah. So this is omega here and this is three omega. So it's third harmonic generation. No, second harmonic generation. This is third, yeah. So second harmonic generation is only active when you have a material where inversion symmetry is broken. So it's a well-known tool to study, for example, further electricity. And third harmonic generation is in principle always possible. It's just that most of the time it's weak. So here actually it's a sizable signal and it's only activated in the superconducting state. So actually the theory of this effect was worked out by Tsuji and Aoki. And what they show that if you, the Anderson pseudo-spin formalism, you can actually compute the nonlinear current and they show that the third order nonlinear current is actually directly linked to the oscillation of the amplitude of the gap. And importantly, this oscillation of the gap is resonant when the frequency of the incoming light omega is exactly equal to delta. So you shine light at delta and you collect light at three delta. So in fact, if you think about it, it's exactly like a Raman process, right? You shine light at delta, you collect light at three delta. So if I were a Raman guy, I would say, okay, so I'm now going to plot everything in terms of Raman shift. So three delta minus delta to delta. It's my two delta peak. Okay, but then you are going to see me wait. Could this be the per-breaking peak there? I will come back to that in a moment. So anyway, so you expect a resonance signal when exactly you are matching the omega equal delta condition. So it's difficult actually to do these measurements at continuously tunable frequencies. So what these people did is actually they tune the gap frequency by tuning the temperature. So if you assume that the gap frequency follows BCS temperature dependence, this is one way of tuning the gap amplitude. And what they show is that indeed, the temperature at which the signal is resonant seem to match at different frequencies. The temperature at which you would expect omega to match delta if it was to follow BCS temperature dependence. Okay, so so far so good. We have seen sort of two manifestation of a two delta mode, one in the time domain in the form of some form of transient response that was oscillating at two delta. And another one, which was sort of a forced oscillation if you want, but that seemed to be linked directly to some kind of non-linear optical susceptibility. And both of them are two delta. So actually once you see this and you know a little bit about Raman, there is of course an alternative explanation at least to this kind of measurements. I think it's a bit less obvious about the transient measurement in the time domain, but at least for the third harmonic generation, there is an obvious alternative which is that it is the pair breaking peak. And actually these people, Tugia and Aoki, when they computed the third harmonic generation response, they worked out in an approximation where the pair breaking peak was zero. And this is because they took essentially constant vertices, so it screened out. But of course, we know from Raman's scattering point of view that this is a special case. And in fact, if you don't take this a special case and you take a very general calculation that was done by Chia and Ben-Fato, you realize that indeed once you compute the third order non-linear susceptibility, so this third harmonic generation, so this is essentially the same diagram as in Raman except that the incoming frequencies are slightly different, but it's essentially the same diagram as with Raman. So you have this first diagram here, which is the one that is known from Raman's scattering and that is going to give you the pair breaking peak energy. And then you have these other diagrams here which are essentially this direct coupling to the Higgs that I was talking to you before. Yes. No, it's a pole, I think. Yeah, it's kind of a borderline case. It's really at the bottom of the continuum here. Okay, so and if you do that, you realize that generically, this contribution is actually several orders of magnitude smaller than the pair breaking contribution. So this is essentially the intensity as a function of omega. Now the bad part of it is that actually both contributions are resonance at delta. Delta to three delta, of course, because we know from Raman that we have to have a mode at two delta. But both of them are resonant at the same frequency, but one of them is at least three orders of magnitude smaller so that this fixed contribution is actually much smaller generically in the BCS approximation of this one. Now there is one way to distinguish between the two which is in the polarization dependence. So in fact, if you take just a very simple model, square lattice with nearest neuron hopping, you can actually compute the polarization dependence of the signal. And what you realize is that the Higgs mode contribution is essentially independent of the angle of the incoming light with respect to the axis. Whereas the pair breaking contribution actually is very strongly dependent on your incoming polarization. And this we know from Raman's scattering calculation that indeed such a response is going to depend very much on the kind of light polarization that you use. So in the case of just a tight binding model with only nearest neighbor hopping, actually the pair breaking contribution vanishes when you excite at 45 degrees of the axis. Whereas the Higgs contribution is completely isotropic. So this tells you that, okay, maybe there is a way to disentangle these two contribution looking at the polarization dependence of the signal. And if you do that, and this is sort of the puzzle, so you can do that in neighbor of nitride. And what you see to make a story short is that the third harmonic generation signal is essentially independent of polarization. Completely within two percent. You hardly detect any polarization dependence. And this is the puzzle because it's very hard for any generic system to have the pair breaking contribution be so independent of polarization orientation. And only the Higgs mode actually guarantees you that. So this is the puzzle. In the BCS approximation, you would expect the Higgs contribution to be orders of magnitude weaker. But yet, in the experiment, it seemed to be the relevant one for these measurements. So I think there is still no good explanation for what reason the Higgs mode apparently seemed to dominate these measurements. So there was some attempt to go beyond the BCS approximation by including retardation effect by coupling to some phonon mode. And these measurements show that if you include retardation, you bring the contribution from the Higgs mode a bit closer to what you would expect from the pair breaking. But I think right now this is a bit still speculative. Okay, so in the remaining part of this second lecture, let me now talk about some recent measurement we did in collaboration with the group of Fuyoshi Mano in Japan, yes. Yes. In the BCS approximation, yeah. Yeah. Yeah, that's really puzzling, yeah. Yeah, that is the puzzling, yeah. And if it's correct, then it sort of also would be a main drive to sort of reconsider also Raman scattering measurements if you're going to operate. So it brings a lot of question. Okay, so now what happens if you, so up to now I discussed about S wave superconductor. So Niagara Nitride is an S wave superconductor. It's not as simple as that because it's a multiband S wave superconductor, but still we think we reasonably understand the superconductor. So now let me briefly talk to you about what's going on in D wave. Okay, so in D wave the amplitude mode would correspond to a homogeneous oscillation of the D wave gap amplitude. So that would be this form. Now it was asked by Barlas and Varma that you could have actually oscillations that break the lattice symmetry, but here let me for now just consider only the conventional Higgs mode in the sense that it's in the A1G symmetry. So it's modulating the gap in a way that it does not break lattice symmetry. Now what are the challenges in probing this Higgs mode for D wave? Well the first thing is that as we discussed in general is damped and in the D wave superconductor and in the D wave superconductor it's even worse because here we have plenty of low energy excitation because there are nodes. So you would expect the damping to be even more dramatic than in the case of an S wave. So this was calculated by Peronacci and coworkers using a quench setup. So similar to the setup I showed you before, essentially quenching the pairing interaction and seeing how it evolves. And in the dotted line this is a case of S wave. And in the red line this is D wave and you see immediately that the damping in the case of D wave is as expected much faster than in the case of the S wave superconductor. So that's one challenge. In the terms of transient dynamics you would expect these two delta oscillations to be much more short lived. Now there are other challenge but there are more technical. So first it's a bit more difficult to produce intense pulse in the spectral range of delta for high Tc cuprays for example. So the delta, the superconducting gap in high Tc cuprays is in several tenths of millivolts and it's a bit harder to produce intense pulse in this energy range. So in other words, the resonance condition is harder to fulfill. And of course the equivalent of that is that in terms of reaching non-adiabaticity it requires really ultra short pulse. Sub hundred femtosecond pulse if you want to reach the non-adiabaticity. And this is quite challenging. So what I'm going to show you is a first attempt to measure this physics but I'm going to focus on essentially probing not this transient oscillation after quench or non-adiabatic excitation of your superconducting state but looking more at this third order nonlinear response that I've been discussing in the context of third harmonic generation. So the setup is the following. So we are working on crystals. So the setup that I showed you where we were looking at the transmission measurements was on on-scene films. So of course on crystals those are bulk materials so you cannot really transmit your terrohertz wave. So what we did is actually to use a setup where you pump with terrohertz but you are going to look at your non-linear response by probing its effect on the optical reflectivity. So high energy response. So this is the form of the terrohertz electric field. So it's relatively high. So it's about one order of magnitude higher in electric field than the experiment on niobium nitride. So because this is much higher. So you really need a much stronger pulse to really affect your superconducting state. And this is centered as 0.6 terrohertz so about one millivolts. So clearly we are in the non-resonant regime. So if you look at the theoretical calculation where you see the resonance signal of the third harmonic generation picking at delta here we are really on the tail of it. So we are in the non-resonant regime. So this is so what we did is that one nice thing about using optical probe in reflectivity configuration is that you can actually tune your light polarization. So you can actually quite easily look at the response as a function of orientation of polarization with respect to the crystallographic axis. So this is experiment on b-smit 2-2-1-2. So change in reflectivity as a function of time. In red here this is e squared of the terrorist pump. And what you see here in blue and red are the change in optical reflectivity in two different configuration polarization. One where the probe electric field and the terrorist electric field are parallel. And the other one where both are perpendicular. So essentially I keep my terrorist electric field along the same direction, but I rotate by 90 degree my probe electric field. So what you see that in both polarization you can see a signal. And this signal follows the square of the pump. You can actually probe for a given configuration you can plot as a function of temperature. And what you see is that this e squared signal indeed shoots up below Tc. So it's really associated to the superconducting state. Now this kind of third order signal is actually, so you heard about the current effect in the previous talk, but actually historically the current effect is defined not in a way that was talked about by Aaron Kapitunnik. In fact, if you look at optics book the current effect more rigorously is a change in the optical constant that depends on the light intensity. So if you look at your equation, your optics equation, you have the index, the optical index, and the optical index is to linear order independent of the electric field. Now if you go to the next order, the next order is actually a change of the optical index that goes as e squared for inversion symmetric materials. And essentially the effect that we are seeing here is a change in the optical index upon radiating the sample via a terrorist electric field. So it's a change of optical index upon impacting it with a terrorist electric field. So this goes as e squared. So it's a change of the optical index upon terrorist pump. So it should follow e squared scaling. And you see here that indeed it follows e squared of the pump. And more generally you can show that the change in optical reflectivity will depend on the third rank tensor that is written here chi ajkl and that is going to be depend on the e squared of the pump. So just like you did this game of extracting the symmetry component of this tensor in the case of Raman measurements, you can actually extract irreducible representation of this tensor using light polarization. And you can actually decompose here your third order tensor. You will have an a1g term that is going to be essentially independent of the light polarization. There is going to be a b1g term that is going to go as cosine two C of the pump and cosine two C of the probe. And there is going to be a b2g term that is going to scale as sine two C of. So very similar to the decomposition that I showed you for Raman scattering. And what you see here is the angular dependence of the signal by fixing the pump and varying only the probe. And what you can see is that there is a constant term and there is a term that is also oscillating and is oscillating as cosine two C of the pump. Now you can actually extract all the components. And what you see is that the signal, the terrod-scarred signal is dominantly a1g. So this is this isotropic component. And there is a subdominant component here in green that goes at cosine two C. So there is a subdominant b1g. Yes, I'm pretty much finished here. So what we did is we did essentially the deping dependence of this feature and this terrod-scarred effect that becomes activated in the superconducting state is essentially visible in all dopings. And in all dopings, it is a1g dominant. Actually, there is an interesting doping dependence. So if you plot the ratio of the b1g to the a1g component, so essentially the b1g component is negligible for under-doped sample. But they become of the same order for over-doped sample. But throughout the doping range, the a1g component is always dominant. Now, you can actually look at diagrams to explain this third-order nonlinear response. There are essentially Raman-like diagrams, but there are more. So for example, in Raman-like diagrams, you would have this kind of diagrams. But when you do pump and probe, you can have such diagrams, for example, where small omega is the optical probe and capital omega is the optical pump. And actually in the non-resonant regime, this is this kind of diagrams that dominates. And you can compute the contribution of this diagram both to the pair-breaking channel and to the Higgs channel. And what you can see is that generically, again, the Higgs mode will only appear in a1g channel. While the pair-breaking peak or the charge density fluctuation contribution, if you want, will be predominantly b1g channel. And this is actually what is observed in the Raman measurement in cuprates. In Raman measurement in cuprates, the dominant contribution is in the b1g channel, the one that is probing the maximum of the superconducting gap. But in this kind of measurements, this is different. It's dominated by the a1g channel. So the tentative interpretation is that the a1g contribution is essentially coming from the d-wave Higgs contribution. And the b1g component likely comes from this pair-breaking contribution that dominates the Raman spectrum. So I'm going to end up here. So of course, this is by no way the last row. I think it's still very puzzling why it seems that the Higgs contribution is dominant in these superconductors while BCS calculation would expect a strongly subdominant contribution. I think it's still an open question. And beyond that, it's also an open question of why these measurements seem to yield symmetry dependence that are very different than Raman. Because after all, they seem to be controlled by the same kind of response function. So I think this is sort of an other way also to probe a superconducting state. And this also brings additional questions as to what are we actually probing with these measurements. And with this, I will conclude. Thank you very much.


Shaka music Lekis guy was here like two years ago But he's back해읈isata Tohambia nini Shaka Mijani misu bang Specialise Nmiki wana kort nama mamiongi me hafere Musiki nife nyupi wuja Tohliya Musiki to na wuja Me Yona san a bakatu na onani katuma yonana zan Bata santen isa sana But he been busy That's why I shaka kuito umbi wazhi tu Injani misi nia Beautiful peace Can be brought to the minister But how have you been, 2 years 2 years by now 2 years TukYo z overwhely kOfinfili But I thank Saint Constraint Leia for the fact that she was alive Rizi niya wei forestым heelandula l syario 1128 kusika, 1129 kusika, 1129 kusika, 1129 kusika, 1129 kusika Hee, hiya Kupa, matu Habu napid Professional Inmano nuri optimized Was very cool M Korean Sad n رoxa man Show crush Yini Proswa Elis on whom was he salt She Miku Ekia Ano wunia Tam Würum tu maka m orbit�� itne mii bon kwa po ki grafa n waiting I thank god siizi curd Right to Freeote ko I think You were part of it Sunoo kanding estu音 summers I could sub kwa a graveyard when I went to happen when was difficult wa na ni musiki mpiku, ma ni ka risai Ah no no Ni ka risai ya mjub, ni ka sa imata hwani kwa mzi kuwata Hei, by that time siku jw akumbe covid-19 then covid-19 kwa happen a ni meriza imkaazi Kwa mbi ya things were tough So upon aza kufikiri yaku kwa mi hare other things Ba bina shkuru mungu pili yo covid-19 t Ultra na kwa hwana, pwesti jeme ki tumoja sana ei, alazi mokuwe open minded minding you what to if it kosekuak lasti muku'u ana plani tuli lazim, she dandos na fanyangam tu nanji wa so many things nami realize yo kiki niki kama inakumungu na brei nivi wakumuga, wakumiu edo wu kakale unizakulu na nanyanya but mimi mejifuzu a lot sana sana na nza sa ma mungu tu muaminif Kani kwa nairobu na jokunza kuwana irobi hapa kusavaitu I nairobu dili kumu maisha zira isi But I thank God for that Besides that, you've also released the number of music Apu tangu kuwa, pa last to now you've released the number of music, right? Ya, by then imagine me release, I think four songs Four? Four songs Okay, we're expecting more, you know? Imagine four songs only I think they will release really This is the end of my first project I've released four songs that I've been talking about So, what's the period? What's the period? Why are you taking so long to release any music? Because music is the number of songs you've released That's the number of songs you've released That's the number of songs you've released Don't ask me if it's your time The number of songs you've released is the number of songs you've released Now, the project was What's the number of songs you've released? What's the number of videos you've released? What's the number of songs you've released? The number of songs you've released is the number of songs you've released So, that's the reason I thank God for the graciousness for you And I think that's the reason why artists During the time you're talking about Maybe they have managed to release one Or even none But God has been gracious And faithful as well Because I want to say that one of those that we've released Is the number of songs you've released Rendition That's the number of songs you've released Is it the number of songs you've released? Yes, it's the number of songs And the letters in your hand I want to know what makes you do the renditions Instead of just maybe writing a song I have songs that are not as good as I thought But I feel that this song Is the number of songs you've released That you've released That you've released That you've released But I'm not sure But I'm not sure I'm not sure But anyone who has a skiza If you're not sure That you've released That's the limit So you're going to blend across all age groups Yes, I'm not sure I encourage people to listen to what they're saying But I'm not sure if they'll listen to it So I'm going to listen to it And feel and f**k what they're saying So I'm going to ask my mum If it's the number of songs you've released That you've released So I'm going to ask my mum I'm going to do it I'm not sure if you'll listen to it But I'm not sure, I want to know But I'm not sure I'm not sure I'm not sure And I'm not sure We'll do it And then we'll do it We'll do it Muzyff Allam classroom papotea lienda papotea lienda Pupote uliyenda, babayanguli tenda mema Pupote uliyenda, babayanguli tenda mema Aba asu belpata Hey, this is Jaycee Sarko Studios This is Jaycee Sarko Studios This is Jaycee Sarko Studios You can be also be part of this Paleo na Facebook page at 22.04 Also in your latest song Nyumbani Video Nye muna video I'm like Okay, this is unique It's not something that I'm used to Iyo video Tell us more about that video Iyo konseptiote Unapata sijumeva Jaycee Umeva unique Nne liyona niga shtukangse maia unibara So, Iyo outfit kuwanza Nne ya ki dambosa Ya 2018 So li kuwaga tukwa nyumbas Uku me eating na za Ikaka tukwa hao Nne lii kuwaga na mstana itwa miss G Kena photoshoot So mi nika iwekanga Tusi kujiwa kumbesi kumode nneza Tu mi kevo visuri So Tukenda tukwa shoot your song Ili kuwe me isha the whole song But kuna Nne performance sana Aina Iyo kitwe neneza Kongezanya nika kuwa Iliweza sana Iliweza Sana Iliweza Iliweza But I want to know the idea Of that outfit Apart from you being given Una relate na yo aje Una kama tukwa So li kuwaga na faizogunia Kenda kupreyu kukwa Sinona nanda play shoot Nini yukwa Nuli mani So nili kuwaga nani For say 20 nitu nyumbani mubuwan But I think yung goeli Speak more than The outfit spoke more than Okay, right there There you go Love it Nene na ka fit Onabili baraka Baraka unaka Karimbu unaka moses Pale Redzi Pale, nani yuka Kutu mungisha kutu peleka Promised land Ili kuwana uchiwomob sana Because tulienda kushut li Choka sana Mami muli mamga nini yuko Koni yuko Wapi yuko Koni iti street nini wapi nili peleka Nani direkta nili peleka But nifa sana All right Well that's really great More, more grace to you Yes Maybe you can mention your YouTube channel And I hope people can support you Yeah So wasse ukiwapale home Nisapot kwa YouTube Facebook Instagram Nani alafu nifolo Kwanza YouTube bana nifri yuku subscribe Tu moalipia bana jami Subscribe to Kofri Enantashkuru sana Everywhere social media platforms Zangu zote nibaraka music Music with the key Social media zote Zangu zote nibaraka music Yes Ni kuna suali Ya unapata There before kuna kolabo kada Uku mefanya guardian angel Think 2, 2 kolabos And since then Live alone even guardian angel Ume hende lesa kutua solo project solo So Tu nga kwa niya kolabote na Ni kuna kolabos mo pier But ni I think resolution yango Imakali kwa ni Kujifide mi mimi mo niya zapa asa So every time niya kolabo na feel Si na iyo siya Siya tiya bidi kama miimi But I think this year Datotua solo But from next year Kolabo Kolabo sa zita kama kwa Zene ziko amandizu datengene Zene ziko Ziko ready Ya ni kuna songs mo Kitu na ni kosa imagine ni Ya video Ya video But sa ii mongu di mongu Nene nene Ni sapote Ni sapotu misani Ni kwa king of financial Yes Wacha mongu nene Yes We don't get any more attention We don't get any more attention Right But From gathering from what you've got You've experienced in life In music Musically Your first song with Garden Angel Now your latest song alone Nyumbani Kuna lesson tu majapu mi Learn That you would like to share With any artist Who is now upcoming And rising up That will encourage and even change His perception about music First of all Kama ni misani Ido en futbola Ido una fana Ya ni iidu kuwe ni director Ukuwe anything Bora ni pashonuna Push na ni dream ni ako Mtangulize mongu Kwanzei the first place Then Fania God For me Ono na we ni li fania wemaako Sikuwa na jo hit song ni ni Like unge ni mbi ata hit song Sikuwa na jo hit song ni ni Mi nili kwa na imba tu Nili kwa juki imbi a God Lasimo imbo ita Ta hit So Apokatikati na pata Ptuna kumbi o song Wanyu miandika Change iwi Fania iwi So for me Ikuwe ni kiyo li changia san Una pata sa uandiki wene Awa andiki content ni Nuna faku andiki Uma change Because umdua li kwanbi Sog ni na fawandiki iwi Nafufanya iwi Batu kia chi a God na ufanya God E mo nyan na jua wanya na push Ngu imbo zaki Kapa e mo nyan wetu Ya ni Bora ni wana fania An na jo wanya na push So for me Resolution ni anguzizi Niku fania God Ya ni Everything na do Ikuwe fania to God Makia I've liked what he said I've really not even liked I've loved it Atial to atu song Naka jo Sinia mungu So ita hit too Lafapokatikati That is faith That is faith eh Apokatikati na uto na puchanganya Kiyo gati na fawandiki Kitukachi Akuna kitukachi Imbiya to God Bora niya God Diya na jevene Maybe papa say Sog ni mu tu moje So for me ni mela niu kituk So anything that na fania Say na fania God Ya Yes His YouTube channel Let me remind you Baraka Music Instagram, Twitter and Facebook And TikTok as well Ya Social media platform Zote Zote Baraka Music Head over there Subscribe to his YouTube channel Follow him on All social media platform As well Guys We support our own app We're supporting you Where to, where to So Kimbiya tu kwa na gonga like Gonga subscribe ni free Also Baraka Music Do you have any greetings Any appreciation Any shout outs That you like to send today Kupsa Kwa zan yanzi na mamangu Kiyopale niya ururu Elmi niya mbiya Manya na dera kwa na So baby So Kose Andakusalimi na mamangu Mombi ena mpenda sa Na God and Bless Andakusalimi na piya familiari Angu Andakusalimi na friendsuangu Everyone Direkturangu Big Chief Alexis producer God of Bless Bila ni nibana Yodumeziku Na piya Nini God of Bless Kazi Fiji Yes God bless you too Na yun na tubari kina Nyumbani Yes, brand new Kamisa Right Aya Mti zame Ii video napa piya perform Wimbo Tamu sana Please do


It is very apt for me to deliver my inaugural lecture in the week of International Women's Day on menopause, a topic which is often regarded as taboo in wider society and in the workplace in particular. What many people don't know is that women experiencing menopause are one of the fastest grown groups in the workforce. In the year that the OEU celebrates its 50th birthday, it feels particularly relevant that we reflect on women rywbeth yma eich gwirioneddau'r cyfrifio oedd yn gweithio ar y ddweud. Felly mae'n gweithio'r cyfrifio'r cyfrifio'r cyfrifio'r cyfrifio'r cyfrifio'r cyfrifio. Felly, rwy'n meddwl i'r cyfrifio.


Then then I would conclude this session and thank you very much for your participation and also more generally because this is also the end of this workshop. I would like to thank everybody for the active participation at this workshop, in particular the panelists and all the speakers that were here and for your engagement with all of us. And for all the questions also that we had, I mean, I already said we had about 150 participants, I think in a way we surpassed what we had expected originally when we set up this program. And it just shows how interesting this whole, let's say, work on this insurance protection gap is and how many people are also interested in this topic. Now, we already said at the beginning we have recorded this event and we will also post it on our website and, as my colleagues also said, we also welcome comments on the paper on this joint ECB IO paper until 15th of June. So if you want to write to us, then please do so. We will be very much appreciative of any comments that you might have. And of course, we will also continue working on this subject so you will hear from us and we are also happy to engage also with other institutions on this topic and so let's hope that we can bring this whole agenda a bit forward and make the world a better place. So thank you very much. Thank you very much for your attendance and have a nice rest of the afternoon, rest of the day, rest of the morning, wherever you are, great for being with us today. Thank you.


We're going to see Disney Junior live on stage. We have got back stage passes. No we don't have back, we have fast passes. But with Toy Story Land opening up, we were talking about so excited to do things new that we've never done before. And then we realized we've never done Disney Junior live. I don't know if that's a good thing or a bad thing. I don't know. We don't even know what's about. But it does close to September 8th this year. So this is our last chance to do it. It's perfect time. So let's go do it. That's pretty nifty. Ooh, sorry. This is very cool. Thank you. I think there's a storm brewing. I'm pretty sure there's definitely a storm brewing. Yes. But I don't mind the wind right now because it's been very hot out. Oh boy. I'm not sure I recognize any of the characters from Disney Junior. I'm just not so much. Oh, I do know who she is. Elena of Avalon. No, that's Sophia. Oh, yeah. Sophia the first. And I do know Jake. I know Donald and Daisy and Mickey and Pluto. I don't think they're a part of this. I don't know. We've never done it. I'm kind of excited. There it is. Disney Junior presented by Huggies Pull Ups. Sounds like we're in the right place. Yes. Happy birthday. Thank you. I've never seen before. Yes. Like the Mickey boxes. Oh, that's Doc McStuffins. I know her from Rafiki's Planet Watch. I know her too. I am thrilled. This is inside. AC. Thank you. Oh boy. Yes. The advice. There's no chairs in here. You have to sit on the floor. Yep. I wasn't expecting that. Okay, Indian style. Let's go. All right. I like it. They like it. I like the AC in here. There's a lot of smog too. I wonder. Go ahead. There's a lot of smog. I'm expecting fog effect. Yeah, fog effect definitely. But I'm wondering what they're going to put in here after it's gone. Oh, probably a starboard or something. Oh, probably. Probably. Wow, it's filling up in here pretty quick. It's like a little hidden gem. Veronica's like in a music loop they got going on. Hi, everyone. And welcome to the Disney Junior live on stage. Wow, look at all of you.  Yeah. Let's try it one more time. Even louder. On the count of three. Are you ready? One, two, three. Do you want to see Vicky? You sure do, Casey. Oh, come on. Make it louder. We need to say the magic word. You sure do, Vicky. The magic word is on the sky. It's got done. What's your thoughts? Yeah, just like the title says. Yeah. A lot of puppets. The puppets are cool. I'm glad we didn't get to actually see it before closed because then we could have never said that we never saw it. It was cute if you get it. Yeah, for kids. Kids will love it. I like the Mickey Mouse Clubhouse. I know that show a lot. I like to watch that. Yeah. But check it out. It does end September 8th, 2018. And let's carry on. Mickey Mouse Clubhouse. So I guess we'll head over here by Toy Story Land just because. Just because it feels like we should. Yes. There it is. Man. Magic backstage dress rehearsal. So they got the doors open for the rehearsal. You can see Woody and the Toy Story Land sign. But you can't go in. Wanna try? Yeah, sure.  All right. Who do I ask? I don't know. That's someone. It is very congested over here in front of Toy Story Mania. It really is. And this is like a dead end down here. So I mean everybody's either going to Toy Story Mania or they're just realizing that there is nothing on the other side of this. Okay. Abort. Abort. Abort. Abort. You have to be a cast member to get in there. Yeah. Days like this make me really wish I was a cast member. I told them I was. Oh yeah? And they said. They said no. They said no, you're not. So to keep in fashion of things we've never done before we're gonna go get something to eat at Pizza Rizzo. We've heard bad things about it. Yeah, we've heard nothing good about it. But we never eat in there. We love going for the dance party. Oh, the dance party, yes. But we heard the pizza is literally the worst. Yes it is. So I'm pretty excited to taste the worst pizza at Disney. Oh no, the sci-fi diner car is gone. Just an empty parking space. Oh no. Now we're gonna take your cool nifty photos. Inside? I guess inside. You're gonna have to pay for that photo. All right, there's Pizza Rizzo. We gotta run because I can feel water droplets coming. Quick. Pizza Rizzo, cover us from the rain. All right. Oh no. Pizza Rizzo is closed. Oh, yes we may. That didn't make it open. Nope. But let's go to the dance party. Yeah, might as well. Wow. It is like echo-ish in here. And nice and cool. It's nice and cold though. Okay, we're on the second floor. Just because Pizza Rizzo is closed, doesn't mean you can't come up here and still enjoy the dance party. I mean, like downstairs the doors are locked. But if you go up the steps, the doors are always open. Oh, yeah. See, doors are always open. So it's closed? Yeah. I guess we'll never know if it's the worst pizza on Disney property or not. Why? We're never coming back again? Oh wait, we probably will come back again. I mean we could always try. Yeah, but for now we need to find somewhere to eat. I'm starving. So I gotta figure out what we're gonna have now. I mean, that's the only place that really we've never eaten before. Yeah, I think so. All right, let's browse a little. And boy, oh boy, it's good food. We decided on the dockside diner. We don't know if it's good or not. Yeah, we've been here before, but not since they had the new menu. I don't remember what we're eating here. But they do have a frozen lemonade. Oh, you want the one with rum? No. No, just the lemonade. And this is what we got. We got kids' meals, actually. And the nachos are the same exact size for the kids and the adults, I think, almost. Almost. Except for you don't get guacamole and pico. And I don't eat that kind of stuff, so. So that's what you've got. And then Nate got the pulled pork. A kid's pulled pork. It cost us $18 because we also got a frozen lemonade. And minus the frozen lemonade, it would have cost us $16. Yeah. But about that. Not too bad. Let's see how it is. They want my food, but they're so cute and you're not supposed to feed them. But they're just so cute. Once again, everyone. I am an animal whisperer. As we were dining, it started raining. So I guess we got a call today. We saw a couple ducks. Yeah. I enjoyed my pulled pork a lot. You like the nachos? They're okay. Alright. Well, I guess that's the end of the day.   First time watching, subscribe to our channel. I like it. And we're gonna get wet. And I didn't feed the ducks. You said that like you did. So Yip's like, hey, let's walk through the gift shop so we can keep out of the rain. Alright. Come on, we're just getting, we're just walking through here to get out of the rain. In America, I love these. Will you please, I didn't spend anything at the warehouse. What? Please? You just got a fresh pair of ears. I did. Thank you so much. And if you're wondering, I stopped at the peel box. And that's where these ears came from. We got a nice card. It's from Jordan, Barbara and Tabitha. I love these ears. They're perfect for my orange bird dress. I actually don't have any ears that match it. So I love this. And then we also got a package from Darla. It's got dry erase tape, which is really cool. Tissues. It's got towels. An LED light. This is for my kitchen aid.  I know you're excited, but looky looky. I'm gonna take it out for you. Yes, I read the letter. This is exactly the stuff my mom sends me. And I love it. I love getting these kinds of packages with random things. So thank you so much. I love you guys. Thank you.


My favorite meal was the adobo chicken thighs.   People always seem to ask this question year after year why are Filipino people so popular but the food isn't. Today Andrew we are analyzing an article by the Gothamist asking why isn't Filipino food more popular in America. It's been endorsed by Anthony Bourdain Andrew Simmerman but it seems like it still hasn't turned a corner in terms of like cuisine popularity now Andrew why would two Chinese Americans be asking this question. All right yeah because also it's actually part of our channel to explore culture you know that's what we always do. We grew up around a lot of Filipino friends. We had Filipino food growing up. I've probably eaten at what maybe 30 different Filipino restaurants in our life so I'm not a Filipino food expert. However I am curious and we do want to help in give any sort of type of suggestions that we can to maybe help make Filipino food more popular or help spark some minds. I don't know. I actually think that there will be a major fast casual Filipino chain anywhere from like 20 to 100 fast casual stores that opens up within the next five years. I have my recommendations. Why do I know? I don't really know but you know I just thought I'd give my recommendations. I just took a look at the article. Andrew when I was in college my favorite meal in the entire UW experience was the adobo chicken thighs at by George cafe. Oh David you're coming back for the adobo. I see you got three servings.  That's pretty funny. I was also going to say that Jollabies is one of my absolute favorite fast food chains in the world and they're mostly cooking American food. They only have a few Filipino dishes on the menu but still Filipino and Max's restaurant is one of my favorite if not my favorite mid-end fast food chain in the world. Dude I mean garlic rice is a better version of rice. Arroz con pollo. Arroz caldo. Arroz caldo is a better kanji. Okay. Lumpia is a better egg roll. I mean I think there are Filipino dishes that clearly shine above the rest. And not only that they got their own dishes too Andrew. Sinigang, halo halo lechon. There's so many different things and you know what the interesting thing about the Philippines is Andrew? It's this mixture of like the original people which kind of has some in commonality with Indonesia. There's a lot of influence from Spain. There's a lot of influence in the cuisine from China as well as the Pacific Islands and it's this crazy mix of those things and different islands might even have like a different ratio distribution so everybody's got their own recipes for cooking dishes but I guess that's one of the complexities about Filipino food is there's not a standardized way to even cook like chicken adobo. All right so real quick I'm going to go through some of the reasons that people have listed on why Filipino food is not as popular as it could be and some of these are pulled off the internet. Some of these are coming from Filipino chefs and restaurant owners themselves so I didn't make these all up right. Number one Andrew it doesn't fall into the decadent high-class vibe like French or Japanese but it also doesn't seem like a everyday lunch fuel up power food. Shout out to Mighty Bulls in New York City that is trying to make Filipino influence food a bull and power food. But I mean I think a lot of cuisine suffer from this like Mexican food really struggle to break those upper echelons. Even Chinese food in America only the past 10 years really started breaking into that $3 sign $4 sign spot like people viewed it as like cheap I just need to eat sustenance food but it was tasty. Number two Andrew it is not particularly spicy for example like Sichuan food Thai food Korean food but it's not particularly fresh with the leaves like viet or Thai food I guess it's existing in the middle zone. Actually I would mostly compare it in temperature and texture Andrew to some deeper cut Cantonese dishes. Yeah I do think Filipinos could even create more like Filipino salads because I know like viet and Thai food are essentially like half of those dishes are like eating salads. Number three Andrew this is not my words we just pulled this off subreddit and you know quoting some chefs it doesn't look particularly good on the outside just due to the stews and sort of like the visual presentation I don't necessarily agree with this but I read this point a lot on different subreddits and quarries. All right the next point is that Filipino food is oftentimes seen as a very homestyle food so your lola will make it better than the restaurant and you know if you grow up with your lola's food and her way of cooking then obviously you're going to prefer that and that's going to deter you from you know paying more at a Filipino restaurant so that's what I've heard from some restaurant owners. And the next point was just that it's a global marketing issue Andrew here is a global chart viewing like every country viewing everybody else's food and this is just like people's perception this is not the reality of what's tasty or not because for example Peruvian's way low on there Filipino's way low on there Argentinian Caribbean is low on there and those all got some absolute 10 out of 10 bangers. Just think about it this way there are 272 million Indonesians worldwide Indonesian food is considered very good and it's still not that popular in America and it has really yet to break through so I mean you know it happens to other tasty cuisines too. And not only that I think that a lot of like cuisines in America they have different levels of penetration for example in New York Mexican food recently had a huge resurgence or not resurgence but a huge just renaissance in 10 years but it's mostly tacos for example in LA in Portland Andrew they love Thai boat noodles in New York they love Pad Thai and there's so many Thai restaurants opening in New York City but they're not on Thai boat noodles because of the use of the pigs blood you know I don't even think a lot of people in New York eat pork for a variety of reasons. Yeah so let's move on to some suggestions we did like a little quick brainstorm on like what might help Filipino food reach that that next level I mean these are just things we're coming up with let us know if you like any of the ideas. I'm saying that we are experts but I'm just saying guys if you guys open up a fast casual chain serving adobo and lumpia let me take a look at the investor deck after these recommendations.  Number one Andrew that leads us to our first point recommendation I guess is focus on the universally loved dishes I know chefs they get attached to the creativity and the deep cut stuff that their great grandma made or their grandma made but you don't even Chinese food we got to recognize Andrew for Cantonese food even though it's so beloved people just like one ton soup and they just like the shield yoke you know the roast meats over rice which is actually very similar to lechon. Yeah I mean I would say like like we said focus on adobo chicken and lumpia I mean I feel like that there's so many dishes that Filipinos do have that if you just focus on maybe like the top six or seven and and kind of like blowing those up I think there's a chance.  Number two Andrew focus on branding the background processes as well as you know business systems and production systems. Number three Andrew focus on some small recipe tweaks that don't jeopardize the original soul of the recipe and also the Latino market. So for example Andrew some of the dishes I'm not telling people what to do could use less sukkha which is the Filipino vinegar. I like synagogue a lot but I'm just saying for like widespread consumption that like sour meat thing it could be throw some people off. Yeah I mean there's definitely a lot of crossover with Latino food where you have like the calamansi and then you might want to squeeze that on top of other things. I mean I think that there's just little tweaks and tricks to even make it appeal to even more of the Latino market which is probably predisposed to a lot of the flavors in Filipino food because it is partially says on right yeah. Number four Andrew I do not think that Filipino food needs to go through the same arc that Chinese food had where it was like you know driven by this community that community you can get cabbage filled community Chinese food in the white things and you get hood Chinese food with the bulletproof glass and like this and this I actually don't think it's going to need to go through the same arc. I think if people focus on a universal branding they can serve mostly lumpia, garlic rice, chicken adobo, halo halo and maybe some pandasal bread and that could be a chain that can have like 50 to 200 restaurants around America but they'd have to really brand it correctly where you could grab the Filipino market Filipino Americans which is a pretty huge demographic only second to Chinese Americans but also grab a wide range of outside people as well to supplement the income. Yo I've actually had some really good Filipino cooked tacos before and I feel like Filipinos one thing that they're really really good at if not if it's not the traditional dishes that really gain traction I think it's Filipino chefs putting their twist on a lot of different types of food such as fried chicken or such as tacos or such as Chinese food and I think it's good yeah it has really as a charm. I think take a look at El Pollo Locos arc torches tacos there's so many different chains of like ethnicities and of course yes they did have to Americanize or Westernize to gain a certain thing but look a look at what Panda Express did.  Let us know in the comment section below what is your favorite Filipino dish what is your favorite Filipino restaurant in your city and what you would do to popularize Filipino cuisine in America because it deserves it because it's got some absolute bangers. All right everybody thank you so much for watching the hot pot boys you know us man we'll talk about everything including food so uh thank you so much for watching hit that like button click subscribe turn on your notifications and leave your comment down below until next time we out. Peace.


Santa knows where all the best toys are and this December, many of the hottest smartphones are just a penny with service in Appalachian Wireless. Stop by your local Appalachian Wireless to check out all of the great smartphone deals that consistently top the nice lists. This Christmas is truly going to be bigger and better than ever. Better service, bigger savings, that is. Ho, ho, ho, ho, ho, ho! That's today's Appalachian Wireless! December is coming to a close and so far our region has seen little more than a trace of snow. But the snow fighting crews at the Kentucky Transportation Cabinet's District 12 maintenance garages are ready with a variety of ways to keep the roads as clear as possible. The salt domes are full and the snow plows are ready to hit the roads. But you may also see trucks similar to this one out before the snow starts falling pre-treating the roads with a liquid called salt brine. Liquid is a prep like if we're giving snow, they usually contact dust and tell us to spray the salt brine down the liquid. It makes it easier on us getting to clear the roads quicker. Salt brine is a mixture of rock salt and water that crews can use on dry roads ahead of a snowstorm. Mullen says it works by settling into the tiny crevices on roadways, creating a layer that prevents ice and snow from bonding with the pavement. And that makes their job a little easier. It keeps the snow from packing in real tight and it makes it a lot easier when you plow it off. Seeing a truck putting a liquid on the road before the temperatures drop below freezing can be a little confusing. The Transportation Cabinet officials say it's actually one of the most effective snow fighting methods they use. The salt brine doesn't freeze, it doesn't have any impact on the road conditions of making anyone have any accidents or anything. All of the salt brine used in District 12's 7 County area is produced here in Pike County at the Shelby Maintenance Garage. But all garages keep a supply on hand for when the forecast calls for snow. Whenever the snow comes, we're prepared and ready for it. Reporting in Pike County for EKB News, I'm Shannon Deskins.


So we're here with the whole center here. So who you hi? My name is Helen Carter. I'm a business developer at Holst Center. We are working at Holst on printed electronics It's a research institute based on in Eindhoven in the Netherlands and here you see an example of So it looks really great in real then my camera is some kind of frame rate something gone But so there's a display on the textile The goal is to integrate it in the future in the textile, but at the moment it's just Behind it. Yes. So there are about two to three thousand LEDs RGB, picot LEDs Place on a thin foil All right, and this is related to the whole center is Works on printed electronics Is it part of mayor mayor burger? No So it's an independence. We are a mayor burger is one of our partners in for intake printers that we use but we also use screen printings and You see more examples here. Yeah, this is an NFC tag That's produced in different ways You also work on thermoforming electronics for example here is Thermoform into 3d surface Moreover we work with Other health related and performance related applications. So for example here is a wristband We have a health patch or a spin patch and Health patches with ECG sensors. What is that? We're looking at here. This is an example of Integration of solar panels on Textile which you can see an actual garment of it here So with this a shirt you can be designed with a touch designer for You can charge your phone In the indoor lights nice. It's charging. Is it is charging my phone? What's the power? It's a two to three watts inside and five watt outside. All right, and further you can see another example of Variables it's a leds into textile integrated so it plays a Play playing with lights here looks awesome. Yes, so what's what's How much do we have to wait before we can buy this in the stores? Well, not much. So you there are some of our products that we develop with our partners That will be soon in the market. Hopefully in a year in the in the coming year, I should say and Is it durable Can it be made durable it's gonna break This is something we work on it for solar panels, but the LEDs Integrating textile are washable.  More than 20 washing cycles. All right, cool. So I can show you another example of A shirt that has sensors to measure your heart rate. So actually it's very thin and integrated into closing So is this this is totally flexible? Yes, totally flexible. Is it printable? Printed on a on a substrate and then integrate it into textile. So is this ready for mass production or? Depends on if the partner wants to develop it, but we are working on it. All right, cool. So Textiles gonna be huge market. No, yeah smart textiles. Yeah, are you the leader in that market? We believe with our thin flexible electronics that are washable. We are leading in that market With our with our prototypes. There's many people interested in that, right? Yes So there's some other companies doing stuff. Yes. So I should say Hall Center is a research Institute So we are interested in collaborating with the different companies in Making new technologies and Accelerating the innovation process. So if you are interested, please contact us. So H&M and all these companies should just send you An email and start working. They probably already work with you. I think so too


Item ██ SCP-989 Object Class Safe Special Containment Procedures SCP-989 is to be stored in Secure Locker ██ in Site-22 until further notice. Secure Locker ██ is to contain electronic scale which is to report the current weight of the object at all times. Any change in the way before testing and after testing that is plus or minus one gram beyond test material is removed as a reporter immediately and containment breach protocol should be enacted. Level-2 clearance is required for research involving SCP-989 but has written permission from a Level-3 staff member. Description SCP-989 is a compound of C-12 H-22-011, sucrose, interlaced with a substance with the chemical formula H-7-X-E-2-04-C-8. The method by which this molecule was created is currently unknown as the current principle of the chemistry disagree with its composition and structure. Research is ongoing. SCP-989 is within an ornate silver shaker with the logo for Marshall, Carter, and Dark Ingrate on the bottom, hereafter referred to as SCP-989-2. There are no visible seams in the shaker, and as such there is no way known at the moment to refill SCP-989-2, though testing at this point has shown no measurable change in weight of the object, suggesting that the substance may replenish itself. This replenishing effect is only observed to occur if the object is left standing for more than two hours without movement. Whether this is a property of SCP-989 or SCP-989-2 is unknown at this time, but it is hypothesized that the interaction of the second compound with the materials of SCP-989-2 creates its effect. When SCP-989 is elevated and released, SCP-989 enters suspension within the air. The crystals of SCP-989 surround whoever threw SCP-989 into the air, and remain there for precisely seven minutes, eighteen seconds. This has shown no adverse effect on the thrower so far, as SCP-989 will not come within two millimeters of the thrower, even if they walk through the cloud of SCP-989. If any other living being enters the cloud of SCP-989, however, SCP-989 will surround the subject and force its way into the mucous membrane of the subject, causing severe lacerations and coating the area with crystalline formations akin to what is colloquially known as rock candy. This is uniformly non-fatal, however, and leaves the subject blind, deaf with moderate difficulty breathing and in severe pain. Attempts to remove the crystalline growth have proven unsuccessful thus far. After exiting suspension with the air, SCP-989 will deposit on any horizontal surfaces until thrown again, worrying that it will return to being in suspension. This effect can only occur if SCP-989 is dry, as the solution to SCP-989 water did not show any anomalous properties. SCP-989 was recovered from the home of ████ in ████, Wales, after several missing persons' cases were connected to ████, and a possible link to Marshal Carter in Dark was confirmed. Also recovered were letter and receipt from Marshal Carter in Dark Limited for the amount of ████ to date, no other samples of SCP-989 have been recovered. Addendum 1, the following is from a letter recovered from the home of ████ to a mister ████. We thank you for the purchase of this fine item. I hope you will find it to your liking, though I'm sure your dinner guests will certainly find it interesting. If we can be of assistance setting up any source swore way for you, we of course would be more than willing to assist. We look forward to continued business with you and trust that you have taken steps to avoid the attention of a certain group as we advised. Sincerely, Mr. Marshal Carter in Dark.