Detention Joel hated detention. Detention in Mr. Briers and his classmates. Detention in Mr. Briers and his classmates. And school in general. Pretty much anything in anyone associated with school he hated. Not that he showed it, though. He was pretty good at playing the game in company and to his parents. But that didn't do anything to reduce his dislike of it all. Detention was at number one, though, on his list of hates. Mr. Briers had picked him out at the end of his final class of the day for some minor infraction. Dumping him in an empty classroom with orders to read a book silently. With the added kicker that he couldn't leave until he'd finished it. He hadn't argued. Mr. Briers had it in for him for some reason. Always singling him out. Always watching him from the corner of his eye.  Joel turned the book over in his hands. It was a light, slim book. The cover a garish cartoon picture of various men dressed in green tights and tunics carrying a variety of swords and wooden staffs except for the one stood in the middle of the group holding a bow and bearing a wide smile on a blonde mustached face beneath a hood. Joel groaned inwardly as he read the title in typical old English font emblazoned across the top. A tale of Sherwood Forest. A choose your own fate, adventure. Great, he thought sarcastically. It was one of those books. The kind where you had to select from a set of options and flip to another page depending on your choice.  The last time he'd read one of these he must have been ten or eleven and even then he'd grown bored with it and hadn't finished. Mr.  Slouching back in his chair, Joel turned to the first page. Welcome adventurer. You have come seeking fame and fortune by joining Robin Hood's Merry Men. Tari not in the woods though. Hold fast to your decisions and you shall find the goal you seek. Joel snorted derisively before continuing on to the first section. 1. Sunlight pierces the canopy of trees high above you, sending shafts of light through the sky of leaves to illuminate your path. Flintered sharewood forest but a short time ago and already it is as if the woods have swallowed you whole. You have on you your trusty sword, three days worth of provisions, flint and tinder, plus a warm cloak which seems a burden on such a fine summer's day. The forest path is wide, the day pleasant and your heart beats strongly in your chest. Today is the day when you shall achieve your goal. You will find Sir Robin of Loxley, the fabled Robin Hood, and join his troop of Merry Men. It's not long before you come upon a fork in the path. To the left, it curls off toward an area of the forest where a villager told you a small river runs through. But there are plenty of man-made fordings available, should you look. To the right, the path is more or less straight, but appears to head into a dark dense part of the forest which looks rather foreboding. If you wish to go left toward the river, turn to eight. If you wish to go right down the ominous forest path, turn to eleven. It read like any of these books he'd picked up before. Joel looked at the options.  He chose accordingly. 8. Before you even see the river, your eyes pick out the sound of swift running water somewhere up ahead. You quicken your pace, eager to both see the source of the sound but also to splash some water in your face to relieve yourself of some of the heat you feel. From such a long walk, you pass a large gnarled oak tree and finally see the fast flowing river, the sunlight bouncing off its surface and is that a fish or two you see slicing around beneath? Kneeling by the bank, you dip your cloth into the cool refreshing water then lift it and place it gingerly on the back of your neck. The initial cold is a shock but a welcome one and you feel the coolness spread across your body. The bigger shock though is when you hear a loud voice calling from across the way. Oh stranger, if you seek to cross this river, you must first pass me. You look up in surprise and see a giant of a man dressed in a dark brown leather jerkin with hands almost as big as the thick beard upon his rugged face stood on the opposite bank next to a large log which breasts the river. In his right hand stands a long thick piece of wood. You recognize it as a quarterstaff and that he must be none other than little John himself, one of the fabled merry men you seek. In an instant you understand his meaning and looking next to the large log on your side of the bank is another quarterstaff obviously for the use of travelers such as you. Finally a chance to prove yourself.  If you wish to fight little John, turn to 15. If you wish to return the way you came and try the other path, turn to 11. Ha! He knew it, barely in and he was already dealing with one of the merry men. Joel wanted this over with so going back wasn't an option. Just to carry on forward and get it done. 15. Eagerly, you sweep the quarterstaff up in your hand and approach the log bridge. As you step on carefully, so does little John, easily twirling the quarterstaff in his hands. You wonder to yourself how many people have come this way before only to find themselves swiftly beaten and pushed into the river. But your opponent is confident there is no doubt but if the stories are true, his naivety is just as strong as his biceps. Should you fight fairly or trick him somehow? If you still wish to retreat and try the other path, turn to 11. If you wish to fight fairly, turn to 18. If you wish to cheat, turn to 23. Now that was an interesting option, he thought. Again, going back wasn't going to happen. Of the other two choices though, Joel knew which one he leaned towards. Fighting fairly might be the more honorable way, but to him, the result was always the key factor to his way of thinking. 23. As you approach him, you raise your quarterstaff in what you hope is a defensive position. He smiles good-humoredly, rolls his shoulders to loosen himself up, winks, and quickly raises his staff for an almighty blow. As his staff reaches its peak, you pretend to look past him and shout, Bear! His head whips round a check, instantly forgetting about you.  Your arms vibrate with the impact, and you think you're going to drop the staff.  His face moves quickly, from confusion to anger, and then dazed. He falls to his knees and topples off the log, but is still able in his days to roughly grab at a protruding broken branch on the underside of the trunk. The cold water returns him partly to his senses, and he slowly grins up at you before speaking. Well done, stranger. Robin has need of men with sense as well as strength. Give me a hand up and I'll take you to him. If you offer him your hand, turn to 26. If you wait for him to climb back up himself, turn to 31. It was a difficult choice, Joel realized. Offering to help him up would put him in a dangerous position. Off balance, little John could pull him into the water or anything. Joel could see the way the book was heading though. Once you bested an opponent in this fairy tale land of good and evil, you always fell back on the honorable option. He thought it was a load of crap, but the answer the book was expecting was obvious at this point. 26. You looked down a little, John, bedraggled and wet and being slammed by the river and offered your hand to help him up.    You quickly strike at his remaining hand, holding onto the branch under the log and hear the satisfying crack of broken bone. He yells once more and releases his hold, the river quickly drawing him under and away. You watch him struggle for a short while, then throw both quarter staffs into the water and carry on your way. 28.  He hadn't expected that at all. Thinking about it, though, it made a lot of sense. Who knew what little John might have tried? His character's response was sensible. He'd lulled his opponent and then acted, removing a potential danger. Joel found himself warming to this book. 28. The path on the other side of the river is barely visible, and so obviously not a commonly used means of moving through Sherwood Forest. Logically therefore, it must be a route used only by the merry men in Robin Hood himself. Gradually the path grows narrower, the trees thinner and closer together on each side until finally the path appears to be a corridor of trees leading to a dead end, but with two large arches with a bowman stood in front of each. They look like twins, an image reinforced by them both speaking at the same time and with the same words as you approach. Greetings, stranger. You have bested little John, but wisdom is as valuable a skill with weapons in Robin's camp. Behind us lie two ways forward. One leads on to the camp, the other to a hidden pit filled with wooden stakes. You may ask one of us a single question, but beware, one of us will lie and the other tell the truth. Which route do you choose? You try to see any differences in the paths beyond the arches, but they look identical. Your only choices appear to be to ask the bowman or take a chance and pick a route in random. If you take the left arch, turn to 36. If you take the right, turn to 38. If you ask one of the bowmen which archway leads to the camp, turn to 42. If you ask one of the bowmen which archway the other bowman will say leads to the camp, turn to 62. If you use intimidation on the bowman, turn to 49. Now that was a curious last option, Joel thought. The first two random choices didn't appeal and whilst he was confident in his logic what the right choice was, he was drawn to the last action. It made a lot more sense to him, skipping the need to risk a correct answer against one he could guarantee if approached right. 49.  Ubreply, you draw your sword, catching them off guard and grabbing the nearest from behind, placing your blade against his throat before the other can react. The one you were holding trembles beneath your grip whilst the other watches you nervously, fingering his bow. If you ask the bowman to tell you which arch leads to the camp or you'll kill the one you're holding, turn to 43. If you kill the bowman you were holding immediately, turn to 47. Another interesting set of options that threats were useful Joel knew from past experience but only if the other guy knew you'd carry them out. Carl in fifth grade had learned that lesson the hard way. The answer was obvious. 47.  He gurgles an alarm as the flesh parts and blood pours forth from the wound across his neck, dropping him to the floor to breathe his last. You point your blade at the stomach of the other bowman. If you ask the remaining bowman to tell you now which arch leads to the camp, turn to 56. If you force the bowman to go ahead of you by sword point through one of the arches, turn to 53. Both choices would work, Joel thought casually, but one of them obviously added an element of insurance to his character's survival. 53. Trotting the remaining bowman with a point of your now bloody sword, you state coldly that what happened to his friend can quite easily happen to him and that he will now lead you through the correct archway to the camp. Reluctantly, he moves toward the right arch. If you follow the remaining bowman through the arch, turn to 68. If you first run the remaining bowman through with your sword, killing him, turn to 65. Joel was caught at this one. It wasn't an obvious answer as the last. Keeping the remaining bowman alive added an element of risk if he tried to escape, but then how far did the man's loyalty to Robin Hood and his cause go? Was it so far that he'd even picked the wrong archway, even if it meant risking his own life? Despite the risks, having the captive bowman along gave Joel more options, he realized. 68. The bowman has been stumbling ahead of you for lonely at sword point for a few minutes when you notice his furtive glances back and the slowing of his pace. Prepared, you wait until he makes his move. Ten steps later, he spins and makes a grab for your sword.  As he falls backwards, the earth ahead of you gives way and his body falls into the trap you had previously been warned about.  Content, he is dead. You make your way back along the path to the two arches.  Once happy with your work, you turn and take the left archway. He'd known he was right to keep him alive. Additional resources were a useful buffer between himself and unpleasant situations like the friends he'd cultivated at school. As long as they could be controlled or manipulated, they were handy to have around. Those that weren't could be discarded easily enough later on should the need arise.  Looking around, you find a suitable tree stump and sit down, digging out from your bag half a loaf and a wedge of strong cheese wrapped in linen. You take a large bite of each and wash them down with some water from the skin hanging from your belt. Whilst you are eating, you pull out the letter that lay beside the bread in your bag, opening it. You read once more the instructions given to you yesterday. Hail and well met. You have come recommended by Prince John himself as a person who can produce results. Most in these parts have heard of the Bandit in the woods, the one who calls himself Robin Hood. He calls himself a champion of the people, but in truth, he is nothing more than a common criminal. However, his propaganda amongst the unwashed and uneducated masses has proven impossible to overcome. No one is willing to come forward and provide information on his whereabouts. Therefore, I need you to enter Sherwood Forest and infiltrate his camp. He has broken the rule of law as have his followers and they must be treated accordingly. Robin Hood must be executed and evidence brought back to me of his demise. Deal with the others as you see fit. Succeed and the rewards will be grain.  Good fortune, the sheriff of Nottingham.  If found on you, the merry men will treat you harshly. By the same token, it would be useful as evidence of your true siding should you encounter any of the sheriff's men. You also realize, if used correctly, it could be planted as evidence against another within the camp, thus sowing division and discord. If you burn the letter, turn to 78. If you keep the letter, turn to 103. Suddenly, a lot more things made sense to Joel. Sure, the character in the book wanted to join the merry men, but his motives had never been fully spelled out before. The fact he actually worked for the sheriff of Nottingham appealed to Joel. It was far more interesting to be a manipulative spy than a two-dimensional woodland terrorist. He also liked the idea of keeping the letter. It would be a risk for his character, but he was guessing an option would come up later to plant it in the camp, or Little John might make another appearance, and if he still had the letter in his possession, one of the options given might be to plant it on Little John himself as a means of discrediting him and any accusations he might make against Joel. 103.   The path you're on twists sharply ahead, and as you follow it round, you suddenly find yourself facing a reasonably sized encampment. Makeshift huts and canopies of thick hide stretch between a rough circle of trees surrounding a large campfire, a bore roasting on the spit above it. Moving in and around the camp, you see a fair number of people, somewhere between 20 and 30, engaged in various activities. Some are checking their bows, a few engaged in mock sword battles, whilst others are mending tunics and shoes.  You go to move forward when you feel the sharp point of an arrow tip sticking into the small of your back.  He does not speak, but prods you in the back a couple of times with the arrow, indicating for you to move. Slowly, you walk forward toward the fire and the hooded man. If you want to try and escape, turn to 92. If you simply continue forward, turn to 79. Why try to escape, thought Joel. His character was where he wanted to be, and he doubted it would end well if his character tried to escape with a drawn bow pressing a sharp arrow into his back. No, now was the time to see how things would play out now that he'd reached his target. 79. As you get closer to the fire, the two men talking to the hooded man notice you and fall silent, turning to look hard-faced at you.  His golden hair and mustache would have been enough identification, but the sardonic grin and twinkle in his eyes introduces him far better than any spoken word. The Earl of Locksley, Robin Hood himself. He waves back the man behind you, appraising you for a moment in silence, and then offers his hand. You reach forward and shake it, and he laughs heartily, slapping you on the shoulder. Haha, welcome friend. To get this far, you must have bested little John and the twins. This shows you have both strength of character and wisdom, both qualities I look for in my merry men. As you see, we don't live comfortably, but we live well enough. The forest provides whilst we work to topple the sheriff and behind him, Prince John. Now, as well as robbing the rich, there are other roles in the camp which need to be done. You have the look of a smithy or a cook to me. Which do you fancy? If you choose to work with a blacksmith, turn to six. If you choose to work with a cook, turn to one twelve. Sure, thought Joel, blacksmithing offered easy access to weapons and the opportunity to thin the herd of Robin's lackeys with them, but it would be a slow process he guessed and would place his character under growing suspicion the more bodies that turned up. No, if his character was to succeed, a quiet, unassuming role in camp would be the ideal place to start. One twelve. Excellent, come with me to meet our resident cook. Oh, fryer tuck, you were complaining just this morning about needing help and see if I haven't answered your laments already. Robin leads you around to the other side of the fire, where sits an overly large man in a fryer's robes, stirring a large pot of vegetables over a smaller fire. He looks up from sipping from a wooden ladle, his cheeks ready and his eyes bright. Well, bless my soul. My prayers have been answered. No time like the present, come help me with this evening's meal. Go gather some herbs from the stew I'm preparing to go alongside the meat. He points vaguely off to the side, returning his attention to the pot. You look over to where he pointed, noticing a small herb garden he must be cultivating. Grabbing a clay bowl nearby, you walk over and start picking handfuls of herb leaves. As you do so, though, you notice any undergrowth nearby, a wild plant growing whose leaves you know to be deadly if consumed and even the smallest quantity. If you return with just the herb leaves, turn to 130. If you return with leaves from both the herb and poisonous plant, turn to 109. Yes, this is good, thought drill, a subtle attack that could incapacitate some, if not all, the merry men at once. It was ideal. He'd done something similar with his stepfather, crushing sleeping tablets into his drink before he'd driven to work one morning. And that had gone quite well. 109. You walk back over casually, being careful to keep the clay bowl hidden by your body, to avoid the fryer's eyes noticing the difference in leaves. You quickly grind the leaves down until they are the same unidentifiable shreds. You pass the mortar to the fryer and he favors you with a pleasant smile of thanks before pouring the contents into his cooking pot. Turn to 72. This should be interesting, thought drill, eagerly turning the pages now. 72.  You also accept a bowl when offered but are careful to dispose of its contents whilst pretending to eat it. It's not long before the first merry man staggers to his feet, clutching his stomach, his breath rasping from his mouth. Several of his fellows dash over to see if they can help, though you can see a few themselves stagger as they do so. The first man falls to his knees, coughing blood from grimaced lips, his eyes bulging in their sockets. He collapses prone on his side, choking weakly on the blood spilling from his mouth. Then stops. Others are now complaining loudly of agonizing pains, one going so far as to stagger uncontrollably into the fire, knocking the roast pig to one side and catching himself on fire. He shrieks in agony as the flames pour up his legs and arms, melting his clothes and skin. A few short steps, and he drops to the ground. None have come to his aid, though, as the carnage continues throughout the camp. Bodies now litter the floor in various states of painful disarray following their individual death throws, gouts of blood abundant everywhere within the light of the flickering flames. You pick your way through the bodies, looking for Robin. As the only one with a hood, it doesn't take long to find him. Surprisingly, he's still breathing, though with difficulty through blood speckled lips.  And so, my dream ends, struck down from within by a traitor. He coughs up a little more blood, but struggles to continue speaking despite the obvious pain he is in. If any honor exists within you, please grant me his final boon, bearing me here with my loyal men and true, do not make me a spectacle for the sheriff I beg. A final cough rips up through his throat, spilling blood and bile down his green tunic. Robin Hood and his merry men are no more. If you honor his final request and bury him with his men, turn to 74. If you ignore his request and return with evidence to the sheriff, turn to 164. Joel barked a laugh. Well, that was surprisingly easy.  Violence had its place as a tool, but it still had that element of unpredictability, far better to plan and strike when least expected, if at all possible. So what to do with Robin Hood's body? Much like his stepfathers, when he'd idly viewed it lying in state, a corpse was just a corpse, a bag of meat and bones with no rights to further affect the living with its demands. The only function it had now was if its demise could be of benefit to those still alive. 164. Rolling Robin Hood's body over with your foot, you examine his eyes for any further sign of life, then drag it over a nearby tree stump. After some effort, you prop his body in place, his neck and head now resting on its flat top. You grab a large axe from the blacksmith's hut, rest the blade gently against his neck for aiming, then raise it high above your head and bring it swiftly down. The blade easily cleaves through, blood spurting from the gaping wound as his head rolls down next to the stump. With effort, you rip the hood from his now decapitated body, slump down against the tree, and wrap his head within it. That done, you take one last look around the camp for any survivors, then pick one of the huts to sleep in till morning. You awake refreshed, and upon exiting the hut are once more greeted by the cold corpses of the now unmarried men surrounding what remains of the spent campfire. Flies are already buzzing around them, and the stench of death will soon become unbearable. A quick search later, you have gathered enough food and water for the return journey to Nottingham. If you take the path you used to enter the camp back to Nottingham, turn to 128. If you decide to go deeper into the forest, turn to 58. Again, another no-brainer. The job was done as far as Joel was concerned, and once your goals are achieved, that was an end of it. No reason to go looking for trouble. 128. The sheriff is ecstatic at your return and the evidence you bring, throwing a large banquet in your honor and showering you with gold. He also mentions that Prince John has decreed that on the successful completion of your mission, you will be both knighted and awarded all the lands previously owned by the late Earl of Loxley. Three days later, dressed in the fine garb of a nobleman and with your own servants, the sheriff bids you farewell from his castle as you leave to take up your new position.  The end. Now turn to 154. What? There's more? Probably a recommendation to read more of the books in the series, thought Joel. He had to admit though, he'd like this book, despite his initial distaste for it. It appealed to him somehow. The answer is more in line with his way of thinking. To his surprise, he found he was interested in seeing what the other books and the line had to offer. 154. Congratulations on completing the story adventurer. But your adventures don't have to stop there. If you've reached this result straight through without cheating, we'll know if you have and are interested in continuing your adventures. Ask the teacher who gave you this book for more details. They recognized something special in you and were always on the lookout for young people with a unique way of looking at the world. Your government needs people like you and we can offer you real life adventures you wouldn't believe. Training and all the cool skills you've read in this book and more and the opportunity to travel the world. If you're interested, please turn to the inside of the back cover and fill in your name and address in the space provided before returning the book. See you soon, adventurer. Joel smiled to himself, a genuine one for a change rather than the one he mainly employed when in social situations. He pulled the pen from the bag at his feet and turned to the inside of the back cover. As he started to write his name, though, the thick paper tore. Joel swore under his breath and tried again slightly farther along from the tear. The same thing happened. Biting his lip to control his annoyance, he looked closer. The paper was far flimsier than it should have been and was that writing visible underneath? Curious now, he tore the paper away and read what was written there. Thank you for your interest. You have decided to farther your adventures with us. Not all are selected, however, and there is one final requirement for your application. If you look closer at the cover of this book, you will find it has two plastic layers. Before returning this book to the teacher who gave it to you, please peel off the thin layer on top of the book just prior to handing it over. Being careful not to touch the cover with your bare hands once you have done so. One to two weeks after your teacher's death, we will contact you farther. Mr. Breyer sat alone in his office, looking through a pile of student folders for new candidates. Two years he'd been at the school.  Out of six possibles over that time, only Joel had come closest. Shame he'd had a good feeling about Joel, he had potential. Despite all the psych profiles and observation, it still came down to the book as the final test in stage one recruitment. Despite your promise, you fail the book, then your journey ended there. Literally. One advantage of the psychology of the kids the agency were trying to recruit, if they failed the test, they were also the most likely candidates for teenage suicide. So closing the loop was easy. He looked over at Joel's book on the corner of his desk. Each candidate had their own book tailored to them specifically and supplied by the agency when they were to be tested. Company rules stated he wasn't allowed to read them himself, just hold onto them for a day after the test and wait for a call. If the call came, the candidate had got through. Otherwise, he just burnt the book, waited a month, and then staged the kids' suicide. Again, it was a shame the call hadn't come through. Joel had shown a lot of promise. Sign. He leaned across his desk and picked the book up, turning it over in his hands, seeing Robin Hood's face beaming up at him amongst his gang of merry men. Yup.  Putting the book in his bag for disposal, he stood up and went to the bathroom to wash his hands. The kid must have spilled his soft drink on the cover or something, judging by the stickiness. Yeah, he had potential, all right, but obviously tidiness wasn't part of it.


This is stock number 9258. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and use Dodge Ram heavy-duty headquarters. We are checking out this super clean 2014 Ram 2500 crew cab long box. This vehicle has the 6.4 liter 4-8 cylinder motor with the MDS system which shuts off four of the cylinders on the highway. From this HD video, you'll be able to tell that this truck is super clean all the way around, bright white clear coat is the color. This one has the Firestone Trans Force LT 27570 R18 tires with the steel rims with the chrome covers. Four-wheel disc brakes all the way around. These tires have just about a little bit under half the tread left, but still a lot of good tread left there. We shoot all of our videos in 1080p, so if you have HD capabilities on your computer tablet or smartphone device turn them on now because it's like you're right here checking out the truck with me. Passenger side rim is in excellent shape as well. No scuffs or scrapes on that. And that tire has just as much tread as the driver's side tire. As we go down this side of the truck, you can see just how clean the body is, how reflective and glass-like that paint is. We take these HD videos, so if you are far away, or even if you're close by and just cannot make the trip down, you can still see the truck here, the truck, and have confidence in the vehicle that you're looking at before you even get here. I did not see any single dents or dings down this side of the truck. The cab looks really good. And down this side, very clean. We want to make sure we give our out-of-state customers the most accurate representation is possible, as long as well as our in-state customers. I understand a lot of people are busy, can't always make the trip down, but if you're still interested in buying the truck, you can still see the truck here, the truck, and have confidence in what you're looking at. Back spring suspension, they started that in 2014, so this is the first year that that was available. See the frame and underbody is very clean. Lower rockers and lips look really good on the bottoms there. 2014 was the first year that they had the rear coil suspension, makes it a lot smoother ride when you're going down the highway empty. Has the full towing package, which includes the four pin and seven pin wiring. Rear bumpers in really nice condition. Tailgate's got a couple little dings on the bottom there, but other than that, very, very nice. This is a work truck. Locking tailgate has a drop in trail FX bedliner. It's in really nice condition. And as you go down this side of the truck, just as clean as the passenger side, I didn't see any dents or dings down this side of the vehicle. Very, very nice condition considering it is a work truck. This one does have the fold out tow mirrors. They also fold in if you need a little to get into your garage or something. Inside the tradesman package gives you the gray cloth interior. There are no rips or tears on these seats. Has factory floor mats throughout. Carpentine is very nice and clean underneath. This one does have automatic headlamps, power windows, and power locks, and power mirrors. Inside you can see that this truck indeed does have 31,412 miles. You have an outside temperature display, as well as a digital speedometer and a mileage display. Cruise controls on that side. That's your information center controls on the left. Has AM, FM, and Sirius XM radio capabilities. Turned out four-wheel drive, factory brake controller, and stability control. Passenger seat is very clean as well. No rips or tears on that. Factory floor mat on that side. And you can see that the carpeting is really nice and clean. You have the three cup center council cup holder storage inside here. And it is a 40-20-40 split bench seating. And all the seats are in really nice condition. Take a quick look at the back seats and then we will check out under the hood. Back seats are in really nice condition as well. No rips or tears back here. It does have the latch child safety system if you wanted to put car seats back here. Under the seats, there's lots of storage. And we have a factory floor mat on this side as well. Has the storage bins in the floor, as you can see, which is nice. You can put ice and drinks and stuff in there. And we'll check out under the hood. 6.4 liter V8 Hemi motor. Engine bay is very clean, runs very smooth. This truck has been fully safe and inspected by our service shop. Has a fresh oil and filter change. All the fluids have been checked and topped off. The truck has been gone through mechanically 100% and is 100% ready to go. And to see more pictures of this truck or one of our other 400 new and used cars, trucks, SUVs, minivans, Wranglers, you name it, we got it.  Videos of every single used vehicle that we have all at www.summitauto.com. Thank you so much for checking out my video. If you want to make this truck yours, give us a call right now,<PHONE_NUMBER>. Our sales professionals are on hand waiting for your call. Once again, that number is<PHONE_NUMBER>. Thanks again for checking out the video. If you want to check out more like this, go to our YouTube channel, which is youtube.com slash summit auto. Remember to like, subscribe, and share on those videos. In fact, in a second, you'll see a link to subscribe to our YouTube videos on your left. A link to more heavy duty truck videos like this one on your right. And if you haven't been to our website on the bottom, a link to this truck on our website, click those. Check us out. And we look forward to helping you with this super clean 2014 Ram 2500 Crew Cab Longbox Hemi V8. Thanks again.


Alright guys welcome back to another video by how to lucid this in this video We're gonna be talking about the top five lucid dreaming techniques and methods This is gonna basically cover how they work roughly how you do them and basically which ones are gonna be more effective And which ones you should probably stay away from until you're at that more advanced level where you can reliably have lucid dreams Anyway, so the first one is the wild now the wild stands for the waking juice lucid dream This is basically a technique for beginners and advanced lucid dreamers. However, it does require a bit of focus You're gonna need to be able to learn how to meditate So the way it works the wild technique what you do is you bait and you can do this when you first go to sleep Or you can do this in the early hours of the morning. So what you do is you lay there You don't move any muscles Okay, you close your eyes and what you're going to do is to try and keep your mind awake While your body falls asleep So this happens to us our bodies fall asleep obviously every night and what happens usually is our bodies enters What's known as sleep paralysis where it basically paralyzes your muscles and make sure that they can't move This is to stop you like acting out your dreams and sort of kicking your spouse or you know kicking the covers off the bed or whatever and it's a very useful Safe thing that your body does to stop you acting out your dreams. However in the wild technique You're going to basically try and keep your mind awake during that process So if you do wake up during the process, you can it can be a bit scary You're gonna experience sleep paralysis. It's gonna be a bit unusual or uncomfortable even But if you push through that and just enter the lucid dream in that way You're gonna have a very stable lucid dream and it's gonna be very hard to shake you out of that So the wild is an interesting technique for beginners However, I would advise looking at some of the other techniques Especially if you've not been meditating and especially if you're completely new to this and you've never lucid dreamed before in your life The second one is probably one of the most commonly known techniques and that is the wake back to bed technique This involves as the name suggests Setting your alarm for the early hours of the morning We experienced the longest period of REM sleep, which is rapid eye movement sleep in the early hours of the morning in our last sleep Cycle so this means that if you interrupt that and actually target that You can enter a lucid dream at the time where your REM sleep is the longest and you're also most likely to become lucid So the way you do this is very simple You set your alarm to go off at about 4 to 5 a.m.  However to actually get this to work properly. It might take a bit of practice It's not gonna probably work the first time you try it But if you do if you do practice it a few times you're gonna have some very good results with this and it's gonna give you some very Vivid and stable lucid dreams So a few things to remember with the wake back to bed technique is that you need to set your alarm for the right time The only way of doing this really is to sort of track your sleep cycles and and roughly when you wake up And then what you want to do is you want to work out roughly 19 minutes before When you naturally wake up that is to say without an alarm so track your sleep for a few days you know maybe up to a week even and Write down your your wake-up time as in when you wake up without an alarm work back 90 minutes and then set your alarm for about then When the alarm goes off It will be hopefully just before you enter your last sleep cycle of the night and at that time you can just Basically enter a lucid dream directly use the wild technique and just lay down go to bed and fall asleep again with the Intention of lucid dreaming just keep telling yourself. I will lucid dream or I am lucid or I will control my dreams You're gonna have some really good results with the wake back to bed. It's one of my personal favorites However, it does make you feel a bit tired if you do this technique I wouldn't advise to do it before a day where you have to be up and energetic all day For example, if you're working full-time Monday to Friday I wouldn't advise doing the wake back to bed until the weekend Just because if you do if you do it wrong if you mistime it if you interrupt your last sleep cycle sort of halfway through There's a very good chance. You're gonna wake up feeling very fatigued and sort of almost confused and annoyed the next day And that that feeling will probably last for the most of the day Which is where the myth that lucid dreamer makes you tired comes from it's basically people trying to do the wake back To bed technique and not quite timing it right so they end up interrupting their sleep and essentially causing themselves to have a Sleep debt which will only be repaid when they fall asleep the following evening and catch up on the lost sleep Well, you know the interrupted sleep cycle that they ruined by mistiming the alarm So make sure you get the timings right, but it can work really really effectively. Okay, so number three We have the mild the mild stands for the mnemonically induced lucid dream and it's basically one of the softer or the Most beginner friendly techniques that I know of it Certainly the technique that I use the most out of all of the techniques I use the mild and the dials more than any of the others because not only are they very reliable But they don't involve interrupting your sleep. You don't have to set any alarms You don't have to interrupt your sleep cycle or time things or even worry about waking up in the middle of the night You can just literally go to sleep as normal and you when you do it right will naturally have lucid dreams more often It doesn't guarantee that you'll have them directly. You can't induce them directly like you can with say the wild however, the mild is a very interesting and Underrated technique in my opinion So the way it works is to essentially just constantly tell yourself and reinforce the idea that you will lose a dream The mnemonic method here is to basically repeat mantras and Affirmations to yourself all throughout the day things like I will lose a dream trying to train yourself and prepare yourself for the eventuality that you are in a dream and You suddenly do a reality check and then you lose a dream It goes without saying by the way that all of these techniques in this video Require you to do the basics which are writing your dreams down in the morning Meditating for about 10 minutes in the morning as well and doing reality checks throughout the day I do have other videos explaining these things just check the description or just go on my channel and have a look on there as well So number four is the s siled I don't know quite how to pronounce that because there are two s's it stands for the senses induced lucid dream And it's a very interesting and fairly new technique actually So the way it works is it basically is a an elaboration of the wait back to bed technique You're going to set your alarm as you would with the wait back to bed And you're going to wake up and then go back to sleep with the intention of lucid dreaming However, when you this time when you go back to sleep with the intention of lucid dreaming You're going to basically focus on all of your senses One by one so you're going to go through and basically as you're falling asleep You're going to first focus on what you can hear Really intently listen to all of the sounds around you the sounds outside the sound of your breathing even the sound of the clock ticking in the background and Then once you've done that for a few minutes roughly five minutes or so then you move on to the next sense What can you smell and then what can you feel and then lastly what can you see which at this point? You should start seeing some hypnotic imagery and some patterns and you know colors and lights and things flashing on your eyelids And then before you know it you will enter a lucid dream very very quickly It might even happen before you've even gone through all of the five senses if it doesn't what you should do is focus on going in cycles So go through all of your senses Focus on each one independently one by one and then just go back to the start again and do it all again Keep doing that until you fall asleep and it trust me it will happen very quickly You will very quickly fall asleep and enter what should be a lucid dream and lastly number five This is actually what I call the all-rounder It's not really it doesn't really have a name But it's a technique that I've developed which I would love to share more about I'm gonna make a new video explaining this technique in detail It basically will combine all of the techniques that I've learned and experienced in a way that makes it very very foolproof especially for beginners but also for anyone who wants to just basically lucid dream as Reliably as possible But also who it's for people who don't want to interrupt their sleep and have that Tired fatigue feeling that you get after ruining your way back to bed or after using supplements or you know all of these things Which have these side effects it's designed and it will be designed to be the most effective and hopefully the most reliable lucid dreaming technique I'm gonna be doing some studies on it. It's a very exciting thing that I've been working on If you do want to see that please go and make sure that you're subscribed to this channel leave a comment turn on the Notifications, I know lots of youtubers say, you know turn on notifications and subscribe It really does help us out and it also helps you out because if you don't do that You just won't see that the future videos you choose algorithm is very strange and strict these days And so unless you actually Interact with the video by leaving a comment or leaving a like I'm sure you've heard this before You won't see any more of those videos or at least, you know, it'll be very it'll be a lot harder for you to see those videos So if you did enjoy this video, it will be a huge benefit for you to subscribe leave a comment And just let me know what you think of this video and what techniques you think I should cover in the future Also, if you do want to learn more about those techniques, I do have videos Explaining exactly how to do all of those techniques. Just click on the links in the description Or if you worked till the end of this video, there should be some pop-ups with related videos or, you know Suggested videos that I have also made as well So that's it for now guys. I'll see you next time and don't forget to subscribe done Thanks for watching guys this video and this channel was supported by my patreon followers Please consider giving just a dollar a month to support this channel or just click the links in the description You'll find links to various lucid dream products articles techniques and tutorials if you did enjoy this video Please click the notification bell and subscribe and I'll see you next time Why are you still watching that you should have clicked one of my related videos by now, right? Or subscribed or gone onto my website or something like that


Okay, good morning. I would like to start by thanking the organizers for the invitation to come to this workshop What I'm going to discuss with you is experiments with a system Which is certainly very small compared to the size of systems that are being discussed at this conference I'm going to talk about experiment with trapped ions with strings of trapped ions and the system is not only small It also has very few constituents So I will present experiments with not more than 20 ions and what I hope to show is that these ions constitute a quantum system, which is extremely well controlled and which has long range of actions, of course and And that we can control the system in such a way that we can for example make ions behave as if they were interacting Acting systems of spins. And so I will spend some time on explaining how we do this and this will compliment What you have heard already from Igor on Monday on these trapped ion systems And then I will go on and present you some experiments where we can investigate then the some non-equilibrium Quantum dynamics in these systems particularly we can look at how quantum correlations spread in these systems How we can understand this spreading in terms of spectroscopy of Yeah, all the particles that we have in the system and then finally how to how we can maybe Characterize quantum states that we create in the system by doing measurements in order to characterize the performance of these Yeah, well-controlled quantum systems now This is work, which is which is done jointly in in sprux So these are the people involved in the experiment together with our theory colleagues Philip Hawke and Peter Soler in in sprux But it involves also collaboration with people from the group led by Martin Plinio and in ohm when it comes to the characterization of quantum states that I want to discuss in the Later part of my talk and also we had input from entry daily from the University of Strathclyde Now the experiments that I want to present belong into the domain of what is called Yeah quantum simulation that is the hope of having a well-controlled quantum system and artificially engineered quantum system that We can control to the degree such that we might be able to learn something about the physics of quantum Many body systems which are hard to simulate on a computer and there are a couple of such systems Which which are quite different. So there are for example experiments with also called atoms that trapped iron experiments But then they're also solid state systems like for example quantum dot arrays or systems of superconducting qubits each of these systems Has some Interactions that can be some yeah that are natural to the system and therefore they might be used to investigate Different different physical models what I want to focus on in my talk are trapped irons which are well suited for among others simulating easing models and so What I want to show you is that we can realize a Hamiltonian to Hamiltonian of a long range Transverse easing model where we have a spin-spin interaction term Together with a with a transfer magnet field that competes with these spins interactions Which these spins interaction have a long range and as described by a power law with a certain experiment alpha There are a couple of yeah different experimental systems Which can be used to simulate such easing models for example? Yeah, we heard about Rittberg atoms yesterday the Rittberg atoms in optical lattices are one candidate They are also yeah, so neutral atoms and molecules and optical lattices or for all the laser dressed trapped iron crystals that I want to discuss today Now there are Yeah, this is a slide just to illustrate what yeah, yeah, what we are doing and what has been done so these are the energy levels of a of a six six spin system and Where you see the energy as a function of the strength of the transverse field These yeah, the the idea of using trapped ions for simulating Transverse easing models has been yeah has been around for a couple of years and many experiments that have been done initially in the group led by Chris Monroe at the University of Maryland and so many of these experiments have focused on the properties of the ground state where people started preparing maybe they the system in a State which was easy to prepare and then adiabatically changed the parameters to go in a regime where the States start to become interesting what I want to discuss with you today is the is physics of the of none of the of excited states here and in a regime where the Transverse field here is considerably bigger than the spin spin coupling And so in that case what you can see here is that the energy levels here fall into yeah fall into groups Depending on whether you have either no spin excitation or one spin excitations two spin excitations and so on and then the The degeneracy of these levels here is then lifted by the the spin-spin interaction term that gives rise then to delocalized yet to delocalization of these these excitations and So what I want to show you is that Yeah, we can do experiments in this this first subspace where we have just one Excitation in our system. This is nice because we can then we can easily understand the physics of what is going on there And we can just look at what I want to show you is that we can look at the dynamics of Yeah, correlations in our system and spectroscopically investigate these low line excitations And then I also want to show you experiments in a regime where the complexity of the Hilbert space is much much bigger where we have half of the irons in the excited state and half of the irons in the in the lower state and in these systems we have been looking into methods of To to characterize the quantum states that are produced by the ising dynamics now Yeah, clearly the when you have a system of trapped irons the long range of action that we have at our disposition is a Coulomb interaction and Already mentioned that this Coulomb interaction gives rise when you when you when you put irons into an external potential and Cool these irons to to low temperatures gives rise to yeah crystalline structures So these weakening crystals where the irons repel each other due to the Coulomb interaction and then find equilibrium positions That is that are given by a by an equilibrium of forces of the Mutual repulsion of the particles and the effect of the confining potential now We make use of this Coulomb action for our experiments because what we what we want to study are not the Positions of the of these these charges that we have in our job But we are rather interested in quantum states that we can encode in the internal levels of our internal electronic levels of our irons and Therefore what we are looking for are now interactions that somehow couple the internal state of Yeah, a couple couple the states of one iron to a state of another iron that is far away And this is something we get we can do by making use of the Coulomb interaction together with laser Lights that that dresses this iron crystal and so the the basic idea behind this approach is is quite easy to understand And this involves a transfer of momentum from the light field to the to the irons So when when you think about for example for a free at for you think about a free atom an atom that absorbs of the photon Yeah obtains is obtains a momentum kick because it's just it's it carries the momentum of the photon However, if the atom is initially in the excited state Then you have the opposite process and you have a stimulated emission process And this process then after the atom gets de-excited You have two photons propagating in the same direction and therefore the atom obtains a momentum kick into the opposite direction So this creates spin dependent forces So the forces that depend on the internal state of the particle and now thanks to the Coulomb interaction if one iron in this way Obtains a momentum kick then this momentum kick is somehow transferred to all of the other irons And therefore if there's a second absorption event on another iron then somehow these these phonons that arise By the by the Coulomb coupling of the irons can then give rise to an effective spin-spin interaction that involves only the internal degrees of freedom of the atom I'll come to that come come back to that later in a moment now I told you we what we need are and trapped irons But also we need lasers to manipulate these irons and for this reason when you when you look into the lab There's what you can see here is the iron type apparatus in a vacuum system here But this takes only the smaller part is only the smaller part of our experimental setup The bigger part is occupied by lasers that we use for different purposes So what we need are lasers in order to create irons in the first place in the trap Then we make use of irons for cooling the particles to low temperatures and we cool them such that we have to Quantize the motion of the potential Have to quantize the motion of the irons in this external potential provided by the iron trap then and we also Make use of dissipative dissipative processes to initialize the irons into a pure quantum state and a pure electronic quantum state Then we make use of irons for here to create an excitation of the particles So this is what is needed when we want to simulate these spin-spin interactions and finally the laser the lasers are important for Detection measurements and so this is when we when we want to measure quantum measurements on the on the iron state Then once again lasers are involved now Whatever the time scales so it takes about a few minutes in general to load an iron string into this Such a trap what is nice is that these irons have provide deep potentials And therefore we can store the irons for a long time meaning that we can experiment typically With an iron string that we have loaded for a day without losing irons or having any other problems with it And this time scale is long compared to the time scale of an individual experiment So by an individual experiment I mean that what we want to do is we want to initialize the iron which involves laser cooling We want to conveniently manipulate them and in the end carry out a quantum measurement This process takes about 20 milliseconds And so if you if you compare these two time scales then you can easily conclude that on one day We can carry out something like a hundred thousand to a million quantum measurements now This sounds like like a lot But you also have to keep in mind that when we do an measurement a quantum measurement on our iron string We get only very little information because a typical quantum measurement for us means that we want to figure out Whether the iron is in its electronic round state or whether it is in some excited metastable state So per iron we get one bit of information and if you want to measure for example for an estimate and Observable it means that we have to do an experiment of this kind over and over again to get an estimation of the value of This expectation value So I told you about time scales Something yeah, it's also interesting to think about length scales So so you have seen that this is a fluorescence picture of an of an iron string that we typically confine in traps Which have oscillation frequencies of in the megahertz range now these oscillation frequencies set the equilibrium distance between the irons and This means that the the biggest length scale our Experiment is the distance between a pair of irons which is only on the order of a few micrometers Now this is nice because it means that this is much bigger than the wave lengths of of lasers that we use for manipulating the irons This is nice to two reasons first of all it enables us to Spatially resolve the fluorescence of these irons when we image them on a ccd camera So we can really look into we can really see the individual components of our quantum system And also it enables us to carry out Experiments where we manipulate the quantum state of one eye and using a strongly focused laser that does not interact with Lays with the irons which are sitting next to the one that we want to manipulate So this is something we can do with yeah with with strongly focused laser light the yeah the bad side of these comparatively large distances are that the The iron-iron distance is much much bigger than the natural length scale of our system Which is a bore radius so there are no naturally occurring spin-spin interactions for example in our system on Experimentally relevant timescale so if we want to to turn this iron crystal here into a quantum many body system We have to do it ourselves by the techniques that that's yeah Eagle already mentioned on on Monday But before coming to that problem, let me tell you about the irons that we use we Experiment with with calcium singly charged calcium 40 irons Which is an iron that is convenient for our purpose and here I would just want you to to look at the most relevant energy levels that we have so so a singly charged Alkali earth Atom here has one valence electron And so it has a level structure similar to what you know about hydrogen So we have an s one half ground state and this s one half ground state can be Yeah is Can be coupled to a state which you do not find in hydrogen and this is a meta stable state a D5 half state Which can decay back only on on an electric portable transition and for this reason it has a long lifetime long on on therefore For atomic physics experiments of about a second and this lifetime is long compared to the duration of an individual experiment Therefore we we can forget it more or less about the the finite lifetime of the state now these two levels here are What we yeah form what we call our our spin one-half system Or maybe I should call this a pseudo spin one-half system because it's not has nothing to do with the electron spin of our our iron and so we have a two-level system that we can manipulate now by a narrowband laser that couples these two transitions here and we can then for example also measure the system by coupling the The the S one half state to this short-lived P one half state that you have here using a second laser And if the iron gets excited to this upper level here Then the upper level can decay back only to the S one half state not to the other state And therefore if the iron is in the S one half state We can scatter millions of photons within one second and therefore we can when we observe the the fluorescence The image the fluorescence onto a camera We see that we have a bright iron in our trap if on the hand the iron is in the in this metastable state It does not couple to the laser and therefore will not scatter any any photons and therefore appear as a dark spot on the on the camera And so in this way we have a quantum state measurement capability that allows us to to detect models with unit efficiency Whether the iron is in in one state or in the other state if we are in a superposition state of the two Then this is a protective measurement which protects the iron on either the ground state or to the metastable state So if you think about this as a pseudo spin system here Then we it means that we identify the S one half state with the spin down state They the D five half state with the spin upstate and then that language then what you carry out here is a spin projection Measurement along the Z axis of the of our our sphere Now we trapped irons in a in the linear trap, which I don't want to describe here in detail What is important is that this linear trap provides a harmonic trapping Potential that we make very unisotropic in such a way that there's a weak axis here So along which the irons will align which has a Nostalation frequency which is about 15 to 20 times weaker than the these strong Directions which confine the irons in the redirection and in these unisotropic potentials the Equilibrium positions of a small number of irons are then linear strings and this is convenient for us because it means that we can then Address irons in a way as I told you using focused laser beams and And so we get them then pictures like this We can spatially resolve the fluorescence of the irons using yeah measurements where we detect the fluorescence for a few milliseconds and that enables us to now to Carry out quantum measurements on all of these irons for example what we can now do is so this would be then the state We're all the irons on the spin down state We can then for example use a strongly focused laser beam to flip the iron Here in the middle the spin of the in the middle in which case then There there seems to be an iron missing it, but it's just an iron that does not emit fluorescence here And in this way we can then yeah individually measure all the irons in our string This strongly focused laser beam can also be quickly moved from one iron to a different location And and this is useful in the context of what I'm Presenting to you today for two purposes first of all we can then for example Engineer certain states initial states where certain irons are flipped But we can also make use of this for measuring other quantities than the ones we can measure by a fluorescence measurement only So I told you this fluorescence measurement corresponds to spin protection measurement along the Z axis Now when we have this strongly focused laser beam We can make use of this for coherently rotating our spin on the block sphere And this means that for example when you have when we do not do these measurements these rotations And we have measurements then we can identify for example these pictures here with with the the quantum states that are sketched here Now what we can do is to have a coherent state rotation prior to the measurement And this allows us to measure other spin projections as well So for example if you if you want to measure the z direction I told you we have to project under the eigen states of this operator if we want to measure the for example the sigma x Operator and you want to project under the x axis We have some to find a way of projecting onto onto the the Superbitions of the ground plus excited state and ground minus excited state which is which can be done by Coherently rotating these eigen states using a laser pulse prior to the measurement And in this way we can then carry out by the so this combination of a spin rotation followed by a fluorescence measurement Corresponds and for example to a measurement of sigma x and in that case So so for example this picture here would then correspond to a measurement of Population in this state here and in this way we can then have then the possibility of carrying out arbitrary Spin correlation measurements that we entered in now How can we make the the spins interact with each other? This is the the the big challenge in in these experiments So the pool of interaction gives rise to this equilibrium positions But it also gives rise to the normal to collective Vibrational modes of the ions around these these equilibrium positions so this is the equivalent of phonons and in a solid state and We can now make you so yeah We can now make use of these collective excitations So this is an example of the center of mass mode of motion Which is not and this is not a not a small excitation that we have here But rather a very big one that in which the ions ring was Externally excited by by some electric field that at that was resonant with the ion motion and another example here Is this this freezing mode in the longitudinal erection now? We can make use of these modes in order to engineer our spin-spin interaction in the following way So this is what I have shown you here And I want to tell you now how we can can achieve such an effective spin-spin interaction so There are if you have n ions in your in a linear string You have n vibrational modes that describe the collective motion of the ion along the axis of the string And then there are a set of of n modes that describe the motion that in one transistor action another set of motions in the other transistor action and When the potential is very unisotropic it turns out that these these Collective modes that describe the ion motion the transistor action tends to bunch together in frequency space quite quite yeah, quite well, and so what you can see here is is a spectrum as we would measure it when we excite the ion on the On this internal transition between the electronic state as catch to you So we can do if we tune the laser to to a frequency such that it is resonant with the atomic transition Then we can excite the ion and it turns out that we can also excite the ion if we tune the laser to a frequency Which is equal to the atomic transitions frequency plus or minus the frequency at which these collective modes of motion occur and for the these chances modes of motion you have here then one set of modes and What we can now do and so sorry, this is this is one example where we have an 18 ion crystal You can see here that here the if you if you count you can see that there are 36 vibrational modes of that describe the transfer of ion motion and On that are that can be yeah can be seen in in laser spectra And that's a second set on on the lower frequency side of this what we call carrier transition now each of these Resonances here corresponds now to a process where upon excitation of the ion from the lower state to the upper state We also increase the vibrational quantum number in this particular mode by one unit by one quantum of motion Or where we decrease it by one quantum of motion now using laser cooling techniques We can cool all these modes to the vibrational ground state And in that case what you see here is that the spectrum gets modified because now if we are in the motion The ground state then there's no no if any equals zero There's no corresponding state to which we could excite the the ion on these red side been transitions Whereas on the blue side then this is still possible So what we do now is we make use of a laser that is by traumatic so that carries two frequencies And that is used to off resonantly excite these vibrational modes that you see here In such a way that the sum of the two laser frequencies equals twice the atomic transition frequency And what happens to the following so imagine that you have that you just pick two irons here Which I assume to be both in the spin downstate and where the where one of these vibrational modes is Prepared in the in the ground state of motion now if if one of these irons now absorbs a photon from this Blue laser here then its spin gets flipped and the vibrational quantum number increases by one unit This is what you see here now if in if the other ion now absorbs also a photon But this time from this this red laser here Then it's it's been gets flipped as well and the vibrational quantum number decreases again back to zero And there's a similar process and so you so you see here what we have done is now We have we have flipped the the two spins to the up upstate and the vibrational state is again in the ground state There's a similar process that involves the spin downspin upstate and that couples it to spin up spin downstate And it turns out that both of these processes have the same strengths So if you look at this now this looks as an effective spin-spin interaction as you find it in the in the easy model Now this is what what I get for a pair of irons the question is now what I what I haven't shown you here Is what are the coupling strengths and for this we have to look into this Vibrational mode structure and see what happens when we have a coupling that is mediated off resonantly by all of these modes here so the idea is to have a now a So a process where we have a to photon to iron process when the irons Change its own internal state mediated by these vibrational modes of motion of the iron crystal Now so this is yeah slightly busy slide, but don't don't worry. So what I want to show you here is Let's maybe first concentrate on what is plotted here. So What I show you here is the How the coupling gets mediated by one of the modes and this is the highest frequency mode the center of mass mode But all the irons move in sync with the same amplitude So this this movement is sketched here by by the blue bars that tell you by how much the iron move and whether they move in face or out of Face and as all the irons move by the same amount it turns out that the coupling strengths that we get Is the same for all irons because what matters here in this in this formula So here are the these are the the the spin spin coupling constant and and I told you in second or the perturbations here We can calculate now the strengths of these spin spin coupling constant And it turns out what we have here is a the sum over all vibrational modes And what enters into the sum is now the product of these factors be I am DJM where I Indicates which iron I'm looking at and M which mode I look at and these factors are then the the amount by with which a certain iron participates in a certain collective mode of motion and Then and so so have these these two amplitudes here And then this gets divided by by a term which more or less is the detuning of the laser from the From this resonance frequency that that we're looking at So if we have this center of mass mode of motion where all the irons move in sync It means that this all these coupling constants here are the same and therefore the spin spin coupling is a Yeah, it's a mean field coupling where each iron couples to each other iron with the same strengths And this is what you can see here and this is big matrix here also in the small one So here the color indicates the strengths and also whether the coupling is ferromagnetic or anti ferromagnetic And in this case we have an anti ferromagnetic coupling which is homogeneous When the coupling is mediated only by this center of mass mode now What happens if we if we pick then this the next the next mode which is the tilt mode where the iron crystal moves like this In that case we have now here a coupling which becomes in homogeneous And it turns out that you see here that ions which are close together They they move in in sync irons that are at opposite end of the string they move out of phase and therefore we have now a coupling that That is that yeah that reinforces the coupling of the center of mass mode if the irons are close together And that is opposite to the coupling that is mediated by the center of mass mode if the irons aren't opposite ends of the string So here you see that and for for close irons you have anti ferromagnetic coupling for irons that are far apart You have ferromagnetic couplings if you add up these two you get what you see here in this in this plot here now You can add more and more modes. So there's a next mode and then in this 11 irons I think so if you add up all of those then what you end up with here is a spin spin coupling matrix which Where you see that now the the coupling strength decreases as a function of distance So it falls off we have now a coupling of finite range and where the coupling is more or less how much in this Along the the direction of the string. So we have more or less the same Coupling for when it comes to nearest neighbor coupling or next to nearest neighbor coupling So because the colors here are the same and by by playing now on the one hand side with the Anisotropy of the potential and that I hasn't on the other hand with the laser detuning We have now some control over the range of the interaction that we can engineer Now what does it look like these are experiments with 15 irons where we looked at at quantum quenches So what we did is and so to hear you Let's just look at the the plot on the left hand side and so time goes upwards What you measure is the magnetization of the irons where the color encodes whether the iron is in spin down or spin up what you can see here as we flip the center iron and Then we have the spin spin coupling which gives rise to a hopping of excitations for this reason this excitation starts to spread out As a function of time and then there are some difference patterns and develop We can now change the range of the interaction and so this was with a with a so alpha here is the Exponent of this power law and so we can go from from yeah long range to maybe even longer range And and what you see here is that I don't know how well this can be seen the there are parts of the excitation which starts to spread out faster and faster but on the other hand the the excitation also stays the main part of the excitation also stays localized for a longer time and This can be so this behavior now can be understood in terms of Yeah, of course the particles present in the system and yeah since this is a workshop about long range of the action I think in principle I should should spend more time on talking about this because this is what by the Long-range character of the interaction comes in but on the other hand I have to hope that Michael first like who was involved in experiment at jqi Maryland which I published in Companion paper and both have some time to talk about this and and so I rely on him to say more about this the spreading of these excitations Now we can do more than just look at the magnetization We can also look at the spreading of quantum correlations so so because from from measurements here It is in principle not clear whether this yeah These are really quantum correlations that we that we see here propagating and for this we have done experiment in a smaller system With only seven irons, but the same type of system But now what we do instead of just measuring the spin projections along the z direction What we can do is now we can pick for example a pair of irons Let's say me the iron which is to the left to the right of this initially flipped iron and then Evolve the system for a certain amount of time and then carry out measurements And can measure all kind of spin correlations between these irons and when we have these measurements We're able to reconstruct the density matrix of the this reduced So the reduced to particle density matrix that you can see here for example for in a time of nine milliseconds This is a real part of the density matrix and you can see here But what is what what this tells you is so there are Elements here which tell you that either the excitation is residing in one iron or in the other iron or In the rest of the system that is not the two irons We're looking at but in addition to that you see that we have also off diagonal elements Which tells you that we have here a coherence of a position between the iron being on the left side and on the right side and From this measure density matrix you can then measure how much entanglement we have in the system This is just can be described by the concurrence and When you do this now for different irons and for different amounts of times you get the curves You can see here which shows you that so this is this this amount of entanglement that we have between the Spares of irons you see that the neighboring irons get entangled then get disentangled again And then the entanglement moves to the next to nearest neighbors two and six and then to the to the irons Which are at the edges of our interest Now this spreading of correlations can be understood in terms of quasi particles propagating in the system and The question is whether we can whether we can do spectroscopy of of these quasi particles Which are which are spin waves in our system now For this we can carry out a Ramsey experiment and many body Ramsey experiment in the Ramsey experiment With a single particle what you do is you have a pi over two pulse that is you you flip your spin then you switch on your interaction if Now the energy of your of the two levels does not coincide with the frequency or with the energy of Off your of your Coupling the two levels then that you will see in that the block vector will start to rotate And this is something you can detect using a second pile of a two pulse By carrying out the spin protection in the equatorial plane now when you have when we when you do this now with With a string of irons where we flip one of the irons and switch on then this easy interaction It means that now this localized Excitation has to be written in terms of the delocalized Excitations of which are the eigenstates of our system here And so now we have that means that we have here a superposition of eigenstates and Since these have different energies This is at the basis of what makes these excitations hop here so that when we then carry out the second pi over two pulse here we measure We can measure mechanization that function that changes as a function of the The time during which we have this easy interaction switched on and in this way we get then a signal which tells us about the Gives us information about the the energy separation between these energy levels that are occupied here from the ground state Now this is a bit difficult if we populate more than one of these levels here because at the moment our Resolution is not not good enough to resolve all of them But what we can do is we can try to create a superposition of the irons in the ground state and in one of these These was a part of insertation states and when we do this and measure that now these these Mechanizations here along different axis and combine the cycles in a suitable way Then we get here a signal that you can fully transform and from the full transformation we see that in this case this state here is shifted downwards by the spin-spin interaction and By it by a certain amount if we do the same with some other state We see it in upward shift this talc and from this we can infer that we have indeed anti-ferromagnetic Interactions and in principle it would be nice if you could carry out a spectroscopy of all these levels in this way now the Resolution in our system at the moment is is limited by the clearance time that we have for this reason We turned to a slightly different technique That is we thought it would be nice if you couldn't measure the energy level differences between two such states here where we have for technically reasons much longer coherence times and For this we then create a state which is roughly a Superposition of the ground state two of these states here and then some higher Higher excitation that we don't have to care about When the time above our system now under the easing interaction and these two states have different energies and therefore we get they will acquire different phase factors here and Then in the end we can carry out a protective measurement here of the this and measure measure the spin protection in the Z direction this time and then we get pictures like this now the the easing interaction Conserves in the limit in which we are the number of excitations in our system and therefore what we can do is we can now now Post-select only those measurements where we have the right number of excitations present in this way We can more or less get rid of population which is here and in these higher excited states And this is a good and in this way we have a signal which is which we would have obtained Had we initially prepared the irons and position of these two states here now? Doing this measurement here We get experimental data which now shows oscillation at a single frequency which match quite well the the Simulations to carry out when you do a Fourier transform of this data here and do this for different Superposition of states then we find indeed that we have here that we have that we can measure the energy separation between these different points across the particle state in this way we construct the Yeah, the the dispersion relation that we have I don't have time to talk about this But we can also in this way look at interactions between cause the particles and show that there are that these cause the particles do Interact in our in our system Now coming to the last part here I want to show you that we can also do experiments in the domain where the system is much more complex Because when you have a single excitation you have even if you have n irons You're the the relevant state space is only n-dimensional So there's still a very very simple quantum system when you have n irons and half of them are in the excited state in the Subspace the subspace grows exponentially with the size of the system and therefore it's much harder to yeah to analyze What is going on in such a subspace and so what we have done is to do similar experiments Starting by in a nail-like state where every second iron was flipped and then we switched on this interaction And then you see that yeah, some some hopping of excitations And at some point then it becomes hard to to to say what what is going on and What we would like to do is to understand in a bit better which kind of quantum states that we Which yeah, which kind of concepts are produced under this dynamic So we can of course do is we can do what I already showed you we can look at that measurements on Subsystems that is we can carry out quantum tomography for example of pairs of neighboring ions when you do this We measure all kinds of correlation functions. We reconstruct density made reduced density matrices And that tells us for example that now after a certain amount of interaction time all the ions become entangled and then become disentangled again But it does not tell us anything about the global state of our quantum system Now the global state of our quantum system can in principle be reconstructed using their quantum state of tomography methods, however The the number of measurements that would be required to measure the density matrix of such a 20 iron system is Is huge and it's clearly out of question to carry out such experiments This has been done this something we have done in the past with up to eight particles But even with eight particles you need something like close to ten thousand different measurement bases And so it involves a lot of measurements and since the number of measurements grows exponentially cannot certainly do this with With more than let's say eight or maybe ten particles so What we have done instead was to do a kind of quantum state tomography. This was in collaboration with our collaborators from Ulm where we Where we say now We have a state which is special in the way that initially the ions are In a product state and then we switch on the interactions We have long-range in the action But nevertheless ions tend to to couple much more strongly to talk much more strongly to the neighbors than to Einstein far apart and Based on this assumption. There's reasonable to assume that now the that now these these entangling elections produced some Yeah, produce correlations, but these correlations should be mostly local and under these assumptions There is a hope that we can make use of of Parameterizations of the quantum states which come in the name of matrix product states which might efficiently capture these correlations and which are Yeah, which are Much more compact way of describing the quantum states and then by by the full quantum state And so the the idea is that what we can try to do is when we evolve our system under the easing interaction that we now carry out measurements of quantum correlations for example of Triplets of spins which might capture the correlation that we have in our system and then based on these measured correlations Now we try to to find the matrix product state which best represents our system This is certainly an approximation because here we represent our system by a pure quantum state We know that our system is not an appeal state every experimental system is in the mixed state and But nevertheless it might be an approach to to learn something about the state. So so what we do is we have These quantum correlations here We have our first data set that we use for for reconstructing such a matrix product state And then in a second step, we have additional measurements that we can then Use in order to to here to to bound the To learn something about the state that we have in our in our lab. I think Given the time I will not say much more about this So so what you can see here are now measurements where we evolve the system This in this case eight irons for variable amounts of times and the the upper case here is so this is a small system But we can easily calculate the quantum state that we expect to find and then we can compare now our Reconstructed quantum state here with the exact quantum state and the we have taken numerically that this now this Reconstructed matrix product state should be a very good representation of our state So so if there's a deviation from if these two do not match perfectly This is not because we have limited ourselves to a reduced set of states But rather because we have some experimental imperfections which give rise to to a reduction of this fidelity that you can see here now but on the other hand if we if we have a curve like this then we We reconstruct the state and we can say how close it is to the state that we expect it to be but We do not yeah It's not clear what we learn about the state that we have experimentally produced because we know that this state is not what we have in our experiment and So for this reason it's also interesting to ask is it possible given such a reconstructed state that by doing additional Measurements that we can now put bounds on how close our our experiment is to this reconstructed state Which in principle which could be also useful even that maybe it and maybe we have the wrong Wrong theory assumptions, so maybe we we believe that we have we should have this state But in fact we have some control parameters which are different and therefore we it's slightly different but what you can see here are now now bounds that we find and It turns out that when we when you look only at it. Yeah, it's it. Yeah, these are bounds which are based on looking at correlations of one two or three spins So it needs at least three spins in order to to get a bound But under the hand these bounds tend to become quite quite weak after short interaction times, which is a bit disappointing now We have I don't have the time to talk about this I believe But yeah, if you're interested in this I would suggest that you come to me and I show you then the data We have here, so this gets worse if we have 14 irons now We can do something In addition to that it is we can try to carry out a direct fidelity estimate measurement of between our state in Our experiment and these reconstructed state This is also a task which becomes exponentially difficult when you have large systems But there are techniques of doing this and we have done this with 14 irons You see that that this gives now values, which I'm much closer to what we what we hope to find from this this simple Matrix producing reconstruction process. Yeah, so this is what I what I hope to show you I skip over this so we have we measure complex Yeah, long poly strings and make use of this to reconstruct this this state And so to to summarize I hope you have seen that that irons are indeed a well-controlled quantum system that can be used for realizing these investigating these long-range easing models and that we can carry out measurements along the lines I have have told you so it will certainly be a challenge to go to a larger number of irons because so far we are in a regime where we Can still understand everything from our Can calculate everything in principle if you could go to 50 irons and this would the situation would change then it would not be possible to do exact simulations of the the the states that we should produce also Creating higher coupling strengths and lowering the dequears in our system is is a concern we have and Then what is also interesting is to see which kinds of interactions Which are not only long-range easing interactions can reduce in our system. Thank you very much