where n is an integer, λ is the de Broglie wavelength of the incident particles, d is the spacing of the grating and θ is the angle of incidence. This matter wave diffraction is analogous to optical diffraction of light through a diffraction grating. Another incidence of this effect is the diffraction of ultra-cold (and therefore almost stationary) atoms by an optical lattice that is pulsed on for a very short duration. The application of an optical lattice transfers momentum from the photons creating the optical lattice onto the atoms. This momentum transfer is a two-photon process meaning that the atoms acquire momentum in multiples of 2ħk, where k is the wavevector of the electromagnetic radiation. The recoil frequency of the atom as can be expressed by: