Figure 1: One layer of a regular array of independent one-dimensional chains of ultracold bosonic atoms created by an optical lattice. The two Bragg pulses are also displayed (blue and green arrows). The inset shows an atom absorbing a photon from the first laser beam followed by stimulated emission into the second beam. This process transfers momentum $\mathrm{ħ}\mathbf{\text{q}}$ and energy $\mathrm{ħ}\nu$ to the atom cloud. Spontaneous emission $\mathrm{\Gamma }$ is suppressed by a large detuning $\mathrm{\Delta }$ from the atomic transition $|g\rangle \leftrightarrow |e\rangle$.