is weak, generally below 1 mK. Thus atoms must be cooled significantly before loading them into the optical lattice. Cooling techniques used to this end include magneto-optical traps, Doppler cooling, polarization gradient cooling, Raman cooling, resolved sideband cooling, and evaporative cooling. Once cold atoms are loaded into the optical lattice, they will experience heating by various mechanisms such as spontaneous scattering of photons from the optical lattice lasers. These mechanisms generally limit the lifetime of optical lattice experiments. Time of flight imaging Once cooled and trapped in an optical lattice, they can be manipulated or left to evolve. Common manipulations involve the "shaking" of the optical lattice by varying the relative phase between the counterpropagating beams, or amplitude modulation of the lattice. After evolving in response to the lattice potential and any manipulations, the atoms can be imaged via absorption imaging. A common observation technique is time of flight (TOF) imaging. TOF imaging works by first waiting some amount of time for the atoms to evolve in the lattice potential, then turning off the lattice potential (by switching off the laser power with an AOM). The atoms, now free, spread out at different rates according to their momenta. By controlling the amount of time the atoms are allowed to evolve, the distance travelled by atoms maps onto what their momentum state must have been when the lattice was turned off. Because the atoms in the lattice can only change in momentum by , a characteristic pattern in a TOF image of an optical-lattice system is a series of peaks along the lattice axis at momenta , where . Using TOF imaging, the momentum distribution of atoms in the lattice can be determined. Combined with in-situ absorption images (taken with the lattice still on), this is enough to determine the phase space density of the trapped atoms, an important metric for diagnosing Bose–Einstein condensation (or more generally, the formation of quantum degenerate phases of matter). Uses Quantum simulation Atoms in an optical lattice provide an ideal quantum system where all parameters can be controlled. Because atoms can be imaged directly – something difficult to do with electrons in solids – they can be used to study effects that are difficult to observe in real crystals. Quantum gas microscopy techniques applied to trapped atom optical-lattice systems can even provide single-site imaging resolution of their evolution. By interfering differing numbers of beams in