Modelling atom diffraction in pulsed and continuous far off-resonant optical lattices

In this thesis we investigate the diffraction of cold atomic gases by optical lattices. Of particular interest to atom interferometry is the implementation of a high momentum-transfer ``beam-splitter,'' which may be achieved by inducing quantum resonance in such an atomic gas. We use Monte Carlo simulations to investigate these quantum resonances in the regime where the gas receives laser pulses of finite duration, and demonstrate that an -pseudoclassical model for the dynamics of the gas atoms reproduces quantum resonant behavior for both zero-temperature and finite-temperature non-interacting gases. We show that this model agrees well with the fully quantum treatment of the system over a timescale set by the choice of experimental parameters. In similar setups, the depth of a laser lattice may be measured by exposing an atomic gas to a series of off-resonant laser-standing-wave pulses, and fitting theoretical predictions for the population found in each of the allowed momentum states. We present an analytic model for the time evolution of the atomic populations of the lowest momentum-states, which is sufficient for a weak lattice, as well as numerical simulations incorporating higher momentum states for both relatively strong and weak lattices at zero and finite temperature. We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, leading to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a zero-temperature analytic formula describing such oscillations, extend it to include atoms with initial momenta detuned from our chosen initial value, and analyze the full finite-temperature response.