Lattice-depth measurement using multi-pulse atom diffraction in and beyond the weakly diffracting limit

TL;DR

This paper develops an analytical and numerical model for measuring optical lattice depths using multi-pulse atom diffraction, applicable in weak and beyond-weak diffraction regimes, accounting for finite temperature effects.

Contribution

It introduces a comprehensive analytic model and numerical simulations for lattice-depth measurement via multi-pulse atom diffraction, extending accuracy beyond weak lattice assumptions.

Findings

Analytic model accurately predicts atomic populations in weak lattices.

Numerical simulations extend the model to stronger lattices.

Finite temperature effects are incorporated into the measurement analysis.

Abstract

Precise knowledge of optical lattice depths is important for a number of areas of atomic physics, most notably in quantum simulation, atom interferometry and for the accurate determination of transition matrix elements. In such experiments, lattice depths are often measured by exposing an ultracold atomic gas to a series of off-resonant laser-standing-wave pulses, and fitting theoretical predictions for the fraction of atoms found in each of the allowed momentum states by time of flight measurement, after some number of pulses. We present a full 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. Finally, we consider the situation where the initial gas is explicitly assumed to be at a finite temperature.