# Lattice-depth measurement using continuous grating atom diffraction

## TL;DR

This paper introduces a novel method for measuring optical lattice depths by analyzing high-amplitude oscillations in atomic diffraction patterns, which are robust against temperature variations, enabling simultaneous temperature and lattice depth determination.

## Contribution

The authors develop an analytic model for lattice-depth measurement using atomic diffraction oscillations, extending it to finite temperatures and initial momenta, facilitating more accurate and robust characterization.

## Key findings

- Analytic formula for zero-temperature oscillations
- Extension of model to finite-temperature response
- Steady-state solution enabling simultaneous measurement of lattice depth and temperature

## Abstract

We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, which leads to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a simplified model yielding an analytic formula describing such oscillations for a gas assumed to be at zero temperature. This model is extended to include atoms with initial momenta detuned from our chosen initial value, before analyzing the full finite-temperature response of the system. Finally we present a steady-state solution to the finite-temperature system, which in principle makes possible the measurement of both the lattice depth, and initial temperature of the atomic gas simultaneously.