# Squeezed state metrology with Bragg interferometers operating in a cavity

## TL;DR

This paper proposes a scheme to enhance the sensitivity of Bragg interferometers by directly squeezing momentum states via cavity interactions, potentially surpassing the projection noise limit with current technology.

## Contribution

It introduces a novel momentum state squeezing protocol for Bragg interferometers operating in cavities, addressing unique challenges and demonstrating feasibility with existing experimental setups.

## Key findings

- Significant spin squeezing achievable despite atomic momentum width.
- Adaptation of spin squeezing techniques to momentum states in cavity systems.
- Potential to surpass projection noise limit in precision measurements.

## Abstract

Bragg interferometers, operating using pseudospin-1/2 systems composed of two momentum states, have become a mature technology for precision measurements. State-of-the-art Bragg interferometers are rapidly surpassing technical limitations and are soon expected to operate near the projection noise limit set by uncorrelated atoms. Despite the use of large numbers of atoms, their operation is governed by single-atom physics. Motivated by recent proposals and demonstrations of Raman gravimeters in cavities, we propose a scheme to squeeze directly on momentum states for surpassing the projection noise limit in Bragg interferometers. In our modeling, we consider the unique issues that arise when a spin squeezing protocol is applied to momentum pseudospins. Specifically, we study the effects of the momentum width of the atomic cloud and the coupling to momentum states outside the pseudospin manifold, as these atoms interact via a mode of the cavity. We show that appreciable levels of spin squeezing can be demonstrated in suitable parameter regimes in spite of these complications. Using this setting, we show how beyond mean-field techniques developed for spin systems can be adapted to study the dynamics of momentum states of interacting atoms. Our scheme promises to be feasible using current technology and is experimentally attractive because it requires no additional setup beyond what will be required to operate Bragg interferometers in cavities.