Phase Estimation With Interfering Bose-Condensed Atomic Clouds

TL;DR

This paper explores methods to estimate the relative phase of two Bose-Einstein condensates from atom-position measurements, demonstrating that higher-order correlations and center-of-mass detection can surpass shot noise limits, though with experimental challenges.

Contribution

It introduces phase estimation strategies using higher-order correlation functions and center-of-mass detection to achieve sub shot-noise sensitivity in Bose-Einstein condensate interference.

Findings

Higher-order correlation measurements can surpass shot noise limits.

Center-of-mass detection provides sub shot-noise sensitivity.

Experimental implementation of these methods may be challenging.

Abstract

We investigate how to estimate from atom-position measurements the relative phase of two Bose-Einstein condensates released from a double-well potential. We demonstrate that the phase estimation sensitivity via the fit of the average density to the interference pattern is fundamentally bounded by shot noise. This bound can be overcome by estimating the phase from the measurement of $\sqrt N$ (or higher) correlation function. The optimal estimation strategy requires the measurement of the $N$-th order correlation function. We also demonstrate that a second estimation method -- based on the detection of the center of mass of the interference pattern -- provides sub shot-noise sensitivity. Yet, the implementation of both protocols might be experimentally challenging.