Phase Estimation from Atom Position Measurements

TL;DR

This paper explores advanced methods for estimating the relative phase between two Bose-Einstein condensates using atom position measurements, achieving sensitivities beyond the shot-noise limit and approaching the Heisenberg limit.

Contribution

It introduces correlation function techniques and center-of-mass measurements for phase estimation, surpassing traditional shot-noise limits in atom interferometry.

Findings

Correlation functions of order √N or higher enable Heisenberg-limited phase estimation.

Center-of-mass measurements can achieve sub-shot-noise sensitivity.

Overlap effects influence phase estimation accuracy in double-well interferometry.

Abstract

We study the measurement of the position of atoms as a means to estimate the relative phase between two Bose-Einstein condensates. First, we consider $N$ atoms released from a double-well trap, forming an interference pattern, and show that a simple least-squares fit to the density gives a shot-noise limited sensitivity. The shot-noise limit can instead be overcome by using correlation functions of order $\sqrt{N}$ or larger. The measurement of the $N\mathrm{th}$-order correlation function allows to estimate the relative phase at the Heisenberg limit. Phase estimation through the measurement of the center-of-mass of the interference pattern can also provide sub-shot-noise sensitivity. Finally, we study the effect of the overlap between the two clouds on the phase estimation, when Mach-Zehnder interferometry is performed in a double-well.