Spin squeezing of atomic ensembles by multi-colour quantum non-demolition measurements

TL;DR

This paper demonstrates how multi-frequency quantum non-demolition measurements can generate spin squeezing in atomic ensembles, optimizing optical parameters to enhance squeezing and reduce technical noise, with practical configurations analyzed.

Contribution

It introduces a method using multi-frequency dispersive interactions to improve spin squeezing, including two configurations and quantitative analysis for alkali atoms.

Findings

Spin squeezing scales as 1/d with two-frequency light in ideal conditions.

Using two frequencies significantly improves achievable squeezing.

Quantitative analysis shows potential for enhanced squeezing in Cs D1 line.

Abstract

We analyze the creation of spin squeezed atomic ensembles by simultaneous dispersive interactions with several optical frequencies. A judicious choice of optical parameters enables optimization of an interferometric detection scheme that suppresses inhomogeneous light shifts and keeps the interferometer operating in a balanced mode that minimizes technical noise. We show that when the atoms interact with two-frequency light tuned to cycling transitions the degree of spin squeezing $\xi^2$ scales as $\xi^2\sim 1/d$ where $d$ is the resonant optical depth of the ensemble. In real alkali atoms there are loss channels and the scaling may be closer to $\xi^2\sim 1/\sqrt d.$ Nevertheless the use of two-frequencies provides a significant improvement in the degree of squeezing attainable as we show by quantitative analysis of non-resonant probing on the Cs D1 line. Two alternative configurations are analyzed: a Mach-Zehnder interferometer that uses spatial interference, and an interaction with multi-frequency amplitude modulated light that does not require a spatial interferometer.