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

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.

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