Spin squeezing of atomic ensembles by multicolor quantum nondemolition 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 ${\ensuremath{\xi}}^{2}$ scales as ${\ensuremath{\xi}}^{2}\ensuremath{\sim}1/d$, where $d$ is the resonant optical depth of the ensemble. In real alkali metal atoms there are loss channels and the scaling may be closer to ${\ensuremath{\xi}}^{2}\ensuremath{\sim}1/\sqrt{d}$. Nevertheless the use of two frequencies provides a significant improvement in the degree of squeezing attainable as we show by quantitative analysis of nonresonant probing on the Cs ${D}_{1}$ line. Two alternative configurations are analyzed: a Mach-Zehnder interferometer that uses spatial interference and an interaction with multifrequency amplitude modulated light that does not require a spatial interferometer.