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 metal 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 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.

• Received 4 August 2008

DOI:https://doi.org/10.1103/PhysRevA.79.023831