Spin squeezing of atomic ensembles by multicolor quantum nondemolition measurements

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) similar to 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) similar to 1/root 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.