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 ξ2 scales as ξ2∼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 ξ2∼1/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.
@article{arxiv.0808.0516,
title = {Spin squeezing of atomic ensembles by multi-colour quantum non-demolition measurements},
author = {M. Saffman and D. Oblak and J. Appel and E. S. Polzik},
journal= {arXiv preprint arXiv:0808.0516},
year = {2009}
}