  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.
