Spin squeezing of atomic ensembles by multi-colour quantum non-demolition measurements

摘要

We analyze the creation of spin squeezed atomic ensembles by simultaneousdispersive interactions with several optical frequencies. A judicious choice ofoptical parameters enables optimization of an interferometric detection schemethat suppresses inhomogeneous light shifts and keeps the interferometeroperating in a balanced mode that minimizes technical noise. We show that whenthe atoms interact with two-frequency light tuned to cycling transitions thedegree of spin squeezing $\xi^2$ scales as $\xi^2\sim 1/d$ where $d$ is theresonant optical depth of the ensemble. In real alkali atoms there are losschannels and the scaling may be closer to $\xi^2\sim 1/\sqrt d.$ Neverthelessthe use of two-frequencies provides a significant improvement in the degree ofsqueezing attainable as we show by quantitative analysis of non-resonantprobing on the Cs D1 line. Two alternative configurations are analyzed: aMach-Zehnder interferometer that uses spatial interference, and an interactionwith multi-frequency amplitude modulated light that does not require a spatialinterferometer.