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Physical Review A

Spin squeezing in two-level systems

L. Vernac, M. Pinard, E. Giacobino

Published Nov 14, 2000• 59 citations
Publisher

Abstract

Using a quantum theory for an ensemble of two-level atoms driven by a field in an optical cavity, we show that the spin associated with the atomic ensemble can be squeezed. Two kinds of squeezing are obtained: on the one hand, self-squeezing of the spin when the input field is a coherent one and the atomic ensemble exhibits a large nonlinearity; and on the other hand, squeezing transfer from an incoming squeezed field when the atomic ensemble has a quasilinear behavior.

DOI
10.1103/physreva.62.063812

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We present a special quantum effect named electromagnetically induced squeezing of atomic spin in the conventional Λ-type atomic system driven by a strong pump field and a relatively weak probe field in an atomic ensemble. Nearly perfect atomic spin squeezing in the y component can be achieved with fully on resonance at high pump-field intensity, large optical depth of the atomic ensemble, and a low coherence decay rate between the two lower levels. This method would greatly facilitate the generation of atomic spin squeezing by using only coherent laser fields, and may find potential applications in realistic quantum metrology, quantum computation, and quantum information processing.
Ultracold atoms in an ultrahigh-finesse optical cavity are a powerful platform to produce spin squeezing since photon of cavity mode can induce nonlinear spin-spin interaction and thus generate a one-axis twisting Hamiltonian HOAT=qJx2H_{\text{OAT}}=qJ_{x}^{2}HOAT​=qJx2​, whose corresponding maximal squeezing factor scales as N−2/3N^{-2/3}N−2/3, where NNN is the atomic number. On the contrary, for the other two-axis twisting Hamiltonian HTAT=q(Jx2−Jy2)H_{\text{TAT}}=q(J_{x}^{2}-J_{y}^{2})HTAT​=q(Jx2​−Jy2​), the maximal squeezing factor scales as N−1N^{-1}N−1, approaching the Heisenberg limit. In this paper, inspired by recent experiments of cavity-assisted Raman transitions, we propose a scheme, in which an ensemble of ultracold six-level atoms interacts with two quantized cavity fields and two pairs of Raman lasers, to realize a tunable two-axis spin Hamiltonian %H=q(J_{x}^{2}+χJ_{y}^{2})+ω_{0}J_{z}. For proper parameters, the above one- and two- axis twisting Hamiltonians are recovered, and the scaling of N−1N^{-1}N−1 of the maximal squeezing factor can occur naturally. On the other hand, in the two-axis twisting Hamiltonian, spin squeezing is usually reduced when increasing the effective atomic resonant frequency ω0ω_{0}ω0​. Surprisingly, we find that by combined with the dimensionless parameter χ(>−1)χ(>-1)χ(>−1), the effective atomic resonant frequency ω0ω_{0}ω0​ can enhance spin squeezing largely. These results are benefit for achieving the required spin squeezing in experiments.