Tunable two-axis spin model and spin squeezing in two cavities**Project supported by the National Natural Science Foundation of China (Grant Nos. 11422433, 11447028, 61227902, 11434007, and 61275211), the Natural Science Foundation of Zhejiang Province, China (Grant No. LY13A040001), and the Scientific Research Foundation of the Education Department of Zhejiang Province, China (Grant No. Y201122352).

Abstract

Multi-mode cavities have now attracted much attention both experimentally and theoretically. In this paper, inspired by recent experiments of cavity-assisted Raman transitions, we realize a two-axis spin Hamiltonian in two cavities. This realized Hamiltonian has a distinct property that all parameters can be tuned independently. For proper parameters, the well-studied one- and two-axis twisting Hamiltonians are recovered, and the scaling of 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 atomic resonant frequency ω0. Surprisingly, we find that by combining with the dimensionless parameter χ (> −1), this atomic resonant frequency ω0 can enhance spin squeezing greatly. These results are beneficial for achieving the required spin squeezing in experiments.