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The strong light-matter coupling attainable in optical cavities enables thegeneration of highly squeezed states of atomic ensembles. It was shown in[Phys. Rev. A 66, 022314 (2002)] how an effective one-axis twisting Hamiltoniancan be realized in a cavity setup. Here, we extend this work and show how aneffective two-axis twisting Hamiltonian can be realized in a similar cavitysetup. We compare the two schemes in order to characterize their advantages. Inthe absence of decoherence, the two-axis Hamiltonian leads to more squeezingthan the one-axis Hamiltonian. If limited by decoherence from spontaneousemission and cavity decay, we find roughly the same level of squeezing for thetwo schemes scaling as (NC)^(1/2) where C is the single atom cooperativity andN is the total number of atoms. When compared to an ideal squeezing operation,we find that for specific initial states, a dissipative version of the one-axisscheme attains higher fidelity than the unitary one-axis scheme or the two-axisscheme. However, the unitary one-axis and two-axis schemes perform better forgeneral initial states.

One- and two-axis squeezing of atomic ensembles in optical cavities