Investigation Of Spin Squeezing In Cavity Quantum Electrodynamics

Spin-squeezing states are quantum correlated states with reduced fluctuations in one of the collective spin components.Such states not only have an essential relation in many-body entanglement,but also have important applications in atom interferometers and high-precision atom clocks.Now the preparation of spin-squeezing states has become an important subject in quantum information and quantum metrology.A key step to produce spin-squeezing states is how to construct a one-axis twisting Hamiltonian HOAT = qJ_x² or a two-axis twisting Hamiltonian H_TAT = q?J_x²-J_y²?.For the same initial states,the maximal squeezing factor for the one-axis twisting Hamiltonian scales as N-2/3,which becomes N-1 for the two-axis twisting Hamiltonian.Controlling the novel interaction between atomic ensemble and a single-mode photon is a powerful way to produce spin squeezing,because photon of cavity mode can induce nonlinear spin-spin interaction of the one-axis twisting Hamiltonian HOAT = qJ_x².However,the collective interaction strength for the conventional two-level atoms interacting with the single-mode photon is weak,and not adjustable.As a result,it has still been not achieved the required spin squeezing in experiments.In this paper,based on current experimental development,we propose two protocols to largely enhance spin squeezing.The details are given as follows.1.By considering the collective interaction between an ensemble of four-level atoms and a single-mode photon and a pair of classic Raman lasers,we derive,under the adiabatic approximation,a generalized Dicke model,in which the counter-rotating terms?including its magnitude and phase factor?can be controlled independently.Numerical simulation shows that these counter-rotating terms can significantly enhance spin squeezing.We also find that the positive and negative detunings between the atom and photon have an important impact on spin squeezing.2.By considering the collective interaction between an ensemble of six-level atoms and two-mode photons and two pairs of classic Raman lasers,we realize a tunable two-axis spin Hamiltonian H = q?J_x² + xJ_y²?+?0Jz,with independently-adjustable parameters.For the proper parameters,the two-axis twisting Hamiltonian H_TAT=q?J_x²-J_y²?can be reduced,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 effective atomic resonant frequency?0.Surprisingly,we find that by combined with the dimensionless parameter x?>-1?,the effective atomic resonant frequency?0 can enhance spin squeezing largely.The above results are benefit for achieving the required spin squeezing in cavity QED experiments.