No abstract

We study magnetic orders of fermions under cavity-assisted Raman couplings in a one-dimensional lattice at half filling. The cavity-enhanced atom-photon coupling introduces a dynamic long-range interaction between the fermions, which competes with the short-range on-site interaction and leads to a variety of magnetic orders. Adopting a numerical density-matrix-renormalization-group method, we investigate the various magnetic orders and map out the steady-state phase diagram. Interestingly, as all the phase transitions take place outside the superradiant regime, the magnetic orders are associated with cavity-field fluctuations with a vanishing number of photons on the meanfield level.Coherently driven atomic gases inside optical cavities have attracted much research interest of late [1]. In these systems, as the atoms serve as a non-linear media between the external pumping and the cavity fields, the cavity photons feed back on the atomic degrees of freedom, effectively imposing a dynamic potential on the atoms. These dynamic potentials are responsible for interesting non-equilibrium collective dynamics and exotic steady states, which are the subjects of intensive experimental and theoretical study .

We present an experimentally-feasible method to produce a giant and tunable spin squeezing, when an ensemble of many four-level atoms interacts simultaneously with a single-mode photon and classical driving lasers. Our approach is to simply introduce a time-dependent collective atomphoton coupling. We show that the maximal squeezing factor measured experimentally can be well controlled by both its driving magnitude and driving frequency. Especially, when increasing the driving magnitude, the maximal squeezing factor increases, and thus can be enhanced rapidly. We also demonstrate explicitly, in the high-frequency approximation, that this spin squeezing arises from a strong repulsive spin-spin interaction induced by the time-dependent collective atom-photon coupling. Finally, we evaluate analytically, using current experimental parameters, the maximal squeezing factor, which can reach 40 dB. This giant squeezing factor is far larger than previous ones. [2,10,11]. Now the preparation of spin squeezing states has become an important subject in quantum information and quantum metrology [2,3]. In principle, nonlinear spin-spin interactions are necessary for producing spin squeezing states, and moreover, have been constructed experimentally in both multicomponent Bose-Einstein condensates (BECs) [12][13][14][15][16][17][18] and atom-cavity interacting systems [19,20]. However, the generated spin-spin interactions are weak, and thus the corresponding maximal squeezing factors (MSFs) acquired are lower than 10 dB [2,3]. Recently, many proposals [21][22][23][24][25][26][27][28][29][30] have been suggested to enhance the upper limits of the MSFs in laboratory conditions, but the experimental challenges are difficult.Here we present an experimentally-feasible method to achieve a giant and tunable spin squeezing, when an ensemble of many four-level atoms interacts simultaneously with a single-mode photon and classical driving lasers. Recently, a similar setup has been considered experimentally in a BEC-cavity system, and a remarkable quantum phase transition, from a normal phase to a superradiant phase of the Dicke model, was observed [31,32]. The distinct advantage of this setup is that the realized * chengang971@163.com † tjia@sxu.edu.cn ‡ fnori@riken.jp Dicke model has a tunable collective atom-photon coupling through manipulating the intensities of the classical driving lasers [33].The central idea of our work is to simply introduce a time-dependent collective atom-photon coupling in the realized Dicke model. We show that the MSF can be well controlled by both its driving magnitude and driving frequency. In particular, when increasing the driving magnitude, the MSF increases, in contrast to the known results of the undriven Dicke model [2], and thus can be enhanced rapidly. In the high-frequency approximation, we demonstrate explicitly that this spin squeezing arises from a strong repulsive spin-spin interaction induced by the time-dependent collective atom-photon coupling (for the undriven Dicke model, only a weak att...

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 H = q(J 2x + χJ 2 y ) + ω 0 J z 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 ω 0 . Surprisingly, we find that by combining with the dimensionless parameter χ(> −1), this atomic resonant frequency ω 0 can enhance spin squeezing greatly. These results are beneficial for achieving the required spin squeezing in experiments.

No abstract