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arXiv:1407.5199 · Physical Review A

Two-component polariton condensate in an optical microcavity

Yong-Chang Zhang, Xiang-Fa Zhou, Guang‐Can Guo, Xingxiang Zhou, Han Pu, Zhengwei Zhou

Published May 28, 2014• 5 citations
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Abstract

We present a scheme for engineering the extended two-component Bose-Hubbard model using polariton condensate supported by an optical microcavity. Compared to the usual two-component Bose-Hubbard model with only Kerr nonlinearity, our model includes a nonlinear tunneling term which depends on the number difference of the particle in the two modes. In the mean-field treatment, this model is an analog to a nonrigid pendulum with a variable pendulum length whose sign can be also changed. We study the dynamic and ground-state properties of this model and show that there exists a first-order phase transition as the strength of the nonlinear tunneling rate is varied. Furthermore, we propose a scheme to obtain the polariton condensate wave function.

DOI
10.1103/physreva.89.053624

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We present a scheme for engineering the extended two-component Bose-Hubbard model using polariton condensate supported by an optical microcavity. Compared to the usual two-component Bose-Hubbard model with only Kerr nonlinearity, our model includes a nonlinear tunneling term which depends on the number difference of the particle in the two modes. In the mean-field treatment, this model is an analog to a nonrigid pendulum with a variable pendulum length whose sign can be also changed. We study the dynamic and ground-state properties of this model and show that there exists a first-order phase transition as the strength of the nonlinear tunneling rate is varied. Furthermore, we propose a scheme to obtain the polariton condensate wave function.
We propose a scheme which can realize an extended two-component Bose-Hubbard model using polaritons confined in an array of optical cavities. In addition to the density-dependent interactions, this model also contains nonlinear coupling terms between the two components of the polariton. Using a mean-field calculation, we obtain the phase diagram which shows how these terms affect the transition between the Mott insulator and the superfluid phase. In addition, we employ both a perturbation approach and an exact diagonalization method to gain more insights into the phase diagram.
Abstract We investigate the dynamical phase transition of two-component Bose–Einstein condensate with nonlinear tunneling, which is trapped inside a double-well and dispersively coupled to a single mode of a high-finesse optical cavity with one moving end mirror driven by a single mode standing field. In the mean-field approximation, the Hamiltonian of the system with nonlinear tunneling is characterized by the population difference of the particles and relative phase in double wells. The characteristics of the system’s stability points are determined by the corresponding Hessian matrices. However, the number of the system’s stability points depends on the roots of the first derivative of the energy. In the absence of the nonlinearity, the Hamiltonian of the system is a binary quadratic equation. When there is nonlinear tunneling, the Hamiltonian of the system is a binary quartic equation. Therefore, from a mathematical point of view, it can be found that the roots of the equation will increase, which means that the number of stability points in the system will increase. We also build the phase portrait from classical analysis. Considering the strong pair tunneling case, we confirm that nonlinear tunneling interaction leads to an increment of stability points and enriches the phase diagram of the system. We further analyze the phase portrait with the moving end mirror. It is shown that the semiclassical dynamics of the system undergoes a bifurcation of stability points with an increase in the coupling strength or detuning. In other words, the system experiences a phase transition.
The possible existence of quantum crystals phase of polariton condensate in two-dimensional microcavity polariton was studied by using mean-field method for bosons at zero temperature. In this study, we observe the supersolid crystallized (hexagonal, square) and a quantized winding number of the phase in a regime of strong- field interaction in rotating exciton–polariton condensates. First, the ground state of the condensate was found; and the solution was further extended for dynamics state to reach the equilibrium steady-state as well as their density profile and energy diagrams. The supersolid crystal is the result of the considerable deviation induced by the interaction of polaritons of both ground and dynamic states of a dressed dipolar Bose–Einstein condensate. Here, the researchers demonstrated the formation of a hexagonal lattice in the nonlinear regime at high polariton-density where polariton–polariton interactions dominate the behavior of the system. It was identified that stability regimes for ground state increases as the polariton–polariton interaction strength increases. The phase diagram for the stable vortex state will be useful for conducting experimental and theoretical studies on rotating dipolar quantum gases and many other exotic systems.
We demonstrate that polaritons in an array of interacting micro-cavities with strong atom–photon coupling can form a two-component Bose–Hubbard model in which both polariton species are protected against spontaneous emission as their atomic part is stored in two ground states of the atoms. The parameters of the effective model can be tuned via the driving strength of external lasers and include attractive and repulsive polariton interactions. We also describe a method to measure the number statistics in one cavity for each polariton species independently.
Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose–Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose–Hubbard model.