Abstract Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of two-level BEC atoms with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portraits of the system. The rich phase portraits generated by analytical arguments display two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in reaching their attractors. Further, we add an external mechanical pump to the mirror which is capable of changing the mirror frequency through radiation pressure and study the impact of the pump on the phase portraits and the dynamics of the system. We find the external mirror frequency changing the phase portraits and even shifting the critical transition point, thereby predicting a system with controllable phase transition.
Abstract Motivated by the experimental realization of Dicke model in optical cavities, we model an optomechanical system consisting of two-level BEC atoms with transverse pumping. We investigate the transition from normal and inverted state to the superradiant phase through a detailed study of the phase portraits of the system. The rich phase portraits generated by analytical arguments display two types of superradiant phases, regions of coexistence and some portion determining the persistent oscillations. We study the time evolution of the system from any phase and discuss the role of mirror frequency in reaching their attractors. Further, we add an external mechanical pump to the mirror which is capable of changing the mirror frequency through radiation pressure and study the impact of the pump on the phase portraits and the dynamics of the system. We find the external mirror frequency changing the phase portraits and even shifting the critical transition point, thereby predicting a system with controllable phase transition.
In this paper, the quantum phase transitions caused by the interactions between light and atoms, as well as between light and mechanical oscillators, are discussed theoretically in a coupled optomechanical cavity containing two optical field modes (N atoms and mechanical oscillator). By using Holstein-Primak off transformation method, new translational boson operators and four parameters are assumed. The ground state energy functional of the system and a set of equations composed of four parameters are given. The correctness of the assumed translation boson operators is proved by two special cases. In the case of resonance, the characteristics of the obtained solutions are shown by solving the equations, graphical method and Hessian matrix judgment. The stable zero solution is called the normal phase, the unstable zero solution is named the unstable vacuum macroscopic phase, and the stable non-zero solution is referred to as the superradiation phase. The phase can transition from normal phase to superradiation phase, and the point of phase transition can be changed by adjusting the coupling intensity of the two cavity light fields. When the nonlinear photon-phonon interaction caused by radiation pressure is considered, the phase diagram of the system is expanded from the original two phase regions to three phase regions, including the coexistent normal phase and superradiation phase, the bistable superradiation phase, and the unstable vacuum macroscopic phase region, where the bistable superradiation phase is similar to the optical bistable phenomenon. At the same time, there is also a turning point curve, which overlaps with the phase transition point curve, indicating the existence of multiple quantum phase transitions in the system. These predictions can be detected by measuring the average number of photons. The coupled optomechanical cavity that we studied, when considering the coupling of the two-mode optical field and the atomic ensemble but no mechanical oscillator, reflects the interaction between the two-mode optical field and the atom, thus concluding that the transformation point is small and the quantum phase transition is easy to occur. When the coupling between the mechanical oscillator and the two-mode optical field is not considered, the interaction between the single-mode optical field and the atom is reflected, returning to the quantum phase transition of the Dicke model under rotating wave approximation.
This paper is concerned with quantum dynamics of a system coupled to a critical reservoir. In this context, we employ the Dicke model which is known to exhibit a superradiant quantum phase transition (QPT) and we allow one of the mirrors to move under a linear restoring force. The electromagnetic field couples to the movable mirror through radiation pressure just like in typical optomechanical setups. We show that, in the thermodynamical limit, the superradiant phase induces a classical driving force on the mirror without causing decoherence.
We present a detailed study to analyze the Dicke quantum phase transition within the thermodynamic limit for an optomechanically driven Bose—Einstein condensate in a cavity. The photodetection-based quantum optical measurements have been performed to study the dynamics and excitations of this optomechanical Dicke system. For this, we discuss the eigenvalue analysis, fluorescence spectrum and the homodyne spectrum of the system. It has been shown that the normal phase is negligibly affected by the mechanical mode of the mirror while it has a significant effect in the superradiant phase. We have observed that the eigenvalues and the spectra both exhibit distinct features that can be identified with the photonic, atomic and phononic branches. In the fluorescence spectra, we further observe an asymmetric coherent energy exchange between the three degrees of freedom of the system in the superradiant phase arising as a result of optomechanical interaction and Bloch—Siegert shift.
Motivated by experiments observing self-organization of cold atoms in optical cavities, we investigate the collective dynamics of the associated nonequilibrium Dicke model. The model displays a rich semiclassical phase diagram of long-time attractors including distinct superradiant fixed points, bistable and multistable coexistence phases, and regimes of persistent oscillations. We explore the intrinsic time scales for reaching these asymptotic states and discuss the implications for finite-duration experiments. On the basis of a semiclassical analysis of the effective Dicke model, we find that sweep measurements over 200 ms may be required in order to access the asymptotic regime. We briefly comment on the corrections that may arise due to quantum fluctuations and states outside of the effective two-level Dicke model description.
We mainly investigate Dicke phase transition at finite temperature in an optomechanical-atomic cavity by means of the functional path-integral approach. By the thermodynamic equilibrium equation, the mean photon number, the scaled atomic population, the mean phonon number, the average energy and the rich phase diagram are depicted in the existence of the nonlinear atom–photon interaction, the nonlinear photon–photon coupling strength, the pump–cavity detuning and the finite temperature. Beside Dicke phase transition from the normal phase (NP) to the superraidant phase (SP) at finite temperature, the collapse of the SP and the dynamically unstable state (DUS) are revealed showing the effects of the photon–phonon coupling strength ξ and nonlinear atom–photon interaction U. Meanwhile, a new phase transition occurs from the SP to the dynamically unstable state (DUS) at the turning point gt with the existence of ξ or U. The region of the SP can be completely eliminated by the mechanically and thermally stimulated photon-emission. The entropy and corresponding specific heats are presented to demonstrate the corresponding critical behavior at the phase transition point.
Abstract In this paper, we theoretically investigate Dicke phase transition at finite temperature in a hybrid optical-mechanical system. The thermodynamic equilibrium states are presented by means of the functional path-integral approach. We plot the mean photon number of the two cavities and the corresponding phase diagram showing the effects of the coupling strength between the two cavities, the nonlinear photon-phonon interaction strength, the finite temperature, the detuning of the two cavities. The coupling strength between the two cavities can make the phase boundary of the normal phase (NP) to the superradiant phase (SP) shift left with the increase of the atom-field coupling strength. The region of the SP is suppressed completely and the SP disappears completely with the increase of the coupling strength between the two cavities or the nonlinear photon-phonon interaction strength, finally just the NP and the dynamically unstable state (DUS) exist. The nonlinear photon-phonon coupling strength just affects the turning curve, but not the phase boundary. The unstable non-zero photon number state and the SP are coexistent, similar to the optical bistability.