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arXiv:1008.0372 · Physical Review A

Probing the quantum phase transition in the Dicke model through mechanical vibrations

Jessica Paloma Chagas dos Santos, F. L. Semião, K. Furuya

Published Dec 1, 2010• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.82.063801

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Acta Physica Sinica•Jan 1, 2025•0 citations
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.
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.
We make a semi-classical steady state analysis of the influence of mirror motion on the quantum phase transition for an optomechanical Dicke model in the thermodynamic limit. An additional external mechanical pump is shown to modify the critical value of atom–photon coupling needed to observe the quantum phase transition. We further show how to choose the mechanical pump frequency and cavity–laser detuning to produce extremely cold condensates. The present system can be used as a quantum device to measure weak forces.
When an atomic ensemble is coupled with a cavity field governed by the well-known Dicke model , an important quantum phase transition (QPT) from the normal phase to the superradiant phase occurs, which was predicted more than 30 years ago. In this paper, both the atom-photon nonlinear interaction and the driving field are added to the Dicke's Hamiltonian. With the method of Holstein-Primafoff transformation, the ground state energy is given by the theoretical calculation, and the rich phase figures are presented. Meanwhile, these properties are observed experimentally. We mainly dicuss the effects of the atom-photon nonlinear interaction and the driving field on QPT.
In this work, we explore the superradiant behavior of two Dicke models mechanically coupled through a shared vibrating membrane. Using a variational mean-field approach, we analyze the system's critical behavior and derive analytical expressions that reveal a threshold for the mechanical coupling. Below this threshold, the system allows for higher atomic-radiation couplings before resonant damping occurs, thereby extending the superradiant region compared to a single-cavity optomechanical Dicke model. Additionally, we examine the behavior of relevant observables across all regions of the phase diagram. Our findings suggest that these observables provide a more accurate characterization of the system's critical behavior than the traditionally used coupling parameters.
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.
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.