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Physical Review A

Nonequilibrium quantum phase transition of Bose-Einstein condensates in an optical cavity

Ni Liu, Jiangdan Li, J.-Q. Liang

Published May 29, 2013• 20 citations
Publisher

Abstract

A link to the Dicke-model type quantum phase transition (QPT) is established by considering a time-dependent driving of the atom-field coupling and nonlinear atom-photon interaction as well, which make a notable impact on the ground-state properties. Motivated by the recent pioneer experiment [K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Nature (London) 464, 1301 (2010)], in this paper we demonstrate theoretically a rich multistable structure and nonequilibrium QPTs in terms of the Floquet theory and generalized rotating wave approximation. The positive nonlinear interaction does not lead to the change of the order-parameter curve except for a slight shift of the critical point. However, an additional full atomic population of the excited state is generated by the negative interaction resulting in the coexistence region of normal and superradiant phases. When both driving and nonlinear interaction exist the single order-parameter curve of the superradiant phase spreads out and a wide area of multiple local minima emerges in addition.

DOI
10.1103/physreva.87.053623

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A link to the Dicke-model type quantum phase transition (QPT) is established by considering a time-dependent driving of the atom-field coupling and nonlinear atom-photon interaction as well, which make a notable impact on the ground-state properties. Motivated by the recent pioneer experiment [K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Nature (London) 464, 1301 (2010)], in this paper we demonstrate theoretically a rich multistable structure and nonequilibrium QPTs in terms of the Floquet theory and generalized rotating wave approximation. The positive nonlinear interaction does not lead to the change of the order-parameter curve except for a slight shift of the critical point. However, an additional full atomic population of the excited state is generated by the negative interaction resulting in the coexistence region of normal and superradiant phases. When both driving and nonlinear interaction exist the single order-parameter curve of the superradiant phase spreads out and a wide area of multiple local minima emerges in addition.
In this paper we explore the rich structure of macroscopic many-particle quantum states for a Bose-Einstein condensate in an optical cavity with a tunable nonlinear atom-photon interaction [K. Baumann et al., Nature (London) 464, 1301 (2010)]. Population inversion, bistable normal phases, and the coexistence of normal-superradiant phases are revealed by adjusting the experimentally realizable interaction strength and pump-laser frequency. For the negative (effective) cavity frequency we observe, remarkably, an inverted quantum phase transition (QPT) from the superradiant to the normal phases with an increase in atom-field coupling, which is just opposite the QPT in the normal Dicke model. Bistable macroscopic states are derived analytically in terms of the spin-coherent-state variational method by taking into account both normal and inverted pseudospin states.
In this paper we reveal the rich ground-state properties induced by the strong nonlinear atom-photon interaction which has been found in the recent experiment about a Bose-Einstein condensate coupling with a high-finesse cavity [Nature (London) 464, 1301 (2010)]. Two detuning-dependent phase diagrams are revealed by investigating the experimentally measurable atomic population. In particular, two quantum phase transitions from the superradiant phase or the normal phase to a dynamically unstable phase are predicted in the blue detuning. Moreover, the three-phase coexistence points are found. It is also demonstrated that these predicted quantum phase transitions are the intrinsic transitions governed only by the second-order derivative of the ground-state energy. Finally, we also point out that the region involving coexistence of the superradiant phase and the normal phase previously predicted cannot happen in the ground state.
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 paper we investigate the finite-temperature properties of a Bose-Einstein condensate (BEC)-cavity system with a strong nonlinear atom-photon interaction by means of a functional path-integral approach. It is shown that the experimentally observed phase diagram [Baumann, Guerlin, Brennecke, and Esslinger, Nature (London) 464, 1301 (2010)] can be better explained in our finite-temperature theory. More importantly, we identify a new dynamical unstable phase in this experiment. By tuning various experimental parameters, we reveal some rich temperature-driven phase diagrams and, in particular, predict a four-phase coexistence point. Finally, we find analytically that the specific heat in the superradiant phase increases exponentially at lower temperatures. Moreover, it has a large jump at the temperature-driven critical point where the superradiant-normal phase transition occurs. As a result, we argue that the specific heat can serve as a powerful tool to probe the thermodynamic properties of the BEC-cavity system.
We investigate in this paper the macroscopic quantum states of multiple atoms in an optical cavity with non-Hermitian coupling motivated by recent experiments. The tunable atom-photon nonlinear interaction is included to demonstrate the variety of quantum phases in the realistic realization of Dicke phase transition with cold atoms. The energies of macroscopic quantum states are obtained in terms of the spin-coherent-state variational method, in which the nonunitary operator of the similarity transformation is used to diagonalize the effective non-Hermitian Hamiltonian, which is pseudo-Hermitian below the exceptional point (EP). The superradiant phase (SP) and related quantum phase transition (QPT) disappear completely for the non-Hermitian Dicke model (DM) because of imaginary coupling, which leads to instability of states with nonzero photons. The situation is dramatically changed by including the nonlinear atom-photon interaction generated by the pump field. It is found that the second EP emerges at a higher value of coupling. The spectrum is complex between the two EPs and real otherwise. Phase diagrams are obtained for red and blue cavity pump field detunings, showing explicitly the revival of the SP and QPT, respectively. However, the QPT from the SP to the normal phase with the increase of coupling is opposite to the transition in the normal DM. The critical property of the Berry phase indicates the first-order nature of the QPT, which again is different from the DM, where the QPT is known as the second order.
An extended Dicke model, which includes atom-atom interactions and a driving classical laser field, is established for a Bose-Einstein condensate inside an ultrahigh-finesse optical cavity. A feasible experimental setup with a strong atom-field coupling is proposed, where most parameters are easily controllable and thus the predicted a second-order superradiant-normal phase transition may be detected by measuring the ground-state atomic population. More intriguingly, second-order phase transition from the superradiant phase to the ``Mott'' phase is also revealed. In addition, a rich and exotic phase diagram is presented.