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arXiv:1301.1869 · Physical Review A

First-order superfluid–Mott-insulator transition for quantum-optical switching in cavity-QED arrays with two cavity modes

Kenji Kamide, Makoto Yamaguchi, T. Kimura, Tetsuo Ogawa

Published May 29, 2013• 11 citations
arXivHTMLPDF

Abstract

We theoretically investigated the ground states of coupled arrays of cavity-quantum-electrodynamical (cavity-QED) systems in the presence of two photon modes. Within the Gutzwiller-type variational approach, we found the first-order quantum phase transition between Mott-insulating and superfluid phases as well as the conventional second-order one. The first-order phase transition was found only for specific types of emitter models, and its physical origin is clarified based on the analytic arguments which are allowed in the perturbative and semiclassical limits. The first-order transition of the correlated photons is accompanied with discontinuous change in the emitter states, not only with the appearance of intercavity coherence in the superfluid phase. We also discuss the condition for the first-order transition to occur, which can lead to a strategy for future design of quantum-optical switching devices with cavity-QED arrays.

DOI
10.1103/physreva.87.053842

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We theoretically investigated the ground states of coupled arrays of cavity-quantum-electrodynamical (cavity-QED) systems in the presence of two photon modes. Within the Gutzwiller-type variational approach, we found the first-order quantum phase transition between Mott-insulating and superfluid phases as well as the conventional second-order one. The first-order phase transition was found only for specific types of emitter models, and its physical origin is clarified based on the analytic arguments which are allowed in the perturbative and semiclassical limits. The first-order transition of the correlated photons is accompanied with discontinuous change in the emitter states, not only with the appearance of intercavity coherence in the superfluid phase. We also discuss the condition for the first-order transition to occur, which can lead to a strategy for future design of quantum-optical switching devices with cavity-QED arrays.
In this paper we construct a type of cavity array, in each cavity of which multiple two-level atoms interact with two independent photon modes. This system can be totally governed by a two-mode Dicke-lattice model, which includes all of the counter-rotating terms and therefore works well in the ultrastrong coupling regime achieved in recent experiments. Attributed to its special atom-photon coupling scheme, this model supports a global conserved excitation and a continuous U(1) symmetry, rather than the discrete Z2{Z}_{2}Z2​ symmetry in the standard single-mode Dicke-lattice model. This distinct change of symmetry via adding an extra photon mode strongly impacts the nature of photon localization and delocalization behavior. Specifically, the atom-photon interaction features stable Mott-lobe structures of photons and a second-order superfluid--Mott-insulator quantum phase transition, which share similarities with the Jaynes-Cummings-lattice and Bose-Hubbard models. More interestingly, the Mott-lobe structures predicted here depend crucially on the atom number of each site. We also show that our model can be mapped into a continuous XXXXXX spin model. Finally, we propose a scheme to implement the introduced cavity array in circuit quantum electrodynamics. This work broadens our understanding of strongly correlated photons.
The emerging hybrid cavity optomagnonic system is a very promising quantum information processing platform for its strong or ultrastrong photon-magnon interaction on the scale of micrometers in the experiment. In this paper, the superfluid--Mott-insulator quantum phase transition in a two-dimensional cavity optomagnonic array system has been studied based on this characteristic. The analytical solution of the critical hopping rate is obtained by the mean-field approach, second-order perturbation theory, and Landau second-order phase transition theory. The numerical results show that the increasing coupling strength and the positive detunings of the photon and the magnon favor the coherence and then the stable areas of Mott lobes are compressed correspondingly. Moreover, the analytical results agree with the numerical ones when the total excitation number is lower. Finally, an effective repulsive potential is constructed to exhibit the corresponding mechanism. The results obtained here provide an experimentally feasible scheme for characterizing the quantum phase transitions in a cavity optomagnonic array system, which will offer valuable insight for quantum simulations.
The superfluid to Mott insulator transition and the superradiant transition are textbook examples of quantum phase transition and coherent quantum optics, respectively. Recent experiments in ETH and Hamburg have succeeded in loading degenerate bosonic atomic gases in optical lattices inside a cavity, which enables the first experimental study of the interplay between these two transitions. In this Rapid Communication we present the theoretical phase diagram for the ETH Zurich experimental setup, and determine the phase boundaries and the orders of the phase transitions between the normal superfluid phase, the superfluid with superradiant light, the normal Mott insulator, and the Mott insulator with superradiant light. We find that in contrast to the second-order superradiant transition in a weakly interacting Bose condensate, strong correlations in the superfluid nearby a Mott transition can render the superradiant transition to a first-order one. Our results will stimulate further experimental studies of interactions between cavity light and strongly interacting quantum matter.
We study the features of superfluid and Mott-insulator states in a two-dimensional array of cavities with a two-level atom embedded in each cavity which is strongly coupled to the cavity field and immersed in a bosonic bath. Employing a different quasiboson approach, we show analytically how the dissipation and decoherence influence the quantum phase transitions from two aspects and find a localized tendency. For the superfluid state, a dynamical instability will lead to a sweeping to a localized state of photons. For the Mott-insulator state, a dissipation-induced fluctuation will suppress the restoring of long-range phase coherence driven by interaction.
Abstract A two-dimensional hybrid cavity optomechanical array formed by an optomechanical cavity embedded with a two-level atom in each site is introduced to discuss the superfluid–Mott insulator quantum phase transition of light. On account of the optomechanical coupling effects stemmed from the coupled movable oscillator, the energy spectrum of the system changes, and an effective on-site repulsive interaction is reformed by modulating the optomechanically controlled parameters. By adjusting the detuning, an intersection between different critical chemical potentials can be found together with a disappearance of certain Mott lobes physically. The pronounced optomechanical coupling strength is in favor of the Mott insulator phase due to the enhanced effective on-site interactions. Additionally, the Kerr-nonlinearity reduces the average excitation of the high Mott insulator state and diminishes the superfluid regime. The results obtained here provide a novel image for characterizing the quantum phase transitions in optomechanical array systems, which will offer valuable insight for quantum simulations.