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arXiv:2201.08086 · Physical Review A

Superfluid–Mott-insulator quantum phase transition in a cavity optomagnonic system

Qian Cao, Lei Tan, Wu‐Ming Liu

Published Apr 5, 2022• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.105.043705

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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.
Abstract We investigated the superfluid Mott-insulator phase transition within an open coupled cavity optomagnonic array system. Based on the quasibosonic approach and employing perturbation approximation and mean-field theory, we obtain the time-dependent analytical superfluid order parameter. Our analysis revealed that dissipation induces decoherence within the system, while a strong magnon-cavity coupling enhances coherence significantly. Moreover, we explored the mechanisms by which increasing the magnon-cavity coupling strength drives the system towards the superfluid phase. The work holds significant guidance for the study of superfluidMott insulator phase transition under dissipative conditions, and providing a reliable reference for experimental implementation in open quantum systems.
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.
Abstract The superfluid-Mott insulator and ergodic-many body localization transitions based on a two dimension nonlinear cavity optomagnonic system are investigated, where a yttrium iron garnet (YIG) sphere is embedded at each site of a two-dimensional coupled cavity array. We demonstrate that introducing phonon-photon coupling enhances the system’s coherence in the presence of the YIG sphere’s Kerr nonlinearity. In contrast, the photonic Kerr nonlinearity more effectively stabilizes the Mott insulating phase than the magnonic nonlinearity. The underlying physical mechanism is clarified by calculating the system’s effective repulsive potential. For the ergodic–many body localization transition, we find that increasing the disorder strength drives the system from the ergodic to the many-body localized phase, while a higher chemical potential enlarges the ergodic region. This work provides a unified framework for characterizing quantum phase transitions in cavity optomagnonic systems and offers an experimentally feasible route for their realization, paving the way for exploring complex many-body phenomena in hybrid quantum platforms.
In this paper, we employ a new kind of quasi-boson approach and the mean field theory to study analytically the Hamiltonian of an array of cavities with a three-level atom embedded in each cavity in the process of two-photon resonant transition under the influence of a bosonic bath. The superfluid order parameter of the system is obtained analytically and then analyzed numerically to investigate the effects of dissipation on the quantum phase transition from the superfluid to the Mott-insulator phase. It is shown that when the two-photon resonance is achieved one can have the superfluid phase at (ZJ/)= (ZJ/)c' 0.34 in the related ideal case. Furthermore, the system while in the two-photon resonant process has a larger dissipation rate as compared with that in the one-photon resonant process, thus leading to the suppression of the long-range coherence time and enhancement of the critical hopping rate for restoring coherence.
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 impact that the environment has on the quantum phase transition of light in the Dicke-Bose-Hubbard model is investigated. Based on the quasibosonic approach, mean-field theory, and perturbation theory, the formulation of the Hamiltonian, the eigenenergies, and the superfluid order parameter are obtained analytically. Compared with the ideal cases, the order parameter of the system evolves with time as the photons naturally decay in their environment. When the system starts with the superfluid state, the dissipation makes the photons more likely to localize, and a greater hopping energy of photons is required to restore the long-range phase coherence of the localized state of the system. Furthermore, the Mott lobes depend crucially on the numbers of atoms and photons (which disappear) of each site, and the system tends to be classical with the number of atoms increasing; however, the atomic number is far lower than that expected under ideal circumstances. As there is an inevitable interaction between the coupled-cavity array and its surrounding environment in the actual experiments, the system is intrinsically dissipative. The results obtained here provide a more realistic image for characterizing the dissipative nature of quantum phase transitions in lossy platforms, which will offer valuable insight into quantum simulation of a dissipative system and which are helpful in guiding experimentalists in open quantum systems.