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Journal of the Optical Society of America B

Simulating the Bose–Hubbard model with a one-dimensional cavity optomechanical system

Da‐Wei Wang, Shi‐Lei Chao, Chengsong Zhao, Zhen Yang, Ling Zhou

Published Nov 1, 2021• 0 citations
Publisher

Abstract

We propose a scheme to simulate a one-dimensional Bose–Hubbard model with a coupled cavity optomechanical system. By eliminating the cavity field under the condition of large detuning, an effective Bose–Hubbard model can be achieved. By adiabatically adjusting the classical pumping, we show that the effective Hamiltonian can fully explain transitions from the Mott-insulating phase to the superfluid phase. In addition, we show that the system allows the quantum state transfer after including the dissipation of the oscillators.

DOI
10.1364/josab.439497

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We propose a scheme to simulate a one-dimensional Bose–Hubbard model with a coupled cavity optomechanical system. By eliminating the cavity field under the condition of large detuning, an effective Bose–Hubbard model can be achieved. By adiabatically adjusting the classical pumping, we show that the effective Hamiltonian can fully explain transitions from the Mott-insulating phase to the superfluid phase. In addition, we show that the system allows the quantum state transfer after including the dissipation of the oscillators.
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An array of coupled cavities, each of which contains an N four-level atom, is investigated. When cavity fields dispersively interact with the atoms, an effective Bose—Hubbard model can be achieved. By numerically comparing the full Hamiltonian with the effective one, we find that within the parameters region, the effective Hamiltonian can completely account for the Mott-insulator as well as the phase transition from the similar Mott-insulator to superfluid. Through jointly adjusting the classical Rabi frequency and the detuning, the nonlinearity can be improved.
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.
In a recent experiment [A. Vochezer, T. Kampschulte, K. Hammerer, and P. Treutlein, Phys. Rev. Lett. 120, 073602 (2018)], a novel kind of hybrid atom-optomechanical system has been realized by coupling atoms in a lattice to a membrane. While such a system promises a viable contender in the competitive field of simulating nonequilibrium many-body physics, its complete steady-state phase diagram is still lacking. Here we study the phase diagram of this hybrid system based on an atomic Bose-Hubbard model coupled to a quantum harmonic oscillator. We take both the expectation value of the bosonic operator and the mechanical motion of the membrane as order parameters and thereby identify four different quantum phases. Importantly, we find the atomic gas in the steady state of such a nonequilibrium setting undergoes a superfluid--Mott-insulator transition when the atom-membrane coupling is tuned to increase. Such a steady-state phase transition can be seen as the nonequilibrium counterpart of the conventional superfluid--Mott-insulator transition in the ground state of the Bose-Hubbard model. Further, no matter which phase the quantum gas is in, the mechanic motion of the membrane exhibits a transition from an incoherent vibration to a coherent one when the atom-membrane coupling increases, agreeing with the experimental observations. Our present study provides a simple way to study nonequilibrium many-body physics that is complementary to ongoing experiments on the hybrid atomic and optomechanical systems.
We describe a scheme that allows for the transfer of a quantum state between a trapped atomic Bose condensate and an optomechanical end mirror mediated by a cavity field. Coupling between the mirror and the cold gas arises from the fact that the cavity field can produce density oscillations in the gas which in turn acts as an internal Bragg mirror for the field. After adiabatic elimination of the cavity field we find that the coherent dynamics of the atomic condensate--mirror hybrid system is described by an effective state transfer beam-splitter Hamiltonian. The state transfer fidelity is limited principally by the quantum noise associated with the intracavity field.
We study the many-body state of ultracold bosons in a bistable optical lattice potential in an optomechanical resonator in the weak-coupling limit. Interesting physics arises as a result of bistability and discontinuous jumps in the cavity field. Of particular interest is the situation where the optical cavity is engineered so that a single input beam can result in two radically different stable ground states for the intracavity gas: superfluid and Mott insulator. Furthermore, the system we describe can be used as an adjustable template for investigating the coupling between cavity fields, nanomechanical systems operating in the quantum regime, and ultracold atomic gases.