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arXiv:1905.03411 · Physical Review A

Nonequilibrium quantum phase transition in a spinor quantum gas in a lattice coupled to a membrane

Xingran Xu, Zhang Zhi-dong, Zhaoxin Liang

Published Nov 19, 2019• 4 citations
arXivHTMLPDF

Abstract

Recently, a novel kind of hybrid atom-optomechanical system, consisting of atoms in a lattice coupled to a membrane, has been experimentally realized [A. Vochezer et al., Phys. Rev. Lett. 120, 073602 (2018)], which promises a viable contender in the competitive field of simulating nonequilibrium many-body physics. Here we are motivated to investigate a spinor Bose gas coupled to a vibrational mode of a nanomembrane, focusing on analyzing the role of the spinor degrees of freedom therein. Through an adiabatic elimination of the degrees of freedom of the quantum oscillator, we derive an effective Hamiltonian which reveals a competition between the force localizing the atoms and the membrane displacement. We analyze the dynamical stability of the steady state using the Bogoliubov--de Gennes approach and derive the stationary phase diagram in the parameter space. Then, we investigate the first-order nonequilibrium quantum phase transition (NQPT) from a localized symmetric state of the atom cloud to a shifted symmetry-broken state, characterized by the occurrence of a hysteresis. Moreover we present a detailed analysis of the effects of the spin degree of freedom on NQPT. Our work presents a simple way to study the effects of the spinor degree of freedom on the nonequilibrium nonlinear phenomena that is complementary to ongoing experiments on the hybrid atom-optomechanical system.

DOI
10.1103/physreva.100.053616

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Recently, a novel kind of hybrid atom-optomechanical system, consisting of atoms in a lattice coupled to a membrane, has been experimentally realized [A. Vochezer et al., Phys. Rev. Lett. 120, 073602 (2018)], which promises a viable contender in the competitive field of simulating nonequilibrium many-body physics. Here we are motivated to investigate a spinor Bose gas coupled to a vibrational mode of a nanomembrane, focusing on analyzing the role of the spinor degrees of freedom therein. Through an adiabatic elimination of the degrees of freedom of the quantum oscillator, we derive an effective Hamiltonian which reveals a competition between the force localizing the atoms and the membrane displacement. We analyze the dynamical stability of the steady state using the Bogoliubov--de Gennes approach and derive the stationary phase diagram in the parameter space. Then, we investigate the first-order nonequilibrium quantum phase transition (NQPT) from a localized symmetric state of the atom cloud to a shifted symmetry-broken state, characterized by the occurrence of a hysteresis. Moreover we present a detailed analysis of the effects of the spin degree of freedom on NQPT. Our work presents a simple way to study the effects of the spinor degree of freedom on the nonequilibrium nonlinear phenomena that is complementary to ongoing experiments on the hybrid atom-optomechanical system.
We consider a hybrid quantum many-body system formed by a vibrational mode of a nanomembrane, which interacts optomechanically with light in a cavity, and an ultracold atom gas in the optical lattice of the out-coupled light. The adiabatic elimination of the light field yields an effective Hamiltonian which reveals a competition between the force localizing the atoms and the membrane displacement. At a critical atom-membrane interaction, we find a nonequilibrium quantum phase transition from a localized symmetric state of the atom cloud to a shifted symmetry-broken state, the energy of the lowest collective excitation vanishes, and a strong atom-membrane entanglement arises. The effect occurs when the atoms and the membrane are nonresonantly coupled.
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.
Abstract We show that a hybrid atom-optomechanical quantum many-body system with two internal atom states undergoes both first- and second-order nonequilibrium quantum phase transitions (NQPTs). A nanomembrane is placed in a pumped optical cavity, whose outcoupled light forms a lattice for an ultracold Bose gas. By changing the pump strength, the effective membrane-atom coupling can be tuned. Above a critical intensity, a symmetry-broken phase emerges which is characterized by a sizeable occupation of the high-energy internal states and a displaced membrane. The order of this NQPT can be changed by tuning the transition frequency. For a symmetric coupling, the transition is continuous below a certain transition frequency and discontinuous above. For an asymmetric coupling, a first-order phase transition occurs.
We report on a nonequilibrium quantum phase transition (NQPT) in a hybrid quantum many-body system consisting of a vibrational mode of a damped nanomembrane interacting optomechanically with a cavity, whose output light couples to two internal states of an ultracold Bose gas held in an external quasi-one-dimensional box potential. For small effective membrane-atom couplings, the system is in a homogeneous Bose-Einstein condensate (BEC) steady state, with no membrane displacement. Depending on the transition frequency between the two internal atomic states, either one or both internal states are occupied. By increasing the atom-membrane couplings, the system transitions to a symmetry-broken self-organized BEC phase, which is characterized by a considerably displaced membrane steady-state and density-wave-like BEC profiles. This NQPT can be both discontinuous and continuous for a certain interval of transition frequencies and is purely discontinuous outside of it. Published by the American Physical Society 2024
Ultracold atomic gases loaded into optical cavities constitute one of the most versatile platforms for the study of out-of-equilibrium dynamics and quantum simulation of many- body systems. In this thesis, we explore these two possibilities, motivated by current state-of-the-art atom-cavity experiments, uncovering novel phenomena and opening up new theoretical and experimental avenues into the intriguing world of quantum many- body physics. First, we study a gas of ultracold atoms coupled to three optical resonators. We show that the inherent Z2 symmetries, associated with each atom-cavity coupling, can be combined into a global SO(3) rotational symmetry which can be spontaneously broken. We determine the phase diagram of the system, which shows the emergence and breaking of the continuous symmetries and displays first- and second-order phase transitions. We argue that by coupling the atoms equally to n different modes, it will in general be possible to generate a global SO(n) symmetry. Second, we investigate the dynamics of a spinor BEC inside an optical cavity. We focus on a two-component Dicke model with complex light-matter couplings, accounting for photon losses. We compute the steady-state phase diagram and find dynamical in- stabilities in the form of limit cycles, heralded by the presence of exceptional points and level attraction. We show that the instabilities are induced by dissipative processes that generate nonreciprocal couplings between the two collective spins. Lastly, we explore the dynamics of a BEC inside an optical cavity in the presence of an optical lattice. We derive an effective master equation by adiabatically eliminating the cavity field. In the bad-cavity regime, we find an infinite-temperature steady state, but with relaxation dynamics that can be highly nontrivial. For small hopping, the interplay between dissipation and strong interactions leads to an algebraic relaxation of the system, whereas for large hopping, the approach to the steady state is exponential. In the good- cavity regime, we show that the system allows for optical pumping between momentum modes, enabling cavity cooling.
We present an experimental study on nonequilibrium dynamics of a spinor condensate after it is quenched across a superfluid to Mott insulator (MI) phase transition in cubic lattices. Intricate dynamics consisting of spin-mixing oscillations at multiple frequencies are observed in time evolutions of the spinor condensate localized in deep lattices after the quantum quench. Similar spin dynamics also appear after spinor gases in the MI phase are suddenly moved away from their ground states via quenching magnetic fields. We confirm these observed spectra of spin-mixing dynamics can be utilized to reveal atom number distributions of an inhomogeneous system, and to study transitions from two-body to many-body dynamics. Our data also imply the nonequilibrium dynamics depend weakly on the quench speed but strongly on the lattice potential. This enables precise measurements of the spin-dependent interaction, a key parameter determining the spinor physics.