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.

Highlights

  • Using the concept of phase transitions, a great variety of different physical systems can be classified in terms of their emergent collective behaviour [1,2,3]

  • 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

  • The order of this nonequilibrium quantum phase transition can be changed by tuning the transition frequency

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Summary

INTRODUCTION

Using the concept of phase transitions, a great variety of different physical systems can be classified in terms of their emergent collective behaviour [1,2,3]. We show that the internal state coupling scheme allows for a NQPT, whose order can be readily tuned by changing the atomic transition frequency. Both a first- and a second-order NQPT can be realized in the same physical set-up by only changing a directly accessible control parameter. We show this for the membrane-in-the-middle-setup [23], where the adiabatic elimination of the light field yields an effective coupling between the membrane and the transition between two states in the atom gas, see Fig. 1.

MODEL AND ADIABATIC ELIMINATION OF THE LIGHT FIELD
Linearized Coupling of the Membrane and the Light Field
Adiabatic Elimination of the Light Field and Effective Equations of Motion
TUNING THE ORDER OF THE QUANTUM PHASE TRANSITION
Single Mode Approximation and Cumulant Expansion
Nonequilibrium Potential and Steady-State Configuration
Landau Expansion of the Nonequilibrium Potential
Hysteresis in the First-Order Regime
SPECTRUM OF COLLECTIVE EXCITATIONS AND ENTANGLEMENT
Collective Excitations and Atom-Membrane Entanglement
Excitation Spectrum Along the Hysteresis
EXPERIMENTAL REALIZATION
CONCLUSION
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