Dynamical phases of a BEC in a bad optical cavity at optomechanical resonance

Abstract

We study the emergence of dynamical phases of a Bose-Einstein condensate that is optomechanically coupled to a dissipative cavity mode and transversally driven by a laser. We focus on the regime close to the optomechanical resonance, where the atoms' refractive index shifts the cavity into resonance, assuming fast cavity relaxation. We derive an effective model for the atomic motion, where the cavity degrees of freedom are eliminated using perturbation theory in the atom-cavity coupling and benchmark its predictions using numerical simulations based on the full model. Away from the optomechanical resonance, perturbation theory in the lowest order (adiabatic elimination) reliably describes the dynamics and predicts chaotic phases with unstable oscillations. Interestingly, the dynamics close to the optomechanical resonance are qualitatively captured only by including the corrections to next order (non-adiabatic corrections). In this regime we find limit cycle phases that describe stable oscillations of the density with a well defined frequency. We further show that such limit cycle solutions are metastable configurations of the adiabatic model. Our work sheds light on the mechanisms that are required to observe dynamical phases and predict their existence in atom-cavity systems where a substantial timescale separation is present.

11 pages, 5 figures

References in corpus (25)

• Cold atoms in cavity-generated dynamical optical potentials
• Long-range interacting quantum systems
• Cavity Nonlinear Optics at Low Photon Numbers from Collective Atomic Motion
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Observation of a continuous time crystal
• Self-organization of a Bose-Einstein condensate in an optical cavity
• Mott insulator states of ultracold atoms in optical resonators
• Bose-glass phases of ultracold atoms due to cavity backaction
• Self-oscillating pump in a topological dissipative atom-cavity system
• Exact solution of a boundary time-crystal phase transition: time-translation symmetry breaking and non-Markovian dynamics of correlations
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Prethermalization of atoms due to photon-mediated long-range interactions
• Density-wave ordering in a unitary Fermi gas with photon-mediated interactions
• The nonlinear semiclassical dynamics of the unbalanced, open Dicke model
• Entanglement and replica symmetry breaking in a driven-dissipative quantum spin glass
• Dissipation-engineered family of nearly dark states in many-body cavity-atom systems
• Mode softening in time-crystalline transitions of open quantum systems
• Structural transitions of ion strings in quantum potentials
• Surprises from quenches in long-range interacting systems: Temperature inversion and cooling
• Self-organized Limit Cycles in Red-detuned Atom-cavity Systems
• Realizing limit cycles in dissipative bosonic systems
• Superradiant optomechanical phases of cold atomic gases in optical resonators
• Observation of a phase transition from a continuous to a discrete time crystal
• Dissipative Dicke time crystals: an atoms' point of view
• Dynamics of spin-momentum entanglement from superradiant phase transitions