Self-organized Limit Cycles in Red-detuned Atom-cavity Systems

Abstract

Recent experimental advances in the field of cold-atom cavity QED provide a powerful tool for exploring non-equilibrium correlated quantum phenomena beyond conventional condensed-matter scenarios. We present the dynamical phase diagram of a driven Bose-Einstein condensate coupled with the light field of a cavity, with a transverse driving field red-detuned from atomic resonance. We identify regions in parameter space showing dynamical instabilities in the form of limit cycles, which evolve into chaotic behavior in the strong driving limit. Such limit cycles originate from the interplay between cavity dissipation and atom-induced resonance frequency shift, which modifies the phase of cavity mode and gives excessive negative feedback on the atomic density modulation, leading to instabilities of the superradiant scattering. We find interesting merging of the limit cycles related by a $Z_2$ symmetry, and identify a new type of limit cycle formed by purely atomic excitations. The effects of quantum fluctuations and atomic interactions are also investigated.

8 pages, 7 figures

References in corpus (22)

• The Quantum Internet
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Anderson Transitions
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Cold atoms in cavity-generated dynamical optical potentials
• Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays
• Supersolid formation in a quantum gas breaking continuous translational symmetry
• Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Dynamical phase transition in the open Dicke model
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Tunable-range, photon-mediated atomic interactions in multimode cavity QED
• Self-organization of a Bose-Einstein condensate in an optical cavity
• Fractional Quantum Hall State in Coupled Cavities
• Collective Dynamics of Bose--Einstein Condensates in Optical Cavities
• Emergent limit cycles and time crystal dynamics in an atom-cavity system
• Nonequilibrium Phase Transition of Interacting Bosons in an Intra-Cavity Optical Lattice
• REVIEW. Quantum optics with ultracold quantum gases: towards the full quantum regime of the light-matter interaction
• A Superradiant Topological Peierls Insulator inside an Optical Cavity
• Dissipation-induced instabilities of a spinor Bose-Einstein condensate inside an optical cavity
• Meissner-like effect for synthetic gauge field in multimode cavity QED
• The nonlinear semiclassical dynamics of the unbalanced, open Dicke model

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• Nonequilibrium Nonlinear Effects and Dynamical Boson Condensation in a Driven-Dissipative Wannier-Stark Lattice
• Phase transition, phase separation and mode softening of a two-component Bose-Einstein condensate in an optical cavity
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• Dynamical Tipping in a Quantum Limit Cycle