Emergent limit cycles and time crystal dynamics in an atom-cavity system

Abstract

We propose an experimental realization of a time crystal using an atomic Bose-Einstein condensate in a high finesse optical cavity pumped with laser light detuned to the blue side of the relevant atomic resonance. By mapping out the dynamical phase diagram, we identify regions in parameter space showing stable limit cycle dynamics. Since the model describing the system is time-independent, the emergence of a limit cycle phase indicates the breaking of continuous time translation symmetry. Employing a semiclassical analysis to demonstrate the robustness of the limit cycles against perturbations and quantum fluctuations, we establish the emergence of a time crystal.

6 pages, 6 figures

References in corpus (8)

• Quantum fluids of light
• Cold atoms in cavity-generated dynamical optical potentials
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Absence of Quantum Time Crystals
• Dynamical phase transition in the open Dicke model
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Self-organization of a Bose-Einstein condensate in an optical cavity
• Limit cycle phase in driven-dissipative spin systems

Cited by in corpus (4)

• Classical approaches to prethermal discrete time crystals in one, two, and three dimensions
• Dissipative time crystal in an atom-cavity system: Influence of trap and competing interactions
• Superradiant optomechanical phases of cold atomic gases in optical resonators
• Universality in Non-Equilibrium Quantum Systems