Torus Bifurcation of a Dissipative Time Crystal

Area of Science:

• Quantum physics
• Condensed matter physics
• Nonlinear dynamics

Background:

• Dissipative continuous time crystals exhibit unique dynamical phases.
• Understanding transitions between different dynamical states is crucial in quantum many-body systems.

Purpose of the Study:

• To experimentally observe and theoretically analyze the instability of a dissipative continuous time crystal.
• To investigate the underlying mechanism of the transition to a new time crystalline state with dual oscillation frequencies.

Main Methods:

• Utilized a Bose-Einstein condensate coupled to an optical cavity with a transverse pump laser.
• Employed mean-field approximation and Floquet analysis for theoretical confirmation.
• Applied Takens' embedding theorem to intracavity photon dynamics for experimental reconstruction.

Main Results:

• Observed an instability in the dissipative continuous time crystal.
• Identified a transition to a time crystalline state with two prominent oscillation frequencies.
• Theoretically confirmed the transition as a torus bifurcation between limit cycle and limit torus attractors.

Conclusions:

• The study demonstrates a novel transition in a quantum gas system.
• Confirms the torus bifurcation as the underlying mechanism for this many-body system transition.
• Provides experimental validation for theoretical models of complex quantum dynamics.