Correspondence between dissipative phase transitions of light and time crystals

TL;DR

This paper predicts a novel dissipative time crystal in an optical system, linking it to a second-order phase transition through Liouvillian symmetry analysis, and demonstrating their equivalence in different frames.

Contribution

It introduces the concept of a dissipative time crystal generated by an incoherently driven nonlinear optical oscillator, connecting it to phase transitions via Liouvillian analysis.

Findings

A second-order dissipative phase transition occurs in the rotating frame.

A boundary (dissipative) time crystal emerges in the laboratory frame.

The phenomena are related through the Liouvillian spectrum and symmetries.

Abstract

We predict the emergence of a time crystal generated by an incoherently driven and dissipative nonlinear optical oscillator, where the nonlinearity also comes from dissipation. We show that a second-order dissipative phase transition of light occurs in the frame rotating at the cavity frequency, while a boundary (dissipative) time crystal emerges in the laboratory frame. We relate these two phenomena by using the Liouvillian superoperator associated with the Lindblad master equation and its symmetries. These results connect the emergence of a second-order dissipative phase transition and a dissipative time crystal in the thermodynamic limit, allowing to interpret them as the same phenomenon in terms of the Liouvillian spectrum, but just in different frames.