Universal quantum melting of quasiperiodic attractors in driven-dissipative cavities

TL;DR

This paper investigates how quantum fluctuations cause the melting of quasiperiodic attractors in driven-dissipative cavities, revealing a universal quantum critical phenomenon with experimental implications.

Contribution

It introduces a novel analysis of quantum melting of classical quasiperiodic structures using Liouvillian spectral theory and the truncated Wigner approximation.

Findings

Quantum fluctuations induce finite lifetimes of quasiperiodic modes.

Liouvillian gaps vanish algebraically in the classical limit, indicating a critical crossover.

Universal scaling laws are observed in system size and time.

Abstract

Nonlinear classical mechanics has established rich phenomena. These include limit tori defined by toroidal attractors supporting quasiperiodic motion with incommensurate frequencies. We study the fate of such structures in open quantum systems using two coupled driven-dissipative Kerr cavities modeled via the Lindblad master equation. Combining Liouvillian spectral theory with the truncated Wigner approximation, we characterize the quantum-to-classical crossover. In the classical limit, two pairs of purely imaginary Liouvillian eigenvalues signal persistent quasiperiodic modes. Quantum fluctuations induce small negative real parts to these eigenvalues, giving rise to finite lifetimes and leading to the quantum melting of the torus. The associated Liouvillian gaps vanish algebraically in the classical limit, indicating a dynamical critical crossover with spontaneous breaking of time-translational symmetry. Quantum trajectory analysis reveals that this melting is driven by fluctuation-induced dephasing. Using a circular-variance-based order parameter, we uncover universal scaling in system size and time. These results establish quantum melting of limit tori as a distinct and robust non-equilibrium critical phenomenon, with clear experimental signatures in trapped ions and superconducting circuits.