Universal quantum melting of quasiperiodic attractors in driven-dissipative cavities

Nonlinear classical mechanics has established countless intriguing and profound phenomena. These include limit tori defined by toroidal attractors that support quasiperiodic motion of at least two incommensurate frequencies. Here we address the question, whether and how such phenomena persist in open quantum systems. We develop a quantum description of limit tori within the Lindblad master-equation formalism for a system of two coupled driven-dissipative Kerr cavities. Using the spectral theory of the Liouvillian and the truncated Wigner approximation, we analyze the system across the quantum-to-classical transition. In the classical limit, we identify two pairs of purely imaginary Liouvillian eigenvalues, corresponding to persistent quasiperiodic modes of the limit torus. Quantum fluctuations induce small negative real parts to these eigenvalues, giving rise to finite lifetimes of these modes. The corresponding Liouvillian gaps vanish algebraically in the classical limit. This behavior signals a genuine continuous dynamical phase transition, marked by the spontaneous breaking of time-translational symmetry. Analysis of individual quantum trajectories reveals quantum-fluctuation-induced dephasing as the primary mechanism behind this "quantum melting" of the torus. We quantify this dephasing using a circular-variance-based order parameter, revealing universal scaling with both system size and time. These scaling laws are robust and independent of microscopic parameters. Our results establish the quantum melting of limit tori as a distinct non-equilibrium critical phenomenon and provide concrete signatures for experimental observation in trapped ions and superconducting circuits.