Manifestations of flow topology in a quantum driven-dissipative system

TL;DR

This paper explores how flow topology in phase space influences the stability and transitions of non-equilibrium states in a quantum driven-dissipative system, revealing topological signatures that persist in quantum dynamics.

Contribution

It demonstrates that classical flow topologies have quantum counterparts in driven-dissipative systems, revealing new phases and topological signatures beyond traditional Liouvillian gap analysis.

Findings

Quantum dynamics retain classical topological features

Identification of new quantum phases via flow topology

Signatures detectable through quantum state tomography

Abstract

In driven-dissipative bosonic systems, the interplay between coherent driving, inter-particle interactions and dissipation leads to a rich variety of non-equilibrium stationary states (NESS). In the semiclassical limit, the flow topology of phase-space dynamics governs the stability and structure of these dynamical phases. Consequently, topological transitions occur when the number of NESS, their chirality, or their connectivity changes, reflecting global reorganization in the system's dynamical phase-space landscape. Here, we study the corresponding topological signatures in a driven-dissipative quantum Kerr oscillator. Employing a Lindblad master equation and quantum trajectory methods, we reveal that quantum dynamics retain key topological features of the underlying classical flows, with clear signatures accessible via quantum state tomography and linear response. In this manner, we predict new phases that are not signaled by Liouvillian gap closing, thereby generalizing the conventional criteria for diagnosing phase transitions. Our findings position phase-space flow topology as a powerful tool to identify and control robust quantum phases, enabling advances in error correction and sensing.