Dissipative Quantum Chaos as a property of Individual Stochastic Quantum Trajectories

The study of chaos and integrability in open quantum many-body systems is central in many research areas, from high-energy physics to quantum optics, from quantum technologies to condensed matter. To date, dissipative quantum chaos is understood on the basis of the universal predictions of non-Hermitian random matrix theory: in presence of chaos, the generator of the dissipative dynamics (the so-called Liouvillian superoperator) behaves as a large random matrix. In our work, we introduce a novel definition of dissipative quantum chaos based on the stochastic unraveling of the Lindblad master equation. We regard an open quantum system as exhibiting chaotic behavior if its Liouvillian spectral structure is described by random matrix theory and if this structure significantly impacts individual stochastic realizations of the dynamics, commonly referred to as quantum trajectories. We apply our theoretical framework to two paradigmatic bosonic models: the driven-dissipative Bose-Hubbard model in one dimension and the circuit quantum electrodynamics architecture for the dispersive readout of a superconducting transmon qubit. We clarify how dissipative quantum chaos can impact the properties of quantum technologies.