Reaction-diffusive dynamics of number-conserving dissipative quantum state preparation

Abstract

The use of dissipation for the controlled creation of nontrivial quantum many-body correlated states is of much fundamental and practical interest. What is the result of imposing number conservation, which, in closed system, gives rise to diffusive spreading? We investigate this question for a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one band and to populate the other, which had been introduced before for the dissipative stabilization of topological states. Going beyond the mean-field treatment of the dissipative dynamics, we demonstrate the emergence of a diffusive regime for the particle and hole density modes at intermediate length- and time-scales, which, interestingly, can only be excited in nonlinear response to external fields. We also identify processes that limit the diffusive behavior of this mode at the longest length- and time-scales. Strikingly, we find that these processes lead to a reaction-diffusion dynamics governed by the Fisher-Kolmogorov-Petrovsky-Piskunov equation, making the designed dark state unstable towards a state with a finite particle and hole density.

25 pages, 11 figures

References in corpus (9)

• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Dissipative preparation of Chern insulators
• Induced self-stabilization in fractional quantum Hall states of light
• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
• Lindblad master equation approach to the topological phase transition in the disordered Su-Schrieffer-Heeger model
• Generation and spectroscopic signatures of a fractional quantum Hall liquid of photons in an incoherently pumped optical cavity
• Hydrodynamic theory of scrambling in chaotic long-range interacting systems

Cited by in corpus (9)

• Theory of free fermions under random projective measurements
• Universality in driven open quantum matter
• Large-scale universality in quantum reaction-diffusion from Keldysh field theory
• Diffusive modes of two-band fermions under number-conserving dissipative dynamics
• Population Dynamics of Schrödinger Cats
• Kinetics of Quantum Reaction-Diffusion systems
• Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Driven-Dissipative Dynamics of Ultracold Atoms Trapped in an Array of Harmonic Potentials
• Diffusion in quantum state preparation: From passive cooling to system-bath engineering