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

TL;DR

This paper explores how number conservation influences dissipative quantum state preparation, revealing a reaction-diffusion regime governed by the Fisher-Kolmogorov-Petrovsky-Piskunov equation, which affects the stability of the target state.

Contribution

It demonstrates the emergence of reaction-diffusion dynamics in dissipative quantum systems with number conservation, extending beyond mean-field analysis and identifying long-term limiting processes.

Findings

Diffusive regime for particle and hole densities at intermediate scales.

Reaction-diffusion dynamics described by the Fisher-Kolmogorov-Petrovsky-Piskunov equation.

Instability of the dark state due to long-time reaction processes.

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.