Defect production due to time-dependent coupling to environment in the Lindblad equation

TL;DR

This paper investigates how defect production scales during Lindbladian quantum dynamics when the environmental coupling is ramped linearly in time, revealing a universal linear scaling with the drive speed unaffected by exceptional points.

Contribution

It extends previous non-Hermitian defect scaling studies by including the full Lindbladian evolution with quantum jumps and derives exact algebraic conditions for defect scaling.

Findings

Defect density scales linearly with the ramp speed of environmental coupling.

Exceptional points do not alter the linear defect scaling in Lindbladian dynamics.

Transient states exhibit exceptional points that influence defect production.

Abstract

Recently defect production was investigated during non-unitary dynamics due to non-Hermitian Hamiltonian. By ramping up the non-Hermitian coupling linearly in time through an exceptional point, defects are produced in much the same way as approaching a Hermitian critical point. A generalized Kibble--Zurek scaling accounted for the ensuing scaling of the defect density in terms of the speed of the drive and the corresponding critical exponents. Here we extend this setting by adding the recycling term and considering the full Lindbladian time evolution of the problem with quantum jumps. We find that by linearly ramping up the environmental coupling in time, and going beyond the steady-state solution of the Liouvillian, the defect density scales linearly with the speed of the drive for all cases. This scaling is unaffected by the presence of exceptional points of the Liouvillian, which can show up in the transient states. By using a variant of the adiabatic perturbation theory, the scaling of the defect density is determined exactly from a set of algebraic equations. Our study indicates the distinct sensitivity of the Lindbladian time evolution to exceptional points corresponding to steady states and transient states.