Defect production due to time-dependent coupling to environment in the Lindblad equation
arXiv:2101.11334 · doi:10.1103/PhysRevB.103.205153
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.
10 pages, 6 figures
References in corpus (14)
- The physics of exceptional points
- Quantum trajectories and open many-body quantum systems
- High-fidelity projective readout of a solid-state spin quantum register
- Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
- Observation of quantum jumps in a superconducting artificial atom
- Quantum back-action of variable-strength measurement
- Excited state quantum phase transitions in many-body systems
- Detecting topological invariants in nonunitary discrete-time quantum walks
- Adiabatic approximation in open quantum systems
- Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
- Adiabatic dynamics in open quantum critical many-body systems
- Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions
- Universal anti-Kibble-Zurek scaling in fully-connected systems
- Non-Hermitian Kibble-Zurek mechanism with tunable complexity in single-photon interferometry