Lindbladian dynamics with loss of quantum jumps

TL;DR

This paper introduces a non-linear Lindblad master equation to analyze the effects of partial quantum jump elimination, revealing new dynamics such as the postselected skin effect and providing insights into non-Hermitian quantum systems.

Contribution

It derives a non-linear Lindblad equation from quantum trajectories, classifies jump-reduction dynamics, and demonstrates the postselected skin effect with unique steady-state properties.

Findings

Identification of trivial and nontrivial classes of jump-reduction dynamics

Discovery of the postselected skin effect with scale-invariant steady state

NLME effectively captures entanglement and skin effects in non-Hermitian systems

Abstract

The Lindblad master equation (LME) describing the Markovian dynamics of the quantum open system can be understood as the evolution of the effective non-Hermitian Hamiltonian balanced with random quantum jumps. Here we investigate the balance-breaking dynamics by partly eliminating jumps from postselection experiments. To describe this dynamics, a non-linear Lindblad master equation (NLME) is derived from quantum trajectory method. However, the NLME shows significant advantages in analytical analysis over quantum trajectory method. Using the NLME, we classify the dynamics into two classes. In the trivial class, the process of reducing jumps is completely equivalent to weakening the coupling from the environment. In contrast, the nontrivial class presents more complex dynamics. We study a prototypical model within this class and demonstrate the existence of the postselected skin effect whose steady state is characterized by the accumulation of particles on one side. The steady-state distribution can be fitted by a scale-invariant tanh function which is different from the uniform distribution of LME. Furthermore, the NLME can give a reasonable framework for studying the interplay and competition between the non-Hermitian Hamiltonians and dissipative terms. We show this by capturing the characteristics of the trajectory-averaged entanglement entropy influenced by non-Hermitian skin effect and Zeno effect in the model of postselected skin effect.