Anomalous waiting-time distributions in postselection-free quantum many-body dynamics under continuous monitoring

TL;DR

This paper studies the waiting-time distributions of quantum jumps in monitored quantum many-body systems, revealing anomalous behaviors in subsystems that depend on measurement strength and system size, with implications for experimental diagnostics.

Contribution

It introduces a spectral framework to analyze nontrivial waiting-time distributions in subsystems, highlighting the impact of measurement strength and system size on quantum jump dynamics.

Findings

Half-chain WTD exhibits an anomalous tail deviating from Poissonian behavior.

Spectral analysis links the tail to the eigenvalue $\\lambda_0$ of the superoperator.

System-size dependence of $\lambda_0$ changes with measurement strength, indicating different scaling regimes.

Abstract

We investigate waiting-time distributions (WTDs) of quantum jumps in continuously monitored quantum many-body systems, whose unconditional dynamics lead to the trivial infinite-temperature state. We demonstrate that the WTD of a half-chain subsystem exhibits an anomalous tail, markedly deviating from the Poissonian distribution in stark contrast to that of the whole system. By analyzing the spectral properties of the superoperator $\mathscr L_0$, which is defined by removing the jump terms associated with the half-chain subsystem from the full Liouvillian, we find that the long-time behavior with the anomalous tail of the half-chain WTD is governed by the eigenvalue $\lambda_0\:(<0)$ with the largest real part. We further reveal a qualitative change in the system-size dependence of $\lambda_0$ as a function of the measurement strength: for sufficiently weak measurement, $\lambda_0$ decreases proportionally to the system size, while for strong measurement, $\lambda_0$ scales independently of the system size, signaling the persistence of the anomalous half-chain WTD in the thermodynamic limit. The WTD is extracted solely from the spacetime record of quantum jumps $\{t_i,x_i\}$ and can be experimentally accessed without postselection. Our work establishes a spectral framework for understanding nontrivial WTDs in subsystems of monitored quantum dynamics and provides a novel diagnostics to assess many-body effects on WTDs.