Spikes in Poissonian quantum trajectories

TL;DR

This paper investigates the occurrence of spikes in quantum trajectories of a monitored qubit under Poissonian noise, revealing that spikes occur similarly to Brownian noise cases and analyzing their statistics across different scenarios.

Contribution

It demonstrates that spikes are present in Poissonian quantum trajectories and provides a comprehensive analysis of their statistics using stochastic resetting models.

Findings

Spikes occur in Poissonian quantum trajectories, not just Brownian cases.

Spike and jump statistics are analytically derived for various measurement scenarios.

Numerical simulations support the analytical results.

Abstract

We consider the dynamics of a continuously monitored qubit in the limit of strong measurement rate where the quantum trajectory is described by a stochastic master equation with Poisson noise. Such limits are expected to give rise to quantum jumps between the pointer states associated with the non-demolition measurement. A surprising discovery in earlier work [Tilloy et al., Phys. Rev. A 92, 052111 (2015)] on quantum trajectories with Brownian noise was the phenomena of spikes observed in between the quantum jumps. Here, we show that spikes are observed also for Poisson noise. We consider three cases where the non-demolition is broken by adding, to the basic strong measurement dynamics, either unitary evolution or thermal noise or additional measurements. We present a complete analysis of the spike and jump statistics for all three cases using the fact that the dynamics effectively corresponds to that of stochastic resetting. We provide numerical results to support our analytic results.