Computing the Rates of Measurement-Induced Quantum Jumps

TL;DR

This paper analytically computes measurement-induced quantum jump rates in continuously monitored quantum systems using the SME formalism, with broad applicability to systems under strong noise conditions.

Contribution

It provides a general analytical method to determine quantum jump rates for any Lindbladian evolution under continuous measurement.

Findings

Jump rates can be computed analytically for any Lindbladian.

The jumpy behavior of the density matrix is confirmed under tight measurement.

The method applies to strong noise limits in stochastic differential equations.

Abstract

Small quantum systems can now be continuously monitored experimentally which allows for the reconstruction of quantum trajectories. A peculiar feature of these trajectories is the emergence of jumps between the eigenstates of the observable which is measured. Using the Stochastic Master Equation (SME) formalism for continuous quantum measurements, we show that the density matrix of a system indeed shows a jumpy behavior when it is subjected to a tight measurement (even if the noise in the SME is Gaussian). We are able to compute the jump rates analytically for any system evolution, i.e. any Lindbladian, and we illustrate how our general recipe can be applied to two simple examples. We then discuss the mathematical, foundational and practical applications of our results. The analysis we present is based on a study of the strong noise limit of a class of stochastic differential equations (the SME) and as such the method may be applicable to other physical situations in which a strong noise limit plays a role.