Continuous measurement of a qudit using dispersively coupled radiation

TL;DR

This paper investigates continuous measurement techniques for qudits using dispersively coupled radiation, deriving stochastic master equations and analyzing measurement back-action effects with different amplification methods.

Contribution

It introduces a comprehensive framework for modeling qudit measurement via dispersive coupling, including derivation of Lindblad operators and comparison of amplification schemes.

Findings

Measurement back-action causes spiraling in state space during collapse.

Average behavior is similar for phase-preserving and phase-sensitive detection.

Individual trajectories collapse at different rates depending on measurement axis.

Abstract

We analyze the continuous monitoring of a qudit coupled to a cavity using both phase-preserving and phase-sensitive amplification. The quantum trajectories of the system are described by a stochastic master equation, for which we derive the appropriate Lindblad operators. The measurement back-action causes spiraling in the state coordinates during collapse, which increases as the system levels become less distinguishable. We discuss two examples: a two-level system and an $N$-dimensional system and meter with rotational symmetry in the quadrature space. We also provide a comparison of the effects of phase-preserving and phase-sensitive detection on the master equation, and show that the average behavior is the same in both cases, but individual trajectories collapse at different rates depending on the measurement axis in the quadrature plane.