Continuous measurement of a qudit using dispersively coupled radiation

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.