Conditional relaxation of a charge state under continuous weak measurement

TL;DR

This paper studies how a charge state in a quantum system relaxes conditionally under continuous weak measurement, revealing faster relaxation dynamics and dependence on measurement choices, with potential verification in interferometer setups.

Contribution

It introduces the concept of conditional relaxation of a charge state under weak measurement, highlighting properties distinct from back-action dephasing and proposing experimental verification methods.

Findings

Conditional relaxation occurs faster than dephasing.

Relaxation direction depends on output lead choice.

Current-current correlation reveals relaxation features.

Abstract

We investigate the conditional evolution of a charge state coupled to a mesoscopic detector under continuous weak measurement. The state suffers relaxation into a particular state with a definite charge when electrons in a particular output lead are monitored in the detector. The process of the conditional relaxation is not restricted by the shot noise of the detector, unlike the case of the back-action dephasing. As a result, the relaxation of conditional evolution is much faster than the current-sensitive part of dephasing. Furthermore, the direction of the relaxation depends on the choice of the output lead. We propose that these properties can be verified in a two-path interferometer containing a quantum dot capacitively coupled to a detector. In this setup, the current-current correlation between the interferometer and the detector reveals characteristic features of conditional relaxation.