Does the measurement take place when nobody observes it?

TL;DR

This paper investigates how continuous quantum measurements influence particle decay in reservoirs with finite bandwidth, revealing the measurement's impact depends on the reservoir's properties and the measurement timing.

Contribution

It provides an analytical expression for decay rates under continuous measurement in non-Markovian environments, linking measurement effects to detector-induced decoherence.

Findings

Decay rate depends on measurement interval for finite bandwidth reservoirs.

Detector's decoherence rate influences the measurement's impact.

Optimal measurement timing aligns with the detector's signal distinguishability.

Abstract

We consider {\em non-selective} continuous measurements of a particle tunneling to a reservoir of finite band-width ($\Lambda$). The particle is continuously monitored by frequent projective measurements ("quantum trajectory"), separated by a time-interval $\tau$. A simple analytical expression for the decay rate has been obtained. For Markovian reservoirs ($\Lambda\to\infty$), no effect of the measurements is found. Otherwise for a finite $\Lambda$, the decay rate always depends on the measurement time $\tau$. This result is compared with alternative calculations, with no intermediate measurements, but when the measurement device is included in the Schr\"odinger evolution. We found that the detector affects the system by the decoherence rate ($\Gamma_d$), related to the detector's signal. Although both treatments are different, the final results become very close for $\tau=2/\Gamma_d$. This $\tau$ corresponds to the minimal time for which the detector's signal can be distinguished by an "observer". This indicates a fundamental role of information in quantum motion and can be used for the extension of the quantum trajectory method for non-Markovian environments.