Detection of a semitransparent object with no exchange of quanta

TL;DR

This paper theoretically investigates how to optimize a Fabry-Pérot cavity for detecting partially absorbing objects without photon exchange, revealing conditions that maximize detection probabilities and offering insights into interaction-free measurement schemes.

Contribution

It provides a theoretical analysis of cavity optimization for detecting semi-transparent objects without photon exchange, highlighting the advantages of undercoupled cavities.

Findings

Undercoupled cavities maximize detection probability product.

Transmission detection is preferable over reflection in certain conditions.

Results differ from perfect absorber scenarios, informing realistic object detection.

Abstract

In this paper, we theoretically analyze the optimization of a Fabry-P\'{e}rot cavity for the purpose of detecting partially absorbing objects placed inside without photon exchange. Utilizing the input-output formalism, we quantitatively relate the probability of correctly inferring the presence or absence of the object to the probability of avoiding absorption. We show that, if the cavity decay rate due to absorption by the object is comparable to that of the empty cavity and to the object-induced detuning, the product of the two probabilities is maximized by an undercoupled cavity, in which case detection in transmission is favorable to that in reflection. These results are contrary to the case of a perfect absorber, thus adding to the body of work pertaining to interaction-free measurement schemes and providing insight into optimizing their efficiency when detecting realistic objects.