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arXiv:2411.15384 · Optics Express

Detection of a semitransparent object with no exchange of quanta

Vedran Vujnović, Nenad Kralj, Marin Karuza

Published Dec 9, 2024• 3 citations
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Abstract

In this paper, we theoretically analyze the optimization of a Fabry-Pérot 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 different interaction-free measurement schemes and providing insight into optimizing their efficiency when detecting realistic objects.

DOI
10.1364/oe.544178

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In this paper, we theoretically analyze the optimization of a Fabry-Pérot 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 different interaction-free measurement schemes and providing insight into optimizing their efficiency when detecting realistic objects.
Summary form only given.The purpose of an interaction-free measurement is to detect the presence of an object without letting any energy quanta be absorbed by the object. In this work we present interaction-free measurement results using a Fabry-Perot interferometer as a measurement apparatus. If the cavity of the interferometer is empty, an incoming photon will be transmitted through the interferometer. If an absorbent is placed between the mirrors, the photon will be reflected by the first mirror. By detecting which way the photon takes, we will gain information about the presence of the absorbent without losses/interaction. For a perfect measurement, the figure of merit will be equal to the mirror reflectivity R. Thus, in theory, one can approach the perfect interaction-free measurement simply by increasing R.
Absorption-free (also known as ``interaction-free'') measurement aims to detect the presence of an opaque object using a test particle without that particle being absorbed by the object. Here we consider semitransparent objects that have an amplitude $\ensuremath{\alpha}$ of transmitting a particle while leaving the state of the object unchanged and an amplitude $\ensuremath{\beta}$ of absorbing the particle. The task is to devise a protocol that can decide which of two known transmission amplitudes is present while ensuring that no particle is absorbed by the object. We show that the probabilities of being able to achieve this are limited by an inequality. This inequality implies that absorption-free distinction between complete transparency and any partial transparency is always possible with probabilities approaching 1, but that two partial transparencies can only be distinguished with probabilities less than 1.
Interaction-free measurements were realized using a high-finesse Fabry-P\'erot cavity as a measurement apparatus. A figure of merit based on the maximum likelihood estimation, which takes into account real experimental conditions, is used to analyze the efficiency of this measurement scheme. The probability of detecting the presence of an object within the cavity without any photons actually ``hitting'' the object was approximately 85%. The probability of asserting the absence of the object was approximately 75%. Assuming that the a priori probability of the object being present was 1/2, the likelihood of knowing whether the object was present or not was 80%. The obtained results and the limitations of our setup are discussed.
Interaction-free measurement infers the presence of an absorbing object from a photon that, in the counterfactual sense, never interacted with it, and is widely described as a route to minimally invasive sensing. We ask what it actually buys, in estimation-theoretic terms. Written as a channel-estimation problem, the Elitzur-Vaidman interferometer carries exactly half the Fisher information about the object's transmissivity that direct transmission probing does, and the two schemes deliver identical Fisher information per absorbed photon. For measuring how transparent something is, the interferometer buys nothing. The advantage lies in discrimination, and we show that what it requires is not that the object be opaque but that the competing hypothesis be the object's absence. Against empty space the Chernoff information per absorbed photon grows almost linearly, as the number of Zeno cycles times its logarithm, even for a weakly absorbing object; between two partial transparencies it does not grow at all. Parasitic loss in the cycle caps the advantage. The number of conclusive interrogations per absorbed photon reaches a maximum inversely proportional to the loss per cycle, at an optimal cycle number that is likewise inversely proportional to it, which identifies the loss per cycle as the figure of merit governing how far interaction-free sensing can be pushed. Finally, the negative result is not special to the interferometer. For a single photon meeting a memoryless, non-dispersive object any number of times through arbitrary fixed optics, the accessible quantum Fisher information never exceeds that of the same incident flux spent on independent single-pass probes, and is generically far below it. This recovers the bound of Massar, Mitchison and Pironio for this class, by a short argument that also identifies when it is tight.
An interaction-free measurement system with a polarization-based Mach-Zehnder interferometer structure is analyzed for semitransparent objects. Here, it is shown that the interaction-free measurement of such objects with 100% detection efficiency is possible in principle if the system loss is negligible. The influence of two system imperfections, the system loss and the low quantum efficiency of the photon detectors, on the interaction-free measurement is also analyzed. Although the two system imperfections limit the maximal detection efficiency that can be achievable, the quantum efficiency of the photon detectors is less important when the system loss becomes small.