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arXiv:1605.01084 · Journal of Physics Conference Series

Interaction-Free Measurements of Optical Semitransparent Objects

Z Blanco-Garcia, Óscar Rosas-Ortiz

Published Mar 1, 2016• 3 citations
arXivHTMLPDF

Abstract

We substitute the fully absorbing obstacle in the Elitzur-Vaidman experiment by a semitransparent object and show that the probabilities of detection can be manipulated in dependence of the transparency of such an object. Then, we connect our results with the delayed choice experiment proposed by Wheeler. It is found that the transparency of the obstacle determines either a particle-like or a wave-like behaviour of a test photon.

DOI
10.1088/1742-6596/698/1/012013

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We substitute the fully absorbing obstacle in the Elitzur-Vaidman experiment by a semitransparent object and show that the probabilities of detection can be manipulated in dependence of the transparency of such an object. Then, we connect our results with the delayed choice experiment proposed by Wheeler. It is found that the transparency of the obstacle determines either a particle-like or a wave-like behaviour of a test photon.
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.
Wheeler’s gedanken experiment is the most fascinating and subtle illustration of wave-particle duality [1]. If we consider a single-photon light pulse in a Mach-Zehnder interferometer, one can either measure the interference at the output – evidencing the “wave-like” behavior of the photon- or one can detect the path followed by the photon – evidencing its “particle-like” behavior. In order to pinpoint how surprising this is, John Wheeler considered a “delayed-choice” regime where the choice of measuring either property is done only after the photon has entered the interferometer.
Delaying Quantum Choice Photons can display wavelike or particle-like behavior, depending on the experimental technique used to measure them. Understanding this duality lies at the heart of quantum mechanics. In two reports, Peruzzo et al. (p. 634 ) and Kaiser et al. (p. 637 ; see the Perspective on both papers by Lloyd ) perform an entangled version of John Wheeler's delayed-choice gedanken experiment, in which the choice of detection can be changed after a photon passes through a double-slit to avoid the measurement process affecting the state of the photon. The original proposal allowed the wave and particle nature of light to be interchanged after the light had entered the interferometer. By contrast in this study, entanglement allowed the wave and particle nature to be interchanged after the light was detected and revealed the quantum nature of the photon, for example, it displays wave- and particle-like behavior simultaneously.
The gedanken experiment of Elitzur and Vaidman showing wave-particle duality was realized as a demonstration at a scientific exposition. Presence or absence of a mirror in one arm of an interferometer was measured while detecting one photon at a time. A reasonable fraction of events was ‘‘interaction-free,’’ which means that the conclusion that there was a mirror in the beam could be drawn from the signal of a photon that had not interacted with the mirror. The demonstration was found to be thought-provoking.
Bohr's complementarity notion is at the heart of quantum physics. It suggests that quantum systems are observed as waves or particles depending on the type of measurement, i.e., the experimental arrangement, they are subjected to. For instance, sending single photons to an open or closed Mach-Zehnder interferometer (MZI) leads to the observation of particle or wave behaviours, respectively. In 1984, Wheeler proposed a "Gedanken" delayed-choice experiment in which the interferometer configuration is chosen at will by the experimentalist only after the photon has already passed the input beam-splitter (BS_in) of the device. This experiment was realized using a single photon source and showed that Bohr's complementarity notion was still obeyed.It was recently proposed to take Wheeler's experiment one step further by employing an output "quantum beam-splitter" (QBS), i.e.,preparing BS_out in a coherent superposition of being absent and present. This allows choosing the type of measurement, i.e., wave or particle, only after having determined the state of the QBS, which can be (in principle) infinitely delayed.We realized such an experiment by exploiting the resource of entanglement, in this case pairs of polarization entangled photons. The behaviour of one of the paired photons, called the test photon, is analysed using a MZI having a QBS at its output. This QBS is enabled by entanglement and made of a polarization dependent beam-splitter. The other photon, called the corroborative photon, allows determining the state of the QBS, and consequently, which test photon behaviour (wave, particle, or both) is observed.By manipulating the corroborative photon polarization state, we demonstrate a continuous morphing of the test photon from wave to particle behaviour. This refutes simple models of single photons behaving exclusively as waves or particles. The state of the QBS is determined via the measurement of the corroborative photon only after the test photon has already been detected. The space-like separation between the two measurements invalidates local-hidden variable models associated with pre-existing information about the measurement outcomes. In other words, when the test photon is detected, no information is available about the type of measurement it underwent. These results still perfectly obey Bohr's complementarity notion and its extension.
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.