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arXiv:1610.05529 · Proceedings of the National Academy of Sciences

Quantifying the momentum correlation between two light beams by detecting one

Armin Hochrainer, Mayukh Lahiri, Radek Łapkiewicz, Gabriela Barreto Lemos, Anton Zeilinger

Published Jan 31, 2017• 41 citations
arXivHTMLPDF

Abstract

Significance Entanglement as a fundamental concept of quantum physics is manifested in correlations between particles. The correlation between two particles is usually measured by detecting both of them. Here, we present the results of an experiment based on a unique concept, where the momentum correlation between two photons is measured by detecting only one of them. This measurement is possible by exploiting the quantum mechanical complementarity between path-distinguishability and interference. Our approach can potentially be generalized to measure other higher-order correlations in lower order, which would enable experimental access to a broader class of correlated quantum systems, particularly in situations in which technical limitations make it impossible to efficiently detect one of the correlated particles.

DOI
10.1073/pnas.1620979114

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Significance Entanglement as a fundamental concept of quantum physics is manifested in correlations between particles. The correlation between two particles is usually measured by detecting both of them. Here, we present the results of an experiment based on a unique concept, where the momentum correlation between two photons is measured by detecting only one of them. This measurement is possible by exploiting the quantum mechanical complementarity between path-distinguishability and interference. Our approach can potentially be generalized to measure other higher-order correlations in lower order, which would enable experimental access to a broader class of correlated quantum systems, particularly in situations in which technical limitations make it impossible to efficiently detect one of the correlated particles.
The measurement of the correlation between two quantum systems or particles has a broad significance in physics and also plays a central role in the fields of quantum optics and quantum information science. We propose a method of measuring the correlation between the transverse momenta of two photons, in which one only needs to detect one of the photons. We show that it is possible to generate a single-photon fringe pattern by using two spatially separated identical biphoton sources. The fringes are similar to the ones observed in a Michelson interferometer and possess certain remarkable properties. A striking feature of the fringes is that although the pattern is obtained by detecting one photon only of each photon pair, the fringes shift due to a change in the optical path traversed by the undetected photon; the shift is characterized by a combination of wavelengths of both photons. Using this method one can, therefore, measure the wavelength of a photon without detecting it. The visibility of the fringes diminishes as the correlation between the transverse momenta of twin photons decreases: visibility is unity for maximum momentum correlation and zero for no momentum correlation. This dependence allows us to determine the momentum correlation between both photons from the visibility of the fringe pattern obtained by detecting one of the photons only. Our method can potentially be generalized to other quantum entities.
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Double-double-slit thought experiment provides profound insight on interference of quantum entangled particles. This paper presents a detailed experimental realisation of quantum double-double-slit thought experiment with momentum entangled photons and theoretical analysis of the experiment. Experiment is configured in such a way that photons are path entangled and each photon can reveal the which-slit path information of the other photon. As a consequence, single photon interference is suppressed. However, two-photon interference pattern appears if locations of detection of photons are correlated without revealing the which-slit path information. It is also shown experimentally and theoretically that two-photon quantum interference disappears when the which-slit path of a photon in the double-double-slit is detected.
Although most physics experiments are carried out with independent particles, it is the collective nature of entangled particles that reveals the most fascinating and unexpected aspects of the quantum world. It was Erwin Schrodinger who first said “entanglement is not one but rather the characteristic trait of quantum mechanics”. One curious aspect of the behavior of a pair of particles in an entangled state is that, though each individual particle exhibits an inherent uncertainty, the joint entity of an entangled pair can exhibit no such uncertainty. As an example, while the time of arrival of an individual particle may be totally random, an entangled pair must always arrive simultaneously. This property offers a unique tool for carrying out absolute measurements. Our goal here is to explore the myriad implications and significance of entanglement and to exploit it for the development of a new type of optical measurement—quantum optical metrology. The existence of unique non-classical correlations between twin photons generated in the nonlinear process of spontaneous parametric origins. The non-classical link between such twin quanta is not diminished by arbitrarily large separations between the twins, even when they lie outside the light cone. Twin states have been used with great effectiveness over the past two decades for carrying out definitive quantum experiments that lead to counterintuitive results; among these are those arising from the EinsteinPodolsky-Rosen (EPR) paradox such as various tests of Bell’s inequalities [1-12], as well as non-local dispersion cancellation, entangled-photon–induced transparency, and entangled-photon spectroscopy with monochromatic light. The availability of these twin beams has made it possible to conduct such experiments without having to resort to
An operational way of measuring entanglement in a balanced two-path interferometers is presented, where path information is carried by some internal degree of freedom which, in turn, gets entangled with an ancilla system. The analysis is based on a tripartite description involving paths, an internal qubit degree of freedom, and some ancillary states entangled with the internal degree of freedom. It is then applied to two physically distinct experimental situations: a modified Stern-Gerlach interferometer with spin-1/2 particles and a Mach-Zehnder interferometer with photons carrying polarization. The ancilla degree of freedom may not be experimentally accessible. Tracing out the ancillary system, and employing a quantum erasing procedure based on the internal degree of freedom, it is demonstrated that a concurrence-based measure of the entanglement, between the internal degree of freedom and the ancilla, can be extracted directly from measurable asymmetry of the two output channels. These results show that loss of coherence, quantum erasure, and entanglement estimation in interferometric experiments arise from the same underlying correlation structure and provide a compact experimentally accessible framework for quantifying entanglement in qubit systems.
Quantum theory permits interference between indistinguishable paths but, at the same time, restricts its order. Single-particle interference, for instance, is limited to the second order, that is, to pairs of single-particle paths. To date, all experimental efforts to search for higher-order interferences beyond those compatible with quantum mechanics have been based on such single-particle schemes. However, quantum physics is not bound to single-particle interference. We here experimentally study many-particle higher-order interference using a two-photon-five-slit setup. We observe nonzero two-particle interference up to fourth order, corresponding to the interference of two distinct two-particle paths. We further show that fifth-order interference is restricted to 10^{-3} in the intensity-correlation regime and to 10^{-2} in the photon-correlation regime, thus providing novel bounds on higher-order quantum interference.