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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Experimental characterization of multi-photon entanglement with intensity correlation functions

I. N. Agafonov, Maria V. Chekhova, T. Sh. Iskhakov

Published Jun 15, 2007• 0 citations
Publisher

Abstract

We consider possible ways to recognize multi-photon entangled states in experiment. A commonly used technique is to measure higher-order multi-photon correlation functions and their dependence on certain phase delays (multi-photon interference). Theoretically and experimentally, we show that multi-photon interference can have very high visibility for classical sources: up to 81.8% in the three-photon case and up to 94.4% in the four-photon one. Therefore, the visibility of multi-photon interference should not be used as a criterion of multi-photon entangled states generation. Instead, we suggest to characterize multi-photon entanglement by the photon-number dependence of the normalized correlation functions.

DOI
10.1117/12.751460

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We consider possible ways to recognize multi-photon entangled states in experiment. A commonly used technique is to measure higher-order multi-photon correlation functions and their dependence on certain phase delays (multi-photon interference). Theoretically and experimentally, we show that multi-photon interference can have very high visibility for classical sources: up to 81.8% in the three-photon case and up to 94.4% in the four-photon one. Therefore, the visibility of multi-photon interference should not be used as a criterion of multi-photon entangled states generation. Instead, we suggest to characterize multi-photon entanglement by the photon-number dependence of the normalized correlation functions.
Generation of multi-photon states (such as for instance three- and four-photon states) is one of the most challenging problems of modern quantum optics. In many works the authors claim to have produced such states by means of overlapping photon pairs generated in spontaneous parametric down-conversion (SPDC). Moreover three- and four-photon states generated this way have been used for observing Greenberger-Horne-Zeilinger (GHZ) polarization states testing Bell's inequalities for spin-1 quantum systems preparing W-states and other applications. In this paper we show that the criterion for obtaining three- or four-photon states is the behavior of the corresponding normalized Glauber's correlation function. Calculations carried out for the case of SPDC or even PDC in the stimulated regime demonstrate that these processes are not capable of generating three- or four-photon states: photon statistics reveals typically two-photon behaviour. We suggest a method of measuring higher-order correlation functions in the pulsed regime which allows one to study multi-photon correlations for these and many other processes.
It is shown theoretically and experimentally that the third-order interference of intensities, which is studied in many works performed in the last decade and is usually attributed to three-photon entanglement, can also be observed for classical light with a high visibility up to 81.8%. The calculations show that classical sources ensure an even higher visibility of the interference pattern up to 94.4% for fourth order intensity interference. Thus, a large visibility of the interference pattern of the third and higher orders cannot be considered an attribute of the nonclassical character of the effect.
Abstract Quantum interference is known to become extinct with distinguishing information, as illustrated by the ubiquitous double-slit experiment or the two-photon Hong–Ou–Mandel effect. In the former case single particle interference is destroyed with which-path information while in the latter bunching interference tails-off as photons become distinguishable. It has been observed that when more than two particles are involved, these interference patterns are in general a non-monotonic function of the distinguishability. Here we perform a comprehensive characterization, both theoretically and experimentally, of four-photon interference by analyzing the corresponding correlation functions, contemplating several degrees of distinguishability across different parameters. This study provides all the necessary tools to quantify the impact of multi-photon interference on precision measurements of parameters such as phase, frequency, and time difference. We apply these insights to quantify the precision in the estimation of an interferometric phase in a two-port interferometer using a four-photon state. Our results reveal that, for certain phase values, partially distinguishable multi-photon states can achieve higher Fisher information values compared to the two-photon experiment. These findings highlight the potential of distinguishable multi-photon states for enhanced precision in quantum metrology and related applications.
Multiparticle quantum interference is critical for our understanding and exploitation of quantum information, and for fundamental tests of quantum mechanics. A remarkable example of multi-partite correlations is exhibited by the Greenberger-Horne-Zeilinger (GHZ) state. In a GHZ state, three particles are correlated while no pairwise correlation is found. The manifestation of these strong correlations in an interferometric setting has been studied theoretically since 1990 but no three-photon GHZ interferometer has been realized experimentally. Here we demonstrate three-photon interference that does not originate from two-photon or single photon interference. We observe phase-dependent variation of three-photon coincidences with (92.7±4.6)% visibility in a generalized Franson interferometer using energy-time entangled photon triplets. The demonstration of these strong correlations in an interferometric setting provides new avenues for multiphoton interferometry, fundamental tests of quantum mechanics, and quantum information applications in higher dimensions.