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arXiv:1109.1636 · Proceedings of the National Academy of Sciences

Nonmonotonic quantum-to-classical transition in multiparticle interference

Young-Sik Ra, Malte C. Tichy, Hyang‐Tag Lim, Osung Kwon, Florian Mintert, Andreas Buchleitner, Yoon-Ho Kim

Published Jan 7, 2013• 77 citations
arXivHTMLPDF

Abstract

Quantum-mechanical wave-particle duality implies that probability distributions for granular detection events exhibit wave-like interference. On the single-particle level, this leads to self-interference--e.g., on transit across a double slit--for photons as well as for large, massive particles, provided that no which-way information is available to any observer, even in principle. When more than one particle enters the game, their specific many-particle quantum features are manifested in correlation functions, provided the particles cannot be distinguished. We are used to believe that interference fades away monotonically with increasing distinguishability--in accord with available experimental evidence on the single- and on the many-particle level. Here, we demonstrate experimentally and theoretically that such monotonicity of the quantum-to-classical transition is the exception rather than the rule whenever more than two particles interfere. As the distinguishability of the particles is continuously increased, different numbers of particles effectively interfere, which leads to interference signals that are, in general, nonmonotonic functions of the distinguishability of the particles. This observation opens perspectives for the experimental characterization of many-particle coherence and sheds light on decoherence processes in many-particle systems.

DOI
10.1073/pnas.1206910110

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Quantum-mechanical wave-particle duality implies that probability distributions for granular detection events exhibit wave-like interference. On the single-particle level, this leads to self-interference--e.g., on transit across a double slit--for photons as well as for large, massive particles, provided that no which-way information is available to any observer, even in principle. When more than one particle enters the game, their specific many-particle quantum features are manifested in correlation functions, provided the particles cannot be distinguished. We are used to believe that interference fades away monotonically with increasing distinguishability--in accord with available experimental evidence on the single- and on the many-particle level. Here, we demonstrate experimentally and theoretically that such monotonicity of the quantum-to-classical transition is the exception rather than the rule whenever more than two particles interfere. As the distinguishability of the particles is continuously increased, different numbers of particles effectively interfere, which leads to interference signals that are, in general, nonmonotonic functions of the distinguishability of the particles. This observation opens perspectives for the experimental characterization of many-particle coherence and sheds light on decoherence processes in many-particle systems.
Quantum interference constitutes one of the sharpest divides between our classical intuition and the weirdness of the quantum world. Whenever there are multiple paths leading to the same outcome, it is the interplay of associated probability amplitudes that determines measurement results. In the double slit experiment, wave-like interference governs the distribution of particles on a detection screen. Extending to multiple particles allows behaviour that cannot be described by a classical wave, such as the bunching of photon pairs in Hong-Ou-Mandel interference. In both these examples, the ability to distinguish the interfering paths leads to degradation of interference and a return to behaviour described by probabilities. Understanding how this transition evolves for larger multiparticle quantum systems is of fundamental interest and also vital for developing photonic quantum technologies that rely on many-photon interference. In this thesis we investigate the role of distinguishability in the interference of three and four independent photons by using polarisation and time delays. For three photons, a new type of collective distinguishing phase appears that goes beyond a pairwise description of the similarity of quantum states. We use nonlinear photon sources and a fibre interferometer to experimentally demonstrate the ability to tune and isolate this phase in interference statistics. Extending to four photons we show that, contrary to intuition from two-photon experiments, the interference of photons prepared in distinguishable states is possible due to a four-particle phase. This is confirmed experimentally using a bulk four-mode interferometer. We then extend our study to include the effects of state impurity in the interference of three photons. New properties of this interference enable diagnosis of realistic experimental imperfections and characterisation tasks impossible using only two photons. Finally, we link discussions of state distinguishability to the group representations underpinning the exchange symmetry of multiparticle wavefunctions.
Wave-particle duality, as complementarity displayed in interferometry, has been investigated extensively from both theoretical and experimental perspectives. In this work, we quantify coherence in multipath interference via quantum Fisher information and illuminate its basic properties. We prove that any rational quantifier of coherence satisfying monotonicity under incoherent operations is nonincreasing in the presence of path detectors. This quantitatively implies that increase on the path information will lead to the loss of coherence or interference (wave feature), which is consistent with wave-particle duality. Furthermore, we provide an operational illustration of wave feature as quantum Fisher information of phase shift parameters encoded in each interference path. By dividing the variance of a quantum state relative to a von Neumann measurement into quantum uncertainty and classical uncertainty, we establish a coherence-predictability-correlations triality relation, with coherence (wave feature) quantified by quantum Fisher information, predictability quantified by purity of a classical probability distribution, and correlations quantified by classical uncertainty relative to the von Neumann measurement determined by the interference paths. Finally, we make a comparison between this triality relation and the wave-particle-mixedness triality relation in the literature.
Multiparticle interference is a fundamental phenomenon in the study of quantum mechanics. It was discovered in a recent experiment [Y.-S. Ra et al., Proc. Natl. Acad. Sci. USA 110, 1227 (2013)] that spectrally uncorrelated biphotons exhibited a nonmonotonic quantum-to-classical transition in a four-photon Hong-Ou-Mandel (HOM) interference. In this work, we consider the same scheme with spectrally correlated photons. By theoretical calculation and numerical simulation, we found the transition not only can be nonmonotonic with negatively correlated or uncorrelated biphotons, but also can be monotonic with positively correlated biphotons. The fundamental reason for this difference is that the HOM-type multiphoton interference is a differential-frequency interference. Our study may shed new light on understanding the role of frequency entanglement in multiphoton behavior.