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arXiv:1407.1758 · New Journal of Physics

Comment on ‘Non-monotonic projection probabilities as a function of distinguishability’

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

Published Nov 28, 2014• 5 citations
arXivHTMLPDF

Abstract

A recent work (Björk and Shabbir 2014 New J. Phys. 16 013006 ) claims that nonmonotonic structures found in the many-particle quantum-to-classical transition (Ra et al 2013 Proc. Natl Acad. Sci. USA 110 1227–31 ; Tichy et al 2011 Phys. Rev. A 83 062111 ) are not exclusive to the many-body domain, but they also appear for single-photon as well as for semi-classical systems. We show that these situations, however, do not incorporate any quantum-to-classical transition, which makes the claims unsustainable.

DOI
10.1088/1367-2630/16/11/118003

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We reiterate that a non-monotonic behavior of projection probabilities can occur for most states irrespective of the number of particles involved, based solely on the choice of the projectors chosen for measurement. We further clarify that, contrary to the claim in the comment, our analysis is not intended to demonstrate quantum to classical transition. However, our results show that a non-monotonic behavior is not a necessarily a signature of such a transition.

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A recent work (Björk and Shabbir 2014 New J. Phys. 16 013006 ) claims that nonmonotonic structures found in the many-particle quantum-to-classical transition (Ra et al 2013 Proc. Natl Acad. Sci. USA 110 1227–31 ; Tichy et al 2011 Phys. Rev. A 83 062111 ) are not exclusive to the many-body domain, but they also appear for single-photon as well as for semi-classical systems. We show that these situations, however, do not incorporate any quantum-to-classical transition, which makes the claims unsustainable.
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.
Typically, quantum superpositions, and thus measurement projections of quantum states involving interference, decrease (or increase) monotonically as a function of increased distinguishability. Distinguishability, in turn, can be a consequence of decoherence, for example caused by the (simultaneous) loss of excitation or due to inadequate mode matching (either deliberate or indeliberate). It is known that for some cases of multi-photon interference, non-monotonic decay of projection probabilities occurs, which has so far been attributed to interference between four or more two photons. We show that such a non-monotonic behaviour of projection probabilities is not unnatural, and can also occur for single-photon and even semiclassical states. Thus, while the effect traces its roots from indistinguishability and thus interference, the states for which this can be observed do not need to have particular quantum features.
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.