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arXiv:1009.4998 · Physical Review A

Four-photon indistinguishability transition

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

Published Jun 14, 2011• 52 citations
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Abstract

We demonstrate the formation of many-particle interferences of different degrees to determine the transmission of four photons of tunable indistinguishability through a four-port beam splitter array. The probability of certain output events depends nonmonotonically on the degree of distinguishability, due to distinct multiparticle interference contributions to the transmission signal.

DOI
10.1103/physreva.83.062111

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We demonstrate the formation of many-particle interferences of different degrees to determine the transmission of four photons of tunable indistinguishability through a four-port beam splitter array. The probability of certain output events depends nonmonotonically on the degree of distinguishability, due to distinct multiparticle interference contributions to the transmission signal.
One of the central principles of quantum mechanics is that if there are multiple paths that lead to the same event and there is no way to distinguish between them, interference occurs. It is often assumed that distinguishing information in the preparation, evolution, or measurement of a system is sufficient to destroy interference. However, it is still possible for photons in distinguishable, separable states to interfere due to the indistinguishability of paths corresponding to possible exchange processes. Here we experimentally measure an interference signal that depends only on the multiparticle interference of four photons in a four-port interferometer despite pairs of them occupying distinguishable states.
Multi-photon interference is the foundation of many applications regarding quantum technologies. Notably, the interference of multiple photons, registered using resolved measurements, is related to the permanent of a matrix, a problem known to be a #P-hard task. Traditionally, achieving high-visibility interference requires a high degree of indistinguishability between the interfering photons. However, this restriction can be circumvented by observing interference in the conjugate variables. This method has been successfully demonstrated using resolved measurements in the temporal and frequency domain. In this work, we extend these approaches to the spatial degrees of freedom of light. Theoretically, we demonstrate that the joint probability of detecting two photons at different positions in the output ports (3 and 4) of a beam-splitter is indeed determined by the permanent of a matrix related to the unitary transformation described by the interferometer. From an experimental perspective, we present experimental results for spatially-resolved interference in position for photons that are distinguishable in transverse momentum. We employ a setup to perform spatially-resolved measurements on photons with an adjustable distinguishability in both the central transverse momentum variable and the lateral displacement from the optical axis. This setup provides full simultaneous tunability over the distinguishability in the spatial variables. Additionally, by varying the lateral displacement, we observe how distinguishability in the position impacts the interference pattern. Overall, our results align well with the theoretical model, reinforcing the validity of our approach. Thus, this work offers new insights into the available degrees of freedom for studying of multi-photonic interference and its applications.
We present the asymptotic analysis of the quantum two-port interferometer in the n→∞n \rightarrow \inftyn→∞ limit of nnn partially indistinguishable photons. Using the unitary-unitary duality between port and inner-mode degrees of freedom, the probability distribution of output port counts can be decomposed as a sum of contributions from independent channels, each associated to a spin-jjj representation of SU(2)SU(2)SU(2) and, in this context, to 2j2 j2j effectively indistinguishable photons in the channel. Our main result is that the asymptotic output distribution is dominated by the O(n)O(\sqrt{n})O(n​) channels around a certain j∗j^*j∗ that depends on the degree of indistinguishability. The asymptotic form is essentially the doubly-humped semi-classical envelope of the distribution that would arise from 2j∗2 j^*2j∗ indistinguishable photons, and which reproduces the corresponding classical intensity distribution.
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.
Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.