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arXiv:1502.06372 · Physical Review A

Suppression laws for multiparticle interference in Sylvester interferometers

Andrea Crespi

Published Jan 8, 2015• 51 citations
arXivHTMLPDF

Abstract

Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or antibunching. In the presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al., [Phys. Rev. Lett. 104, 220405 (2010)] recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multiport beam splitters. Here we study the case in which ${2}^{q}$ particles (either bosonic or fermionic) are injected simultaneously in different ports of a Sylvester interferometer with ${2}^{p}\ensuremath{\ge}{2}^{q}$ modes. In particular, we prove a necessary and sufficient criterion for a significant fraction of output states to be suppressed, for specific input configurations. This may find application in assessing the indistinguishability of multiple single-photon sources and in the validation of boson sampling machines.

DOI
10.1103/physreva.91.013811

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Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or antibunching. In the presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al., [Phys. Rev. Lett. 104, 220405 (2010)] recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multiport beam splitters. Here we study the case in which 2q{2}^{q}2q particles (either bosonic or fermionic) are injected simultaneously in different ports of a Sylvester interferometer with 2p\ensuremath≥2q{2}^{p}\ensuremath{\ge}{2}^{q}2p\ensuremath≥2q modes. In particular, we prove a necessary and sufficient criterion for a significant fraction of output states to be suppressed, for specific input configurations. This may find application in assessing the indistinguishability of multiple single-photon sources and in the validation of boson sampling machines.
Photonic interference is a key quantum resource for optical quantum computation, and in particular for so-called boson sampling devices. In interferometers with certain symmetries, genuine multiphoton quantum interference effectively suppresses certain sets of events, as in the original Hong–Ou–Mandel effect. Recently, it was shown that some classical and semi-classical models could be ruled out by identifying such suppressions in Fourier interferometers. Here we propose a suppression law suitable for random-input experiments in multimode Sylvester interferometers, and verify it experimentally using 4- and 8-mode integrated interferometers. The observed suppression occurs for a much larger fraction of input–output combinations than what is observed in Fourier interferometers of the same size, and could be relevant to certification of boson sampling machines and other experiments relying on bosonic interference, such as quantum simulation and quantum metrology.
The investigation of multi-photon quantum interference in symmetric multi-port splitters has both fundamental and applicative interest. Destructive quantum interference in devices with specific symmetry leads to the suppression of a large number of possible output states, generalizing the Hong-Ou-Mandel effect; simple suppression laws have been developed for interferometers implementing the Fourier or the Hadamard transform over the modes. In fact, these enhanced interference features in the output distribution can be used to assess the indistinguishability of single-photon sources, and symmetric interferometers have been envisaged as benchmark or validation devices for Boson-Sampling machines. In this work we devise an innovative approach to implement symmetric multi-mode interferometers that realize the Fourier and Hadamard transform over the optical modes, exploiting integrated waveguide circuits. Our design is based on the optical implementations of the Fast-Fourier and Fast-Hadamard transform algorithms, and exploits a novel three-dimensional layout which is made possible by the unique capabilities of femtosecond laser waveguide writing. We fabricate devices with m = 4 and m = 8 modes and we let two identical photons evolve in the circuit. By characterizing the coincidence output distribution we are able to observe experimentally the known suppression laws for the output states. In particular, we characterize the robustness of this approach to assess the photons' indistinguishability and to rule out alternative non-quantum states of light. The reported results pave the way to the adoption of symmetric multiport interferometers as pivotal tools in the diagnostics and certification of quantum photonic platforms.
The present thesis deals with the interrelation between entanglement of identical particles and many-particle interference in multimode scattering scenarios. The processes that govern the scattering are shown to characterize the quantum correlations that result from coherent deletion of many-particle which-way information. Part I treats the constitutive situation of two identical particles which are measured by two detectors to provide a consistent definition of identical-particle entanglement. The key quantities that determine the strength and nature of correlations are diagnosed, which allows a formulation of the problem as scattering scenario. Quite counter-intuitively, the effective indistinguishability of the particles is not necessarily reflected monotonically by the strength of quantum correlations, which is explained by an interplay of the entanglement encoded in the initial state with measurement-induced correlations. The subject of Part II is the scattering of many non-interacting particles that are initially injected in an arbitrary number of modes. A comparison of bosons, fermions and distinguishable particles reveals that the dichotomy of bosons and fermions, known from the two-particle case, does, surprisingly, not prevail for many particles: A given output event can be suppressed or enhanced for bosons and fermions simultaneously. Consequently, the bunching behavior of bosons is not apparent at the level of single counting events, where dynamical many-particle interference dominates, and it is only reflected in more coarse-grained quantities that are related to the occupation statistics, for which efficient approximate treatments are derived. The general complexity of the many-particle problem is overcome for the special case of a Fourier multiport beam splitter. The exploitation of its scattering matrix’ symmetries yields a systematic event suppression law for, both, bosons and fermions, which provides a generalization of the two-photon Hong-Ou-Mandel effect to an arbitrary number of particles and modes. As a further characteristic trait of many-particle interference, the transition between indistinguishable and distinguishable particles is reflected non-monotonically by the event probabilities, which is also confirmed by an experiment that was suggested by the present work. Part III combines the formalism for identical-particle entanglement and the tools and notions developed in the context of many-particle scattering for a description of those multipartite entangled states that can be created via the scattering of many identical particles. The formalism is general enough to include virtually any possible scheme for the multipartite entanglement creation with single photons. An analytical treatment reveals fundamental constraints for the set of accessible states. In particular, an intuitive combinatorial bound for the Schmidt number of the target state follows from the finite number of combinations to distribute the particles among the output modes. Furthermore, bosons and fermions have very distinct potential for entanglement creation: Fewer states are accessible for fermions, whereas the success probability of entanglement production is strongly enhanced with respect to bosons.
When two indistinguishable bosons interfere at a beam splitter, they exit through the same output port. This quantum effect, known as Hong-Ou-Mandel interference, underpins many protocols in quantum information. It also generalizes to larger numbers of identical particles, for which interference produces characteristic many-body patterns. So far, experiments have observed the many-particle regime mainly in photonic platforms with unavoidable loss, and atomic realizations have remained challenging. Here we demonstrate Hong-Ou-Mandel interference with up to 12 indistinguishable neutral atoms in a system with negligible loss. Single-particle counting reveals parity oscillations, a bunching envelope and genuine multipartite entanglement, which are defining features of the multiparticle Hong-Ou-Mandel effect. Using the generated quantum states, we demonstrate metrological sensitivities that scale with the number of particles according to the Heisenberg limit. Our technique can be extended to larger ensembles, with wide-ranging applications from high-precision atom interferometry to multiparticle Bell tests.
Hong-Ou-Mandel interference is one of the clearest signatures of quantum behaviour: two identical photons meeting at a beam splitter always leave together. Here we demonstrate that this symmetry can be broken. Using a programmable integrated photonic processor, we interfere imbalanced two-photon states on a variable beam splitter and show that the output state of quantum interference can be continuously tuned, reaching the extreme case where destructive interference suppresses bunching at one output port. The asymmetry creates a forbidden bunching channel: photons may exit together at one port or separately at both ports, but cannot emerge together at the other port.
Identical particles exhibit correlations even in the absence of inter-particle interaction, due to the exchange (anti)symmetry of the many-particle wavefunction. Two fermions obey the Pauli principle and anti-bunch, whereas two bosons favor bunched, doubly occupied states. Here, we show that the collective interference of three or more particles leads to much more diverse behavior than expected from the boson–fermion dichotomy known from quantum statistical mechanics. The emerging complexity of many-particle interference is tamed by a simple law for the strict suppression of events in the Bell multiport beam splitter. The law shows that counting events are governed by widely species-independent interference, such that bosons and fermions can even exhibit identical interference signatures, while their statistical character remains subordinate. Recent progress in the preparation of tailored many-particle states of bosonic and fermionic atoms promises experimental verification and applications in novel many-particle interferometers.