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arXiv:1705.08650 · New Journal of Physics

Experimental generalized quantum suppression law in Sylvester interferometers

Niko Viggianiello, Fulvio Flamini, Luca Innocenti, Daniele Cozzolino, Marco Bentivegna, Nicolò Spagnolo, Andrea Crespi, Daniel J. Brod, Ernesto F. Galvão, Roberto Osellame, Fabio Sciarrino

Published Feb 7, 2018• 43 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/aaad92

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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.
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 ${2}^{p}\ensuremath{\ge}{2}^{q}$ 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.
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 identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multiparticle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transformation in the Fock space. In this work we develop a scalable approach for the implementation of quantum fast Fourier transform using 3-D photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the quantum suppression of a large number of output states with 4- and 8-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms.
The identification of phenomena able to pinpoint quantum interference is attracting large interest. Indeed, a generalization of the Hong-Ou-Mandel effect valid for any number of photons and optical modes would represent an important leap ahead both from a fundamental perspective and for practical applications, such as certification of photonic quantum devices, whose computational speedup is expected to depend critically on multi-particle interference. Quantum distinctive features have been predicted for many particles injected into multimode interferometers implementing the Fourier transform over the optical modes. Here we develop a scalable approach for the implementation of the fast Fourier transform algorithm using three-dimensional photonic integrated interferometers, fabricated via femtosecond laser writing technique. We observe the suppression law for a large number of output states with four- and eight-mode optical circuits: the experimental results demonstrate genuine quantum interference between the injected photons, thus offering a powerful tool for diagnostic of photonic platforms.
The well-known Hong-Ou-Mandel (HOM) effect is the first demonstration of perfect destructive interference of quantum amplitudes in a linear optical system with single photon Fock-states at input. A natural question to ask is whether we are able to predict similar behavior for systems of a general size, that is, predicting forbidden transitions for a given input state and a given linear optical system. Previous studies have found that certain symmetries between the input and output configuration in combination with a symmetric interferometer will always result into so called suppressions. But recently, a few examples have been found of suppressions which do not obey the suppression laws constructed in previous studies. In this work, we parametrize a general three-mode interferometer and we use a numerical optimization algorithm in order to find all three-mode interferometers that demonstrate forbidden transitions. These results help us to gain a better understanding of the fundamental reason behind suppressions. In addition, we compare the quality of the different interferometers for applications in quantum tomography.
Summary form only given. Recently, interference of multi-particle states has raised a strong interest in the scientific community, since it is believed to be at the very heart of post-classical computation. In this context, Boson Sampling [1] devices exploit multi-photon interference effects to provide evidence of a superior quantum computational power with current state-of-the-art technology. Thus, the capability to correctly certify the presence of multi-particle interference and find optimal platforms, becomes a crucial task because is expected to find numerous applications in photonic quantum information as a diagnostic tool for quantum optical devices.We investigate different scenarios, namely, when the consider only a fixed set of input modes, but also for the situation where all input sets can be used. We find that, in certain cases, the best choice for this task consist of Hadamard [2,3] interferometers which we implemented with a novel architecture enabled by the 3D capabilities of femtosecond laser writing. We derive and experimentally demonstrate a novel zero-transmission law based on symmetric interferometers (Fig. 1) and we verifyied the optimality of these platforms by performing further Bayesian analysis and by maximizing the total variation distance between the probability distributions corresponding to indistinguishable and distinguishable particles. The results suggest an immediate application for scattershot Boson Sampling experiments [4], where an exponential advantage in terms of generation rate is obtained with respect to the fixed-input problem. The main advantage of this technique consists in the large fraction of input-output suppressed combinations when these trasformations are injected with indistinguishable photons. In summary, this work represents a further step for quantum interference analysis and it is worth noting that Hadamard matrices naturally appear as the optimal designs for identifying genuine photonic indistinguishability in multimode interferometers and a powerful tool to validate Boson Sampling experiments. We aknowledge QUCHIP and 3D-Quest for funding this work.