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Quantum Information and Measurement (QIM)

Multiphoton Discrete Fractional Fourier Operations in Waveguide Beam Splitters

Roberto de J. León‐Montiel, Konrad Tschernig, Omar S. Magaña‐Loaiza, Alexander Szameit, Kurt Busch, Armando Pérez-Leija

Published Jan 1, 2019• 0 citations
Publisher

Abstract

We show that by injecting N indistinguishable photons in a waveguide beam-splitter, one can create lattice-like structures in the photon number space, which are equivalent to coupled systems that perform discrete fractional Fourier operations.
DOI
10.1364/qim.2019.f5a.16

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We demonstrate that when a waveguide beam splitter (BS) is excited by N indistinguishable photons, the arising multiphoton states evolve in a way as if they were coupled to each other with coupling strengths that are identical to the ones exhibited by a discrete fractional Fourier system. Based on the properties of the fractional Fourier transform, we then derive a multiphoton suppression law for 50/50 BSs, thereby generalizing the Hong–Ou–Mandel effect. Furthermore, we examine the possibility of performing simultaneous multiphoton quantum random walks by using a single waveguide BS in combination with photon-number-resolving detectors. We anticipate that the multiphoton lattice-like structures unveiled in this work will be useful to identify new effects and applications of high-dimensional multiphoton states.
Indistinguishable and/or entangled photons propagating in waveguide arrays (WAs) represent a promising platform whose utility ranges from research on fundamental aspects of quantum mechanics all the way to applications in quantum sensing and quantum information processing. Quantum simulators of decoherence reveal that while decoherence processes inevitably destroy single-particle coherence and any form of multiparticle entanglement, quantum correlations based on particle indistinguishability do endure. Further, by judiciously combining multi-photon states with the idea of synthetic dimensions in WAs yields the notion of a synthetic atom and in turn this provides entirely novel perspectives on the dynamics of such multi-photon states. Similarly, simple beam splitters fed with indistinguishable photons, can be used to perform discrete fractional Fourier transforms or can be tuned to realize exceptional points of any order. The latter setup facilitates efficient quantum-enhanced sensors.
We report on our latest findings on photonic Quantum Walks (QW) of entangled particles in several quantum transport regimes as for instance in photonic Bloch lattices or disordered lattices. Furthermore, the discrete fractional Fourier transform of quantum states is presented in the context of QWs. The propagation of a classical single walker on a random graph is an important field in statistics and can be applied on many domains in nature reaching from a foraging animals over Brownian molecular motion towards the evolution of lead changes in competitive team sports. Its quantum mechanical counterpart, the Quantum Walk (QW), features genuine quantum objects to walk on a random graph and hence, leading to non-classical quantum interference, in particular when considering two or more walkers. Their great potential lies i.a. in their ability to exponentially speed up a multitude of algorithms, as for instance the data bank search algorithm from L. Grover. In this regard, photonic lattices of evanescently coupled waveguides represent an ideal platform to study QW dynamics, since they feature advantages in stability, robustness and miniaturization. Our waveguide lattices were fabricated by means the direct laser inscription technique. In doing so, three dimensional waveguide geometries are realizable, enabling the implementation of various QW graphs. Along these lines, we study QWs of entangled photon pairs in disordered lattices. There we observe Anderson co-localization, meaning that neither the individual photons nor the pair localizes, rather their distance does. It turns out that both photons tend to bunch as they will be found together in the same lattice site, implying that their original correlation remains while performing a QW in a disordered lattice. Further, we investigate QWs of non-local two-photon EPR-states in Bloch-lattices. The experimental results reveal the strong dependence of the correlation output statistics (bosonic-, anyonicor fermionic-like) on the input states' symmetry. Finally, the discrete fractional Fourier transform of quantum states is realized through a discrete QW lattice. The results demonstrate the enormous potential of waveguide lattices in the field of quantum photonics and give rise to further investigations like the Fourier suppression law.
The Hong--Ou--Mandel (HOM) effect is a hallmark of two-photon quantum interference, in which two indistinguishable photons impinging on a balanced beam splitter bunch into the same output port. Here, we show that a giant atom (GA), coupled to two waveguides through two coupling points each, can function as a programmable HOM interferometer, enabling continuous control over single-photon beam splitting and two-photon interference. This programmability arises from coupling-phase differences in the GA, which tune its self-interference and directionality, and thereby its scattering response. To characterize the two-photon interference, we analyze the scattering of two Gaussian single-photon wave packets injected through different waveguides and evaluate the bunching and antibunching (coincidence) probabilities of the resulting four output ports. At the operating point where the GA acts as an effective 50:50 beam splitter for single photons, we observe a pronounced HOM dip as the relative input delay between the two wave packets is varied. Away from this point, adjusting the coupling phases continuously tunes the two-photon output statistics between bunching into the same output port and antibunching across distinct output ports. In addition, we explore an application to quantum parameter estimation, showing that small deviations of coupling phases can be estimated from the two-photon output statistics, with the achievable sensitivity quantified by the classical Fisher information associated with a binary coincidence measurement. Our giant-atom beam splitter thus provides a programmable platform for two-photon interference in waveguide quantum electrodynamics, with potential applications in quantum information processing, quantum communication, and quantum sensing.