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arXiv:1906.07450 · New Journal of Physics

Double-slit interferometry as a lossy beam splitter

Simanraj Sadana, Barry C. Sanders, Urbasi Sinha

Published Oct 18, 2019• 6 citations
arXivHTMLPDF

Abstract

Abstract We cast diffraction-based interferometry in the framework of post-selected unitary description towards enabling it as a platform for quantum information processing (QIP). We express slit-diffraction as an infinite-dimensional transformation and truncate it to a finite-dimensional transfer matrix by post-selecting modes. Using such a framework with classical fields we show that a customized double-slit setup is effectively a lossy beam splitter in a post-selected sense. Diffraction optics provides a robust alternative to conventional multi-beam interferometry with scope for miniaturization, and also has applications in matter wave interferometry. In this work, the classical treatment of slit-diffraction sets the stage for quantization of fields and implementing higher-dimensional QIP like that done with other platforms such as orbital angular momentum.

DOI
10.1088/1367-2630/ab4f46

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Abstract We cast diffraction-based interferometry in the framework of post-selected unitary description towards enabling it as a platform for quantum information processing (QIP). We express slit-diffraction as an infinite-dimensional transformation and truncate it to a finite-dimensional transfer matrix by post-selecting modes. Using such a framework with classical fields we show that a customized double-slit setup is effectively a lossy beam splitter in a post-selected sense. Diffraction optics provides a robust alternative to conventional multi-beam interferometry with scope for miniaturization, and also has applications in matter wave interferometry. In this work, the classical treatment of slit-diffraction sets the stage for quantization of fields and implementing higher-dimensional QIP like that done with other platforms such as orbital angular momentum.
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A major challenge in the theoretical modeling of double-slit interferometry involving matter-wave fields is the appropriate waveform to be assigned to this field. While all the studies carried out to date on this issue deal with variational fields, experiments suggest that the optical field is generated by splitting a single-hump Bose-Einstein condensate into two spatially and temporally entangled pulses indicating the possibility of fully controlling the subsequent motion of the two output pulses. To probe the consistency of variational and exact soliton solutions to the field equation, we solve the Gross-Pitaevskii equation with an optical potential barrier assumed to act as a beam splitter, while including gravity. The exact solution is compared with the two most common variational wavefunctions, namely, the Hermite-Gaussian and super-sech modes. From numerical simulations, evidence is given of the exact solution as being the most appropriate matter-wave structure that provides a coherent description of the generation and spatio-temporal evolution of matter-wave optical fields in a hypothetical implementation of double-slit atom interferometry
Within the second-quantization framework, we develop a formalism for describing a spatially multimode optical field diffracted through a spatial mask and show that this process can be described as an effective interaction between various spatial modes. We demonstrate a method to calculate the quantum state in the diffracted optical field for any given quantum state in the incident field. We also give several additional examples of how the theory works, for various quantum input states, which may be easily tested in the laboratory, including two single-mode squeezed vacuums, single- and two-photon inputs, where we show that the diffraction process produces a two-mode squeezed vacuum, number-path entanglement, and a Hong-Ou-Mandel-like effect analogous to that of a beam splitter.
Building upon the recently introduced particle interpretation of the double-slit experiment [Phys. Rev. Lett. 134, 133603 (2025)] which attributes interference phenomena to detector-coupled (bright) and detector-uncoupled (dark) states of light, we develop a continuous-mode extension of the bright- and dark-state framework. This extension addresses a conceptual distinction between interference and diffraction, that is, the transition from a finite set of discrete paths to a continuum of modes. Through the construction of a complete detector-oriented basis for single-slit diffraction, we demonstrate that the observed diffraction pattern arises from projection of the photon state onto a single bright mode by identifying the detectable and undetectable modes, with photons detected at intensity minima having zero probability, as they reside in modes spanning an infinite-dimensional dark subspace. Our approach thus provides a unified particle-based explanation of diffraction that connects quantum and classical wave optics, and reveals distinctive quantum signatures in higher-order correlations.
Optical beams bearing orbital angular momentum have been recently recognized as potential candidates for realizing DDD-dimensional quantum systems (qudits). In this paper, we propose an optical scheme to implement an orbital angular momentum beam splitter, which changes the outgoing direction with respect to the incoming direction while leaving the qudit state unchanged. Furthermore we demonstrate that such a beam splitter can be used to sort different orbital angular states of a single photon, create arbitrary superpositions of orbital angular momentum states, and implement a high-dimensional Bennett-Brassard 1984 protocol for quantum key distribution.
The wide use of beam splitters in quantum interferometry, attosecond metrology, modern quantum information processing, foundations of quantum mechanics, has been based on coherence of beams emerging from a beam splitter.Here we further develop the approach in which a beam splitter is regarded as a transformer of an incident wave field (photon field or matter wave field) into a field which has narrow maxima at the points along and in close vicinity of two or more particular lines.This description was derived by considering a thin grating as a model of a beam splitter for photons, atoms and molecules.It is applied to answer some questions raised in the discussions on the interpretation of wave particle duality.