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Digest - IEEE Antennas and Propagation Society. International Symposium

Quantum Information Propagation Using Huygens' Principle

Jie Zhu, Dong-Yeop Na, Peter A. Bermel, Weng Cho Chew

Published Jul 5, 2020• 0 citations
Publisher

Abstract

A new computational framework for quantum electromagnetics has recently been proposed (D.-Y. Na, J. Zhu, F. L. Teixeira, and W. C. Chew, arXiv 1911.00947, 2019). In this work, we demonstrate the use of Huygens' Principle for quantum information propagation. Instead of numerical eigenmodes, Fourier modes are used to quantize the field. Wave propagation and second-order correlation function calculated based on this scheme are shown.

DOI
10.1109/ieeeconf35879.2020.9329839

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A new computational framework for quantum electromagnetics has recently been proposed (D.-Y. Na, J. Zhu, F. L. Teixeira, and W. C. Chew, arXiv 1911.00947, 2019). In this work, we demonstrate the use of Huygens' Principle for quantum information propagation. Instead of numerical eigenmodes, Fourier modes are used to quantize the field. Wave propagation and second-order correlation function calculated based on this scheme are shown.
Typically the use of the Rayleigh-Sommerfeld diffraction formula as a photon propagator is widely accepted due to the abundant experimental evidence that suggests that it works. However, a direct link between the propagation of the electromagnetic field in classical optics and the propagation of photons where the square of the probability amplitude describes the transverse probability of the photon detection is still an issue to be clarified. We develop a mathematical formulation for the photon propagation using the formalism of electromagnetic field quantization and the path-integral method, whose main feature is its similarity with a fractional Fourier transform (FRFT). Here we show that because of the close relation existing between the FRFT and the Fresnel diffraction integral, this propagator can be written as a Fresnel diffraction, which brings forward a discussion of the fundamental character of it at the photon level compared to the Huygens-Fresnel principle. Finally, we carry out an experiment of photon counting by a rectangular slit supporting the result that the diffraction phenomenon in the Fresnel approximation behaves as the actual classical limit.
We consider an approach in which the usual wave function ${\ensuremath{\psi}}_{j}({x}_{j})$ in the quadrature representation of mode jjj of the electromagnetic field is further quantized to produce a field operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j}).$ Since the electromagnetic field is already second quantized, this corresponds to an additional or third quantization. The third-quantization approach can be used to perform certain quantum optics calculations in the Heisenberg picture that could only be performed in the Schr\"odinger picture when using the conventional second-quantized theory. This approach also allows an interesting generalization of quantum optics and quantum electrodynamics that is analogous to symmetry breaking in elementary particle theory. The predictions of the generalized theory could be tested using a proposed photon scattering experiment.
Few-photon systems are best described by their wave function rather than by the usual quantum field formalism. In this work, we develop a photon wave function (PWF) formalism suitable for analyzing a wide variety of quantum optical problems related to propagation, diffraction and imaging with quantum states of light. We establish a generalized Huygens-Fresnel (GH-F) principle that describes the propagation of any paraxial N-photon state. This tool is very helpful for predicting photo-detection correlations in space and time due to an initial N-particle entanglement, even in complex situation. The effect of lenses, beam splitters, filters ... on the photon paths can be easily taken into account. We apply the PWF formalism and the GH-F principle to three specific problems in quantum optics. First, we revisit the Hong-Ou-Mandel two-photon interference effect and analyze the effect of photon shape mismatch in space, time and polarization using the PWF formalism. Second, we show how to use the GH-F principle to analyze "ghost" imaging and diffraction experiments with entangled photon pairs such as those realized by Strekalov et al. [Phys. Rev. Lett. 74, 3600 (1995)] and Pittman et al. [Phys. Rev. A 52, R3429 (1995)] in the nineties. Finally, we use the GH-F principle to analyze the resolution enhancement in a recent quantum imaging proposal based on N incoherent single-photon sources [Phys. Rev. Lett. 99, 133603 (2007) and Phys. Rev. A 80, 013820 (2009)].
In this talk we describe an effective method of electromagnetic field quantization based on the characteristic modes. The diagonal form of the scattering matrix in the characteristic mode basis is the key to significant advantages of the proposed approach. It allows the effective calculation of functions of the scattering matrix, in particular high-order correlation functions, generalized Wigner-Smith matrix and quantum Wigner-Smith operator. Furthermore, it opens the way for effective simulations in different fields of quantum metrology such as the time spent by a wave packet in the process of scattering, forces and torques in optomechanics, Fisher information, and Cramer-Rao bounds in quantum sensing.
We quantize the electromagnetic field in the presence of a nonmoving dielectric sphere in vacuum. The sphere is assumed to be lossless, dispersionless, isotropic, and homogeneous. The quantization is performed using normalized eigenmodes as well as plane-wave modes. We specify two useful alternative bases of normalized eigenmodes: spherical eigenmodes and scattering eigenmodes. A canonical transformation between plane-wave modes and normalized eigenmodes is derived. This formalism is employed to study the scattering of a single photon, coherent squeezed light, and two-photon states off a dielectric sphere. In the latter case, we calculate the second-order correlation function of the scattered field, thereby unveiling the angular distribution of the Hong–Ou–Mandel interference for a dielectric sphere acting as a three-dimensional beam splitter. Our results are analytically derived for a dielectric sphere of arbitrary refractive index and size with a particular emphasis on the small-particle limit. As shown in Phys. Rev. A 108 , 033714 ( 2023 ) PLRAAN 1050-2947 10.1103/PhysRevA.108.033714 , this work sets the theoretical foundation for describing the quantum interaction between light and the motional, rotational, and vibrational degrees of freedom of a dielectric sphere.