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Digest - IEEE Antennas and Propagation Society. International Symposium

Quantum Entanglement Computation Using Canonical Quantization in a Waveguide and Scattering Theory

Jie Zhu, Dong-Yeop Na, Weng Cho Chew

Published Jul 14, 2024• 1 citation
Publisher

Abstract

In this work, we propose two approaches of numerical study of quantum entanglement. In the first approach, canonical quantization with numerical mode decomposition is applied to inhomogeneous dispersive media. The initial quantum state is assumed to be a cat state, which is an entangled state with coherent states. Results in$2\mathrm{D}$modeling will be presented. In the second approach, we study the effect of scattering on momentum-entangled photon pair from spontaneous parametric down-conversion. Scattered two-photon wave function is calculated using computational electromagnetics. Schmidt number is calculated numerically to investigate the enhancement of entanglement after scattering compared to the incident state.

DOI
10.1109/ap-s/inc-usnc-ursi52054.2024.10686559

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In this work, we propose two approaches of numerical study of quantum entanglement. In the first approach, canonical quantization with numerical mode decomposition is applied to inhomogeneous dispersive media. The initial quantum state is assumed to be a cat state, which is an entangled state with coherent states. Results in2D2\mathrm{D}2Dmodeling will be presented. In the second approach, we study the effect of scattering on momentum-entangled photon pair from spontaneous parametric down-conversion. Scattered two-photon wave function is calculated using computational electromagnetics. Schmidt number is calculated numerically to investigate the enhancement of entanglement after scattering compared to the incident state.
In this work, we propose two approaches of investigating quantum entanglement. In the first approach, canonical quantization with numerical mode decomposition is applied to in-homogeneous dispersive media. Nonlocal dispersion cancellation effect of energy-time-entangled photon pair is demonstrated. In the second approach, we study the effect of scattering on spatial-entangled photon pair from spontaneous parametric down-conversion. Schmidt number is calculated numerically. Migration of entanglement between amplitude and phase is studied.
We present a computational framework for canonical quantization in arbitrary inhomogeneous dielectric media by incorporating quantum electromagnetic effects into complex solutions of quantum Maxwell's equations. To do so, the proposed algorithm integrates and performs (1) numerical computation of normal modes and (2) evaluation of arbitrary products of ladder operators acting on multimode Fock states. The former is associated with Hermitian-Helmholtz linear systems using finite-element or finite-difference methods; consequently, the complete set of numerical normal modes diagonalizes the Hamiltonian operators up to floating-point precision. Its Hermiticity is retained, allowing its quantization. Then, we perform quantum numerical simulations of two-photon interference occurring in a 50:50 beam splitter to observe the Hong-Ou-Mandel effect. Our prototype model is useful for numerical analyses on various narrow-band quantum-optical multiphoton systems such as quantum metasurfaces, quantum-optical filters, and quantum electrodynamics in open optical cavities.
Understanding the complex interactions of the quantum light with different media provides valuable insights into potential applications in quantum tomography, microscopy, circuit and network design, and imaging. This thesis investigates quantum light interaction with two types of media: I. Random media entailing multiple scattering (Chapters 2-5), and II. Structured media, specifically designed to control quantum interferences (Chapters 6 and 7). In the first part of the thesis, and through solving the Lippmann-Schwinger equation for collections of small scatterers, a first principle scalar model for multiple scattering in finite-sized random media is developed. This efficient numerical model serves as the basis for investigating the coherent backscattering, a manifestation of weak localization in random media, for several bounded random media and various illuminations. Through employing mode expansion, next, the developed model is adapted to a general class of quantum-optical studies and quantum correlations are successfully derived and analyzed in scattering from finite disordered structures as well as systems of few scatterers. In multiple scattering of two-photon states in weak localization regime, the emergence of coherent two-photon backscattering is presented for the first time in coincidence detection, and it is demonstrated that quantum correlations can be used as a probe of entanglement dimensionality. Multiple scattering of two-photon states results in granular patterns known as speckle patterns. The statistical properties of single- and two-photon speckle patterns in scattering of different states are numerically calculated and the speckle visibilities and relevant parameters are derived. Specifically, the deviation of the probability density functions from negative exponential distributions, traditionally recognized as Rayleigh statistics in classical scattering, is identified, and shown to significantly depend on the presence of entanglement. Lastly, a different numerical implementation (based on COMSOL Multiphysics package) is used to consolidate our findings by incorporating the polarization effects. Coherent backscattering and coherent two-photon backscattering are observed for co-polarized fields in scattering from synthesized disordered media. It is demonstrated that depending on the particle exchange symmetry in polarization entangled excitation, the photons can exhibit statistical tendency to bunch together in the same mode, appear in separate modes (antibunching), or show a mixed response after multiple scattering. These bosonic-, fermionic-, and anyonic-like behaviors are studied in connection with coherent backscattering phenomenon, and it is demonstrated that the degree of enhancement in backscattering depends on the exchange symmetries. The simplicity and effectiveness of the implemented scattering analysis and the significance of the consequent conclusions suggest our approach as a promising platform for ‘numerical experiments’ without the limitations of analytical or semi-analytical models, and a practical tool prior to experiments. In the second part of the thesis, the random media operating as multimode platforms are replaced with engineered surfaces, i.e., metasurfaces, to realize targeted quantum interferences. First, a design roadmap for general lossy, asymmetric, and unbalanced coupling networks is presented, allowing to achieve maximum programmability in two-photon interferences. Next, two switchable metasurface-based coupling networks are designed to control nonclassical two-photon interferences via thermally driven crystallographic phase transitions. Numerical simulations confirm smooth transition between coalescence and anti-coalescence, aiming to address the current need in quantum optics for free-space compact devices creating tunable quantum interferences and acting as fast modulators for the second order quantum correlations. Our proposed compact and rapidly controllable devices pave the way towards new quantum applications as well as improving the current free-space quantum systems.
We introduce and experimentally demonstrate a method to measure the Schmidt number of pure two-photon states entangled in transverse-mode structure. Our method is based on the connection between the Schmidt decomposition in quantum theory and the coherent-mode decomposition in classical coherence theory. We apply the method to two-photon states generated by spontaneous parametric down conversion and show that our results are in excellent agreement with numerical calculations based on the Schmidt decomposition.
We investigate quantum information preserving computational electromagnetics. To do so, we propose two different methods which are (1) numerical canonical quantization and (2) quantum finite-difference time-domain scheme. The proposed algorithms find numerical solutions of quantum Maxwell's equations involved in arbitrary inhomogeneous dielectric media based on the macroscopic theory on quantum electrodynamics; hence, they are useful to study the quantum nature of electromagnetic fields in arbitrary passive and lossless quantum optical instruments. We provide a numerical example associated with two photon interference occurring in a quantum beam splitter, which is the underlying principle of recent quantum technologies.
Quantum entanglement, a fundamental phenomenon in quantum mechanics, presents a unique challenge and opportunity for computation. This paper explores the potential of leveraging entanglement for advanced quantum information processing. We propose a novel representation method based on entanglement, aiming to enhance computational efficiency and scalability. The core mechanism involves carefully designing entanglement states to facilitate targeted computations. This work investigates the practical implications of this approach, highlighting its potential to significantly advance quantum computation. The goal is to provide a foundation for more efficient and versatile quantum algorithms.