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United States National Committee of URSI National Radio Science Meeting

Investigating Quantum Entanglement Using Canonical Quantization and Scattering Theory

Jie Zhu, Dong-Yeop Na, Weng Cho Chew

Published Jan 9, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.23919/usnc-ursinrsm60317.2024.10464658

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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.
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.
We present a math-physics modeling approach called canonical quantization with numerical mode decomposition for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic fields are coupled to nonuniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a countably finite set of time-harmonic eigenmodes that diagonalizes the Hamiltonian, and (4) perform the subsequent canonical quantization with mode decomposition. Moreover, we provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations, such as nonlocal dispersion cancellation of an entangled photon pair and the Hong-Ou-Mandel effect in a dispersive beam splitter.