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Quantum Electromagnetic Finite-Difference Time-Domain Solver
Version 1
: Received: 23 March 2020 / Approved: 25 March 2020 / Online: 25 March 2020 (04:23:31 CET)
A peer-reviewed article of this Preprint also exists.
Na, D.-Y.; Chew, W.C. Quantum Electromagnetic Finite-Difference Time-Domain Solver . Quantum Reports 2020, 2, 253-265. Na, D.-Y.; Chew, W.C. Quantum Electromagnetic Finite-Difference Time-Domain Solver . Quantum Reports 2020, 2, 253-265.
Abstract
We employ another approach to quantize electromagnetic fields in the coordinate space, instead of the mode (or Fourier) space, such that local features of photons can be efficiently, physically, and more intuitively described. To do this, coordinate-ladder operators are defined from mode-ladder operators via the unitary transformation of systems involved in arbitrary inhomogeneous dielectric media. Then, one can expand electromagnetic field operators through the coordinate-ladder operators weighted by non-orthogonal and spatially-localized bases, which are propagators of initial quantum electromagnetic (complex-valued) field operators. Here, we call them QEM-CV-propagators. However, there are no general closed form solutions available for them. This inspires us to develop a quantum finite-difference time-domain (Q-FDTD) scheme to numerically time evolve QEM-CV-propagators. In order to check the validity of the proposed Q-FDTD scheme, we perform computer simulations to observe the Hong-Ou-Mandel effect resulting from the destructive interference of two photons in a 50/50 quantum beam splitter.
Keywords
Quantum Maxwell's equations; finite-difference time-domain
Subject
Physical Sciences, Optics and Photonics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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