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Diagonalization of Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode-decomposition (CQ-NMD)
- Source :
- Phys. Rev. A 103, 063707 (2021)
- Publication Year :
- 2021
-
Abstract
- We present a new 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 (EM) fields are coupled to non-uniformly 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 non-local dispersion cancellation of an entangled photon pair and Hong-Ou-Mandel (HOM) effect in a dispersive beam splitter.<br />Comment: submitted to Physical Review A (under review)
- Subjects :
- Quantum Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. A 103, 063707 (2021)
- Publication Type :
- Report
- Accession number :
- edsarx.2101.12184
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevA.103.063707