Quantum Information Propagation Preserving Computational Electromagnetics

Abstract

We propose a new methodology, called numerical canonical quantization, to solve quantum Maxwell's equations useful for mathematical modeling of quantum optics physics, and numerical experiments on arbitrary passive and lossless quantum-optical systems. It is based on: (1) the macroscopic (phenomenological) electromagnetic theory on quantum electrodynamics (QED), and (2) concepts borrowed from computational electromagnetics. It was shown that canonical quantization in inhomogeneous dielectric media required definite and proper normal modes. Here, instead of ad-hoc analytic normal modes, we numerically construct complete and time-reversible normal modes in the form of traveling waves to diagonalize the Hamiltonian. Specifically, we directly solve the Helmholtz wave equations for a general linear, reciprocal, isotropic, non-dispersive, and inhomogeneous dielectric media by using either finite-element or finite-difference methods. To convert a scattering problem with infinite number of modes into one with a finite number of modes, we impose Bloch-periodic boundary conditions. This will sparsely sample the normal modes with numerical Bloch-Floquet-like normal modes. Subsequent procedure of numerical canonical quantization is straightforward using linear algebra. We provide relevant numerical recipes in detail and show an important numerical example of indistinguishable two-photon interference in quantum beam splitters, exhibiting Hong-Ou-Mandel effect, which is purely a quantum effect. Also, the present methodology provides a way of numerically investigating existing or new macroscopic QED theories. It will eventually allow quantum-optical numerical experiments of high fidelity to replace many real experiments as in classical electromagnetics.

17 pages, 11 figures, journal article submitted to Physical review A (under review)

References in corpus (20)

• Quantum Cryptography
• Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics
• Metasurface interferometry towards quantum sensors
• Quantum interference between two single photons emitted by independently trapped atoms
• Spontaneous decay in the presence of dispersing and absorbing bodies: general theory and application to a spherical cavity
• Canonical quantization of macroscopic electromagnetism
• Spontaneous decay of an excited atom in an absorbing dielectric
• QED commutation relations for inhomogeneous Kramers-Kronig dielectrics
• Casimir force in absorbing multilayers
• Field quantization in inhomogeneous absorptive dielectrics
• Optimal photons for quantum information processing
• Casimir forces in the time domain II: Applications
• Casimir effect from macroscopic quantum electrodynamics
• On the equivalence of the Langevin and auxiliary field quantization methods for absorbing dielectrics
• Conditions for two-photon interference with coherent pulses
• Comparison of Quantum and Classical Local-field Effects on Two-Level Atoms in a Dielectric
• Electromagnetic Energy, Absorption, and Casimir Forces. Inhomogeneous Dielectric Media
• Dissipative Quantum Electromagnetics
• Quantum simulations of optical systems
• Interfacing a two-photon NOON state with an atomic quantum memory

Cited by in corpus (4)

• Diagonalization of Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode-decomposition (CQ-NMD)
• Numerical Framework for Modeling Quantum Electromagnetic Systems Involving Finite-Sized Lossy Dielectric Objects in Free Space
• Matrix product states and numerical mode decomposition for the analysis of gauge-invariant cavity quantum electrodynamics
• Circuit quantum electrodynamics: A new look toward developing full-wave numerical models