Quantum information 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 (L.

Quantum Electromagnetic Finite-Difference Time-Domain Solver

“…Many previous theoretical works [2,17,18] showed that, in principle, the concept of the standard canonical quantization in the vacuum can be extended to that of inhomogeneous and anisotropic lossless media once normal modes of the systems are properly found even though their closed form solutions are often restricted due to the geometrical complexity. As an effective solution to such difficulty, for the first time, we recently proposed in Reference [36] the so-called numerical canonical quantization in which normal modes are numerically obtained by solving the Helmholtz wave equations for arbitrary inhomogeneous dielectric media through computational electromagnetic (CEM) tools such as finite-difference or -element methods.…”

“…In a periodic vacuum box, there is an arbitrarily-shaped inhomogeneous dielectric object. To extract traveling-wave normal modes of the system, we use Bloch-periodic boundary condition instead of periodic boundary condition under which only standing-wave normal modes can exist [36].…”

“…Using a countably-finite set (N k = N x number) of numerical normal modes, one can quantize a vector potential operator [36] aŝ…”

“…(40) In our computer simulation, we set x 1 = x l and x 2 = x r , as illustrated in Figure 3, and τ = δx 0 /c [s]. We used same simulation parameters used in Reference [36]. Also, One can evaluate (40) in the same way explained in Reference [36], which is the crucial part of creating quantum effects.…”

“…Also, One can evaluate (40) in the same way explained in Reference [36], which is the crucial part of creating quantum effects. 4 depicts τ versus g (2) (τ) for three different cases: (1) numerical canonical quantization, (2) Q-FDTD with exact initialization (with numerical normal modes obtained from solving the Helmholtz wave equation), and (3) Q-FDTD with approximate initialization by using from (36) to (39). There are excellent agreement in all cases, thus, the Q-FDTD scheme with approximate initialization is correctly validated.…”