Computational quantum electromagnetics: A future pathway for computational electromagnetics

Abstract

First, we emphasize the importance of Maxwell's equations (1865) [1] which have withstood the test of length scales, special relativity (1905) [2], and quantum theory (1927) [3]. Moreover, a differential geometry description of Maxwell's equations (1945) [4] had inspired the Yang-Mills theory (1954) [5], also known as the generalized electromagnetic theory. Vacuum space consists of electron-positron (e-p) pairs that represent nothingness. But when an electromagnetic wave passes through vacuum, the e-p pairs are polarized to form simple harmonic oscillators. The propagation of electromagnetic waves through vacuum is due to the coupling of these simple harmonic oscillators [6]. Figure 1 shows the concept of coupled harmonic oscillators: As more oscillators are coupled together, more resonant frequencies are possible in the system. A continuum of coupled harmonic oscillator (a transmission line) has infinitely many resonant modes. A cavity is a 3D version of a 1D transmission line. The field in a cavity can be decomposed into sum of modes, each of which resonate like a LC tank circuit as shown in Figure 2. Since each of these modes behaves simply like a harmonic oscillator, it can be quantized. From this concept of coupled harmonic oscillators, the quantum Maxwell's equations are derived to be: ∇ × Ĥ(r, t) − ∂ t D(r, t) = Ĵ ext (r, t), ∇ E(r, t) + ∂ t B(r, t) = 0, (1) ∇ · D(r, t) = ϱ ext (r, t), ∇ ·.B(r, t) = 0. (2) The Green's function technique applies when the quantum system is linear time invariant. Hence, past knowledge in computational electromagnetics can be invoked to arrive at these Green's functions. These quantum Maxwell's equations portend well for a better understanding of quantum effects that are observed in many branches of electromagnetics, as well as in quantum optics, quantum information, communication, computing, encryption and related fields. More details about this work can be found in [7-11]. Hence, the combination of computational electromagnetics with quantum theory is cogent for the development of computational quantum optics. In this talk, a new look at the quantization of electromagnetic field will be presented. Examples of field-atom interaction using semi-classical calculation as well as fully quantum calculation will be presented as shown in Figure 3. Connection with computational electromagnetics in these calculations will be pointed out. The use of computational electromagnetics for Casimir force calculation will also be illustrated.