Quantum Electromagnetic Finite-Difference Time-Domain Solver

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.

Numerical framework for modeling quantum electromagnetic systems involving finite-sized lossy dielectric objects in free space

“…Motivated by this, we have dedicated over the past years into building numerical frameworks for modeling quantum optics and circuit quantum electrodynamics (QED) phenomena based on classical computational electromagnetics (CEM) methods by reinterpreting and refining the existing math-physics models using various CEM methods [9,[15][16][17][18][19][20]. We believe that our efforts of transplanting CEM methods into quantum physics will become a stepping stone to further advance the research paradigm in the existing quantum technology, which mostly relies on theory and experiments, and accelerate the realization of quantum science and technology.…”