Quantum Finite-Difference Time-Domain Scheme

In quantum optics, the conventional method to quantize electromagnetic fields is canonical quantization which is analogue to the classical modal expansion method. Here, on the other hand, we show a quantum finite-difference time-domain scheme that can track the time evolution of quantum electromagnetic operators in the coordinate Hilbert space. This can be done by using coordinate-ladder operators derived from mode-ladder operators via the unitary transformation, and quantum hopping functions. This novel methodology will serve as a guideline for the development of advanced computational algorithms to perform numerical experiments on various quantum optical phenomena, particularly, involved in dispersion and dissipative effects.