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Frontiers in Optics

Superradiance and Rabi Oscillation in FDTD Simulation with use of Multi-Level Medium Rate Equations

Yingyan Huang, Zhengquan Zhang, Seng‐Tiong Ho

Published Jan 1, 2008• 0 citations
Publisher

Abstract

Lorentzian-gain model used in FDTD cannot model superradiance and Rabi oscillation. We show that superradiance and Rabi oscillation can occur in the recent multi-level multi-electron FDTD model and shall be dealt with carefully in applications.
DOI
10.1364/fio.2008.fthp5

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When an atom (or two-level system) is illuminated by a coherent beam of photons, it will cyclically absorb photons and re-emit them by stimulated emission, which is called Rabi oscillation. By using the finite-difference time-domain (FDTD) method, Maxwell-Schrödinger equation is solved for modeling the Rabi oscillation. The proposed method is compared with the existing approximate theoretical models. It is found that these approximate models break down in certain cases where a rigorous self-consistent numerical approach is needed. This work is helpful for the EM simulation of emerging nanodevices or next-generation quantum electrodynamic systems.
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Rabi oscillations in semiconductor heterostructures generating superradiance at room temperature have been studied experimentally and theoretically. An anomalously long oscillation decay time has been observed experimentally in structures with a low- Q cavity. A theoretical model of the dynamics of the coherent interaction of an electron–hole system with an electromagnetic field in such a cavity, which is based on the classical Maxwell–Bloch equations, predicts a decay time more than an order of magnitude shorter than that measured experimentally. It is suggested that one of the possible reasons for this effect may be the presence of quantum feedback arising from two counterpropagating electromagnetic waves, which mediate the interaction of two coherent electron–hole ensembles and lead to their quantum entanglement with the electromagnetic field.
A collection of NNN Rydberg atoms and a resonant millimeter-wave cavity are shown to exchange energy back and forth at a rate $2(\frac{d}{\ensuremath{\hbar}}){\mathcal{E}}_{0}\sqrt{N}$, where ddd is the electric dipole matrix element of the atomic transition and E0{\mathcal{E}}_{0}E0​ the "field per photon" in the cavity. This experiment is a demonstration of self-induced Rabi oscillations in a two-level atom system coupled to a single electromagnetic field mode and can also be considered as a very simple illustration of "ringings" in superradiant emission.
A faster numerical method based on FDTD for the four energy level atomic system is present here. The initial conditions for the electrons of each level are achieving while the fields are in steady state. Polarization equation, rate equations of electronic population and Maxwell’s equations were used to describe the coupling between the atoms and electromagnetic wave. Numerical simulations, based on a finite-difference time-domain (FDTD) method, were utilized to obtain the population inversion and lasing threshold. The validity of the model and its theory is confirmed. The time, which we can observe the lasing phenomenon, is much shorter in our new model. Our model can be put into using in large scale simulations in mutiphysics to reduce the total simulated time.