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IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications

Modeling Rabi oscillation by rigorously solving Maxwell-Schrödinger equation

Yongpin Chen, Yu Mao Wu, Wei E. I. Sha

Published Oct 1, 2015• 1 citation
Publisher

Abstract

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.

DOI
10.1109/mape.2015.7510448

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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.
Abstract—A numerical model based on the finite-difference time-domain method is developed to simulate fluctuations which accompany the dephasing of atomic polarization and the decay of excited state’s population. This model is based on the Maxwell-Bloch equations with c-number stochastic noise terms. We successfully apply our method to a numerical simulation of the atomic superfluorescence process. This method opens the door to further studies of the effects of stochastic noise on light-matter interaction and transient processes in complex systems without prior knowledge of modes. Index Terms—Noise, spontaneous emission, stochastic processes, FDTD methods, Maxwell equations I.
A technique for the numerical simulation of coherent optical responses of the photon echo type formed in resonance media with strong inhomogeneous broadening under the action of femtosecond laser pulses is developed. This approach is based on solving the Maxwell-Bloch equations using the finite-difference time-domain (FDTD) method without application of a fast rotating field and slowly varying envelope approximations. The method can be used to simulate coherent responses in different resonance media with a complex structure of energy levels. The technique was validated using the example of describing experiments on narrowing a photon echo pulse and femtosecond echo processing.
The scientific interest in the analytical solution of the quantum Rabi model is due to the widespread use of this simple model in quantum optics, quantum computing, cavity QED, and nanoelectromechanical systems. This interest is related to the need for the theoretical description of the interaction of a two-level system with a quantum oscillator in the case when the rotating wave approximation fails. In this Letter, we present an approach to the exact diagonalization of the quantum Rabi Hamiltonian. This approach is based on the properties of the Pauli operators and allows us to readily solve the stationary Schrodinger equation for a two-level system. First, we demonstrate the applicability of the approach to the Jaynes-Cummings Hamiltonian to get the well-known solution. Then, we obtain the eigenvalues and eigenstates for the quantum Rabi Hamiltonian using the proposed approach. It is shown that the obtained eigenstates can be represented in the basis of the eigenstates of the Jaynes-Cummings Hamiltonian.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.
This technical note describes the physical model, numerical implementation, and validation of multilevel atomic media for lasers and saturable absorbers in Meep: a free/open-source finite-difference time-domain (FDTD) software package for electromagnetics simulation. Simulating multilevel media in the time domain involves coupling rate equations for the populations of electronic energy levels with Maxwell's equations via a generalization of the Maxwell--Bloch equations. We describe the underlying equations and their implementation using a second-order discretization scheme, and also demonstrate their equivalence to a quantum density-matrix model. The Meep implementation is validated using a separate FDTD density-matrix model as well as a frequency-domain solver based on steady-state ab-initio laser theory (SALT).