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Physical Review A

Maxwell-Bloch system on a lattice

N. M. Bogoliubov, Andrei V. Rybin, R. Bullough, JUSSI TIMONEN

Published Aug 1, 1995• 12 citations
Publisher

Abstract

An exactly solvable lattice version of the Maxwell-Bloch system, which describes resonant interaction of light with a medium of two-level atoms, is derived. The Poisson structures of both the discrete and the continuum limit models are analyzed with and without inhomogeneous broadening, and quantizations of all of these cases are described. The eigenenergy spectra are given.

DOI
10.1103/physreva.52.1487

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An exactly solvable lattice version of the Maxwell-Bloch system, which describes resonant interaction of light with a medium of two-level atoms, is derived. The Poisson structures of both the discrete and the continuum limit models are analyzed with and without inhomogeneous broadening, and quantizations of all of these cases are described. The eigenenergy spectra are given.
Maxwell-Bloch system describing the resonant propagation of electromagnetic pulses in both two-level media with degeneracy in angle moment projection and three-level media with equal oscillator forces is considered. The inhomogeneous broadening of energy levels is accounted. Binary Darboux Transformation generating the solutions of the system is constructed. Pulses corresponding to the transition between levels with largest population difference are shown to be stable. The solution describing the propargation of pulses in the medium exited by the periodic wave is obtained. The hierarchy of infinitesimal symmetries is obtained by means of Darboux transformation.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium.The convergence and stability of this numerical method are proved by comparing with the analytic solutions and area theorem derived under special condition.The simulations of arbitrary conditions is discussed by employing this method and analyze the pulse evolution for different detunings,relaxation times and inhomogeneously broadened linewidthes.The established numerical method provides a good way to have further study about the coherent interaction of short optical pulses with resonant mediums,and can be used to solve the corrections of Maxwell-Bloch equations.
A detectable nonlinear response between light and matter depends on one of two key ingredients: Either there is a resonance between the light wave and some natural oscillation mode of the material, or the light is sufficiently intense. In this chapter, the authors let the matter variables themselves play active roles and derive coupled nonlinear differential equations for the electric and matter fields. They outline the use of Schrodinger's equation to derive the Bloch equations, which describe the dynamics of the oscillators of matter and help to derive the Maxwell equation for the envelope of an almost monochromatic electromagnetic wave. The authors analyse the case of two distinct co- or counter-propagating waves interacting with a three-level medium where both waves excite separate quantum transitions sharing a common level. They also help to derive an effective two-level atom model that describes two-photon absorption and stimulated Raman scattering.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations,which describe the optical pulse propagation and interaction with homogeneously broadened two-level medium.The convergence and stability of this numerical method are also proved by comparing with the analytic solutions derived under special condition,and the method maintains its erroneous exponents and is applicable.Simulations of arbitrary conditions are discussed by employing this new method,and the evolutions of pulse and Bloch vectors for different detunings,relaxation times and initial input pulse power are analyzed.The established numerical method can be used to solve the Maxwell-Bloch equations and their corrections.
This tutorial article provides a detailed mathematical overview of the Optical Bloch equation describing the interaction of the two level atom with the Electromagnetic radi- ation field. The equations have been derived in the weak atom field coupling limit. The notion of the optical Bloch equations has been introduced in a systematic process starting from the interaction of the two level atom with the semiclassical radiation field which cannot completely the idea of the Spontaneous emission process later which was included theoretically by,Weigner-Weisskopf theory of spontaneous emission .In the later part of the article the optical Bloch equations has been derived exactly by treating the radiation field quantum mechanically. The radiation field has been quantized using the free field quantization techniques in the Coloumb Gauge with which the Lindblad Master equation has been derived systematically in the weak coupling limit. The optical Bloch equations has been derived for the resonantly driven two level atom from the Lindblad type master equation and later those equations has been solved in the steady state limit. The article also discuss the analytical aspects of describing the theory of atom matter interaction using full-fledged quantum mechanical approach.