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arXiv:quant-ph/0611238 · Journal of Physics A Mathematical and Theoretical

Analytical solutions for two-level systems with damping

Christian Brouder

Published Jul 19, 2007• 4 citations
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Abstract

A method is proposed to transform any analytic solution of the Bloch equation into an analytic solution of the Landau–Lifshitz–Gilbert equation. This allows for the analytical description of the dynamics of a two-level system with damping. This method shows that damping turns the linear Schrödinger equation of a two-level system into a nonlinear Schrödinger equation. As an application, the effect of damping on self-induced transparency is investigated.

DOI
10.1088/1751-8113/40/31/020

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A method is proposed to transform any analytic solution of the Bloch equation into an analytic solution of the Landau–Lifshitz–Gilbert equation. This allows for the analytical description of the dynamics of a two-level system with damping. This method shows that damping turns the linear Schrödinger equation of a two-level system into a nonlinear Schrödinger equation. As an application, the effect of damping on self-induced transparency is investigated.
In this paper, we consider the nonlinear Schrödinger equation describing the light-atom interaction while taking into account damping due to spontaneous emission.We demonstrate that the optical Bloch equations with damping due to spontaneous emission can be derived immediately from the nonlinear Schrödinger equation without any phenomenology and quantization of radiation.The steady-state solutions of the nonlinear optical Bloch equations are obtained and compared with those obtained for linear optical equations.In this approximation, the light scattering by an atom is considered........
The phenomenon that describes the effect of a coherent medium response to an incident electric field, to which the medium is totally transparent and which undergoes lossless propagation, is known as self-induced transparency (SIT). SIT was first discovered by McCall and Hahn (1969) in the case of nondegenerate two-level atoms. Special solutions for the two-level system were found by Lamb (1971), while the initial value problem for the propagation of a pulse through a resonant two-level optical medium was solved by Inverse Scattering Transform (IST) in [1, 2]. It is possible to formulate the SIT equations in the framework of the IST also in the case of a three-level system, as in [3]. While the associated scattering problem is the same as for the coupled nonlinear Schrödinger equation, the time evolution depends on asymptotic values of the material polarizability envelopes and is highly non-trivial. This talk will address the solution of the initial value problem for the SIT equations for three level systems, for generic preparation of the medium, and
The authors develop a theoretical analysis which describes coherent nonlinear resonant effects where two optical pulses of different frequencies undergo two-photon self-induced transparency (two-photon SIT) in an inhomogeneously broadened three-level system. The field (Maxwell) and atomic (Schrodinger; density matrix representation) equations are coupled in a self-consistent manner by virtue of the resultant macroscopic polarizations at the two frequencies. This treatment is accomplished under circumstances where atomic coherence plays a predominant role. The resulting equations yield a new two-photon area theorem which gives first the intensity dependent, two-photon absorption law analogous to Beer's law for the one-photon transition. Secondly, a 2 pi Lorentzian pulse solution is derived which propagates without loss at the modified pulse velocity.