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arXiv:cond-mat/0410661

Dynamics of a two-level system in a broadband light field

Tom Savels, Allard P. Mosk, Ad Lagendijk

Published Oct 26, 2004• 0 citations
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Abstract

We provide analytic solutions of the optical Bloch equations for a two-level system interacting with a broadband light field. We will focus on two special examples: incident light with a Lorentzian spectral density and the limit of incident monochromatic light. The results are used to obtain an expression for the nonlinear polarizability of a two-level atom irradiated by a wave with a Lorentzian spectral density.

DOI
10.48550/arxiv.cond-mat/0410661

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We provide analytic solutions of the optical Bloch equations for a two-level system interacting with a broadband light field. We will focus on two special examples: incident light with a Lorentzian spectral density and the limit of incident monochromatic light. The results are used to obtain an expression for the nonlinear polarizability of a two-level atom irradiated by a wave with a Lorentzian spectral density.
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The polarizability of a two-level atom in the presence of radiative damping alone is derived by a Green function calculation. The rotating-wave approximation is not made, either in the interaction of the atom with the incident light or in its interaction with the scattered optical field. In contrast to previous work, the derivation takes account of the modification of the system ground state brought about by the non-rotating-wave part of the latter interaction. The final expression satisfies the optical theorem in addition to the other general requirements on the polarizability.
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.
Degenerate four-wave mixing using broadband, non-transform-limited (incoherent) laser light having a Lorentzian spectral density is treated analytically for a Bloch two-level system. We consider the configuration in which an incoherent beam from a Lorentzian source is split into two beams having distinct k vectors, k and ${\mathit{k}}^{\ensuremath{'}}$. The twin beam along ${\mathit{k}}^{\ensuremath{'}}$ has been subjected to a controllable delay, \ensuremath{\tau}, relative to k. These twin beams, focused into the sample of interest, generate new fourth fields, the signal at ks{\mathit{k}}_{\mathit{s}}ks​=2k-${\mathit{k}}^{\ensuremath{'}}$ being examined here as a function of \ensuremath{\tau}. A set of factorized time correlation (FTC) diagrams is introduced to organize the calculation and to yield both analytic expressions as well as physical insight. Not only is the signal not symmetric in \ensuremath{\tau} but the signal can peak at \ensuremath{\tau}\ensuremath{\ne}0 even in the absence of inhomogeneous broadening. Finally, the physical insights and the use of the FTC diagrams are extended to rationalize several other incoherent light spectroscopies. \textcopyright{} 1996 The American Physical Society.
We derive a set of optical Bloch equations (OBEs) directly from the minimal-coupling Hamiltonian density of the bound-state quantum electrodynamics (bound-state QED). Such optical Bloch equations are beyond the former widely-used ones due to that there is no electric dipole approximation (EDA) on the minimal-coupling Hamiltonian density of the bound-state QED. Then our optical Bloch equations can describe a two-level atom interacting with a monochromatic light of arbitrary wavelength, which are suitable to study the spectroscopy and the Rabi oscillations of two-level atoms in X-ray laser beams since that the wavelength of X-ray is close to an atom to make the electric dipole approximation (EDA) invalid.