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Journal of the Optical Society of America B

Analytical solutions of the time-dependent radiation force for a two-level atom interacting with a continuous-wave single-mode laser

Heung‐Ryoul Noh, Wonho Jhe

Published Aug 6, 2010• 7 citations
Publisher

Abstract

This work presents an analytical calculation of the time-dependent radiation forces on a two-level atom interacting with a single-mode laser field. Such a closed and compact expression of the radiation forces is derived by solving the optical Bloch equations analytically. It is confirmed, in particular, that the radiation force consists of reactive as well as dissipative components, whose explicit analytical forms of the temporal solutions can be explicitly obtained. The succinct analytical solutions of the radiation forces may be helpful for a convenient and intuitive description of the complex atomic dynamics such as interaction with various laser fields.

DOI
10.1364/josab.27.001712

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This work presents an analytical calculation of the time-dependent radiation forces on a two-level atom interacting with a single-mode laser field. Such a closed and compact expression of the radiation forces is derived by solving the optical Bloch equations analytically. It is confirmed, in particular, that the radiation force consists of reactive as well as dissipative components, whose explicit analytical forms of the temporal solutions can be explicitly obtained. The succinct analytical solutions of the radiation forces may be helpful for a convenient and intuitive description of the complex atomic dynamics such as interaction with various laser fields.
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Theories of radiation pressure based on rate equations and on the optical Bloch equations are developed within a common framework that allows comparison of the two. The latter method is used to determine the time dependence of the mean momentum of a two-level atom subjected to monochromatic coherent light for general values of various broadening parameters and detuning. The expression for the corresponding radiation pressure force in the limit of steady-state atomic level populations includes previous results as special cases. The rate equation method provides a fully quantum-mechanical calculation of an expression obtained by Einstein for the rate of change of mean-square atomic momentum in thermal equilibrium.
We are concerned with an analytic separation approach of the optical Bloch equations in the case of the two-level atom interacting with a classical light. The conditions that permit a complete separation of these equations are extracted in a natural manner and the exact solutions are obtained. A theoretical comparison with Torrey method is given. In this context, we find that the transient regime, valid from the instant of the application of the laser on atom, is significant for the evolution of forces and the dynamics before the steady-state regime will be reached. The case of Eu3 + ion moving in plane-light wave and standing-wave is treated with some details. The implications of the results for operating atoms and ions using laser light are discussed.