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Optica Acta International Journal of Optics

Rate-equation and Bloch-equation Theories of Radiation Pressure on Two-level Atoms

A Al-Hilfy, R. Loudon

Published Sep 1, 1985• 5 citations
Publisher

Abstract

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.

DOI
10.1080/713821831

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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.
The radiation pressure and laser cooling of a V-type three level atom in coherent fields in a squeezed vacuum are considered. From the Hamiltonian of the atomic system, making use of Born-Markoff approximation, the optical Bloch equations are derived. Using the adiabatic approximation, the expression of the mean dissipative force are acquired. The achievable equilibrium temperature is given by the quantum regression theorem and Einstein relation. The dependence of the spontaneous radiation pressure and ultimate temperature on quantum interference, average photon number and Rabi frequency are analyzed. The result shows that temperatures lower than the Doppler limit can be achieved.
The motion of an atom in an intense resonant standing laser wave is studied using the Ehrenfest-Bloch equations. Two approaches are taken to determine the radiation or light pressure force on the atom. The first, an attempt to find a Fourier series solution to the optical Bloch equations failed, but Fourier coefficient recursion formulas were found. The second, a numerical calculation of the Bloch variables and the radiation force was successful in obtaining plots of the instantaneous values. The effect of assuming constant atomic velocity is studied, and Fast Fourier Transform discrete harmonic frequency spectra of one of the Bloch variables and the light pressure force are obtained. Finally, the Ehrenfest-Bloch equations are compared with other theories of resonant radiation pressure. (Thesis).
This paper mainly studies the radiation pressure of a moving ladder-type three-level atom driven by a superposition of a bichromatic laser wave with a broad-band squeezed vaccum and obtains the steady-state expression for the radiation force.Frist,from the master equations for a moving ladder-type three-level atom driven by a superposition of a bichromatic laser wave with a broad-band squeezed vaccum,we derive the equations for the atomic density matrix element.Second,by choosing proper scaled variables,Bloch equations for the atomic population are obtained.Then,from Heisenberg equation for atomic momentum,considering the adiabatic approximation,the mathematical expression of the mean radiation pressure is obtained.At last,by considering the steady-state case in which the atomic population doesn't vary with time and the condition,the steady-state expression of the radiation pressure is obtained.
Radiation pressure and laser cooling of a moving three-level ladder-type atom in bichromatic travelling fields are considered. The dependence of the force on parameters such as detunings, Rabi frequencies and spontaneous decay rates is calculated numerically and shown graphically and analytical expressions for the force are obtained for some special parameter values. It is shown that the radiation pressure shows Doppler-shifted resonance peaks resulting respectively from one-photon and two-photon transitions. Using the present scheme, Doppler cooling of sodium exploiting the 3 2 S 1/2 –3 2 P 3/2 –3 2 D 5/2 cascade transitions is investigated. It is found that temperatures lower than the Doppler limit can be achieved.
The study of the motion of neutral atoms under the action of light fields dates back to work of Albert Einstein published as early as 1916. This chapter describes a sample of molecules subjected to a thermal light field. It discusses atoms having only two levels at some optical energy separation. The chapter also discusses radiation pressure in two important examples of light fields, plane travelling and plane standing waves. The two-level atom interacting with a monochromatic laser mode represents one of the most fundamental models in quantum optics and has been extensively studied. The light-shift is an important phenomenon at the basis of many laser cooling mechanisms. In the presence of interaction, the combined system of an ‘atom plus light-field’ is often referred to as the ‘dressed atom’. The steady state temperature in Equation represents the minimum temperature that can be achieved with radiation pressure cooling and can be quite small.