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Soviet Journal of Quantum Electronics

Cooling of internal degrees of freedom of atoms and molecules using resonance radiation

A. A. Stuchebryukhov

Published Sep 30, 1981• 0 citations
Publisher

Abstract

An analysis is made of the statistics of an ensemble of one-dimensional (classical) nonlinear oscillators in a thermostat excited by an external harmonic force. It is found that, under certain conditions, the action of a harmonic force may suppress the thermal excitation of oscillator vibrations. On the basis of the proposed model, it is concluded that internal degrees of freedom of gas atoms and molecules may be cooled by resonance radiation.

DOI
10.1070/qe1981v011n09abeh008213

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An analysis is made of the statistics of an ensemble of one-dimensional (classical) nonlinear oscillators in a thermostat excited by an external harmonic force. It is found that, under certain conditions, the action of a harmonic force may suppress the thermal excitation of oscillator vibrations. On the basis of the proposed model, it is concluded that internal degrees of freedom of gas atoms and molecules may be cooled by resonance radiation.
Mechanical motions of atoms near their equilibrium geometry are approximated by a universal mapping on a collection of independent harmonic oscillators. The respective frequencies are characteristic to the material, for example, lattice phonons or molecular vibrations. The quantum description of atomic motions involves the solution of the Schrödinger equation for the harmonic oscillator in the space of proper wave functions. The energy levels obtained are shown to be equally spaced where the level spacing is proportional to the oscillator frequency. The stationary solutions are identified in terms of Hermite polynomials, demonstrating remarkable differences from the classical harmonic oscillator. The importance of the zero-point energy is emphasized in the context of the stability of chemical bonds, where the Harmonic approximation is shown to be reasonably valid for typical interatomic bonds in standard thermal conditions. This explains the relevance of the harmonic approximation for analyzing the absorption spectrum of infrared radiation by molecules.
Optimal control theory is applied to laser cooling of molecules. The objective is to cool vibrations, using shaped pulses synchronized with the spontaneous emission. The optimal mechanism is found to operate by a “vibrationally selective coherent population trapping”. The trapping condition is that the instantaneous phase of the laser is locked to the phase of the transition dipole moment of v=0 with the excited population. The molecules that reach v=0 by spontaneous emission are then trapped, while the others are continually repumped.
Theoretical progress in the cooling of internal degrees of freedom of molecules using shaped laser pulses is reported. The emphasis is on general concepts and universal constraints. Several alternative definitions of cooling are considered, including reduction of the von Neumann entropy, −tr{ρ̂logρ̂} and increase of the Renyi entropy, tr{ρ̂2}. A distinction between intensive and extensive considerations is used to analyse the cooling process in open systems. It is shown that the Renyi entropy increase is consistent with an increase in the system phase space density and an increase in the absolute population in the ground state. The limitations on cooling processes imposed by Hamiltonian generated unitary transformations are analyzed. For a single mode system with a ground and excited electronic surfaces driven by an external field it is shown that it is impossible to increase the ground state population beyond its initial value. A numerical example based on optimal control theory demonstrates this result. For this model only intensive cooling is possible which can be classified as evaporative cooling. To overcome this constraint, a single bath degree of freedom is added to the model. This allows a heat pump mechanism in which entropy is pumped by the radiation from the primary degree of freedom to the bath mode, resulting in extensive cooling.
The present state of research on the cooling of atomic ensembles by means of laser radiation pressure is discussed. First the basic theory of resonance radiation pressure is reviewed. The effect of recoil on the drift and fluctuations of the momentum of an atom interacting with resonance radiation is examined. There is an analysis of the forces acting on an atom in some simple light fields: a traveling plane wave, a Gaussian beam, and counterpropagating Gaussian beams. The review then focuses on the monochromatization of atoms by resonance radiation pressure and related methods for laser cooling of atoms. The roles played by the radiation pressure force and by momentum diffusion in shaping the narrow velocity distributions of the ensemble of atoms are analyzed. The lowest temperature obtainable in the radiation cooling of atoms is estimated. The basic experimental methods for laser cooling of atomic beams are described. Problems of the three-dimensional cooling of atomic ensembles and problems of localizing cold atoms in light fields, steady-state magnetic fields, and electrostatic fields are discussed. The review concludes with a discussion of some applications of cold atoms in high-precision spectroscopy, frequency standards, and atomic physics.