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arXiv:1502.00294 · European Journal of Physics

Conservation laws and laser cooling of atoms

Giuseppe Giuliani

Published Aug 28, 2015• 2 citations
arXivHTMLPDF

Abstract

Abstract The straightforward application of energy and linear momentum conservation to the absorption/emission of photons by atoms allows us to establish the essential features of laser cooling of two level atoms at low laser intensities. The lowest attainable average kinetic energy of the atoms depends on the ratio between the natural linewidth and the recoil energy and tends to E R as tends to zero (in one dimension). This treatment, like the quantum mechanical ones, is valid for any value of the ratio and contains the semiclassical theory of laser cooling as the limiting case in which .

DOI
10.1088/0143-0807/36/6/065008

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Abstract The straightforward application of energy and linear momentum conservation to the absorption/emission of photons by atoms allows us to establish the essential features of laser cooling of two level atoms at low laser intensities. The lowest attainable average kinetic energy of the atoms depends on the ratio between the natural linewidth and the recoil energy and tends to E R as tends to zero (in one dimension). This treatment, like the quantum mechanical ones, is valid for any value of the ratio and contains the semiclassical theory of laser cooling as the limiting case in which .
We present a quantum theory of one-dimensional laser cooling of free atoms using a transition with a J = 0 ground state and a J = 1 excited state. This treatment is valid both for broad lines (recoil energy small compared with the energy width ℏ Γ of the excited level) and for narrow lines. For broad lines we recover the well-known cooling limit for a two-level transition (∼ℏΓ/2), whereas for a narrow line the cooling limit is found to be of the order of the recoil energy. The stationary momentum distribution is obtained for both cases and is found to be close to the one obtained by Monte Carlo simulations.
We study laser cooling of atoms with narrow-line optical transition, i.e. in regimes when quantum nature of laser-light interactions results significant effect on atom kinetics. We demonstrate the minimum of laser cooing temperature is reached for the light field detuning close to -3 recoil frequency, i.e. is much differ from standard Doppler cooling theory is used for semiclassical description of laser cooling. We define a set of dimensionless parameters that describe the steady state solution of cold atom distribution in laser light and cooling time. The results can be used for analysis an optimal conditions of laser cooling of atoms with narrow lines Ca, Sr and Mg are of interest for optical time standards.
This paper reviews the basic theory of the mechanical action of light in resonant interaction with atoms. At present the main application is laser cooling, but the approach is applicable to a broader range of phenomena. It is based on an adiabatic elimination philosophy, which turns out to give the lowest-order quantum corrections to the behavior found when the photon momentum goes to zero. Hence it is called a semiclassical theory. In this manner a subjective but consistent approach can be presented; other treatments are incorporated or mentioned at the appropriate places. Both the classical and the quantum-mechanical approach are discussed. Those readers who wish to obtain only a heuristic overview of the phenomena can concentrate on Sec. III, which treats both the photon momentum effects and their connection with photon counting statistics. The detailed theoretical treatment utilizes Wigner functions and Fokker-Planck techniques. The ensuing theory is applied both to the cooling of free particles and trapped ones. The paper ends with an extensive bibliography, where the author lists most papers of interest for research into the mechanical manifestations of light. For completeness, many papers are included that are not explicitly mentioned in the text.
In sub-Doppler laser cooling of atoms, the lowest temperatures are known to occur at low (but not too low) excitation, and the temperature increases roughly linearly with laser intensity. However, under conditions for which the lowest temperatures are obtained, the small velocity capture range and low optical pumping rate limit the number of atoms that can be collected into the cold sample. In this study, we present measurements for laser cooling of Rb and metastable He atoms for two counterpropagating laser beams with orthogonal linear polarization (lin\ensuremath{\perp}lin) over a wide range of saturation parameters and laser detunings, together with results of semiclassical (Fokker-Planck) and quantum density matrix calculations. We find that at higher laser intensity, a larger number of atoms can be collected into a final velocity distribution that is significantly narrower than that given by a linear extrapolation vs the square root of laser intensity. Two cooling mechanisms are at work: the sub-Doppler Sisyphus mechanism and also Doppler cooling. Under certain conditions that we discuss, Doppler cooling aids Sisyphus cooling by collecting high-velocity atoms beyond the Sisyphus capture range. He∗{\mathrm{He}}^{*}He∗ presents a rather unusual situation in that the minimum average kinetic energy (Eav){(E}_{\mathrm{av}})(Eav​) for purely Sisyphus cooling is comparable to the minimum value of Eav{E}_{\mathrm{av}}Eav​ with Doppler cooling alone.
The usual case in laser cooling is that the atomic linewidth ħγ is much greater than the recoil energy ER = ħ2k2/2 m. Considering the recent demonstration of laser cooling to kBT <<ħγ,1 It seems reasonable to reconsider laser cooling where ERħγ. In this case the Doppler shift ħk2/m of a recoil velocity is large compared to the linewidth and an analytic treatment is difficult. We have developed a Monte Carlo simulation of 3-D laser cooling (optical molasses) which applies to any value of ħγ/ER.