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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Semiclassical consideration of laser cooling of unbound atoms in nondissipative optical lattice

Наталья Александровна Матвеева, А. В. Тайченачев, Anatolii M Tumaikin, Valeriy I. Yudin

Published Jun 15, 2007• 0 citations
Publisher

Abstract

The semiclassical theory of laser cooling is applied for the analysis of cooling of unbound atoms with the values of the ground and exited state angular moments 1/2 in a one-dimensional nondissipative optical lattice. We show that in the low-saturation limit with respect to the pumping field a qualitative interpretation of the cooling mechanisms can be made by the consideration of effective two-level system of the ground-state sublevels. It is clarified that in the limit of weak Raman transitions the cooling mechanism is similar to the Doppler mechanism, which is known in the theory of two-level atom. In the limit of strong Raman transitions the cooling mechanism is similar to the known Sisyphus mechanism. In the slow atom approximation the analytical expressions for the coefficients of friction, spontaneous and induced diffusion are given, and the kinetic temperature is estimated.

DOI
10.1117/12.752256

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The semiclassical theory of laser cooling is applied for the analysis of cooling of unbound atoms with the values of the ground and exited state angular moments 1/2 in a one-dimensional nondissipative optical lattice. We show that in the low-saturation limit with respect to the pumping field a qualitative interpretation of the cooling mechanisms can be made by the consideration of effective two-level system of the ground-state sublevels. It is clarified that in the limit of weak Raman transitions the cooling mechanism is similar to the Doppler mechanism, which is known in the theory of two-level atom. In the limit of strong Raman transitions the cooling mechanism is similar to the known Sisyphus mechanism. In the slow atom approximation the analytical expressions for the coefficients of friction, spontaneous and induced diffusion are given, and the kinetic temperature is estimated.
A quasi-classical theory of laser cooling is applied to the analysis of cooling of unbound atoms with the angular momenta 1/2 in the ground and excited states in a one-dimensional nondissipative optical lattice. In the low-saturation limit with respect to the pumping field, the mechanisms of cooling can be interpreted within the framework of an effective two-level system of ground-state sublevels. In the limit of weak Raman transitions, the mechanism of cooling of unbound atoms is similar to the Doppler mechanism known in the theory of a two-level atom; in the limit of strong transitions, the mechanism of cooling is analogous to the well-known Sisyphys mechanism. In the slow-atom approximation, analytical expressions are obtained for the friction (drag) coefficient and the induced and spontaneous diffusion, and the kinetic temperature is estimated.
Using the basis of Wannier states, we study the local dynamics of polarization gradient cooling for an atom driven on a ${J}_{g}=2\ensuremath{\rightarrow}{J}_{e}=3$ transition by a one-dimensional optical lattice. This analysis allows us to formulate a physical picture of the cooling mechanism, analogous to Sisyphus cooling for a ${J}_{g}=1/2\ensuremath{\rightarrow}{J}_{e}=3/2$ atom, which depends strongly on coherences in the Zeeman sublevels of the ground state. In addition, we are able to explain the steady-state properties of the laser-cooled atoms in a regime where the standard semiclassical analysis breaks down.
We present two cooling mechanisms that lead to temperatures well below the Doppler limit. These mechanisms are based on laser polarization gradients and work at low laser power when the optical-pumping time between different ground-state sublevels becomes long. There is then a large time lag between the internal atomic response and the atomic motion, which leads to a large cooling force. In the simple case of one-dimensional molasses, we identify two types of polarization gradient that occur when the two counterpropagating waves have either orthogonal linear polarizations or orthogonal circular polarizations. In the first case, the light shifts of the ground-state Zeeman sublevels are spatially modulated, and optical pumping among them leads to dipole forces and to a Sisyphus effect analogous to the one that occurs in stimulated molasses. In the second case (σ+−σ− configuration), the cooling mechanism is radically different. Even at very low velocity, atomic motion produces a population difference among ground-state sublevels, which gives rise to unbalanced radiation pressures. From semiclassical optical Bloch equations, we derive for the two cases quantitative expressions for friction coefficients and velocity capture ranges. The friction coefficients are shown in both cases to be independent of the laser power, which produces an equilibrium temperature proportional to the laser power. The lowest achievable temperatures then approach the one-photon recoil energy. We briefly outline a full quantum treatment of such a limit.
A theoretical analysis is given for 1-D laser cooling below the Doppler limit of J = 1/2 ground- state atoms. The laser field consists of a pair of counterpropagating, linearly polarized low- power beams, whose polarization directions differ by an angle θ (0 ≤ θ ≤ π/2). For θ ≪ 1, the effective optical pumping time is shown to increase strongly near the nodes of the standing wave and the cooling force can be much larger than that for θ ~1. Moreover, for θ ≪ 1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for θ ~ 1. As a consequence it is possible to achieve an equilibrium atomic distribution that, for θ ≪ 1, is characterized by a mean kinetic energy lower than that predicted to occur for θ = π/2. The equilibrium velocity distribution is not necessarily Maxwellian and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms are trapped in the vicinity of the laser field nodes. An explanation for these effects is given in terms of Sisyphus cooling.
A theoretical analysis is given for one-dimensional laser cooling below the Doppler limit of J=1/2 ground-state atoms. The laser field consists of a pair of counterpropagating, linearly polarized, low-power beams, whose polarization directions differ by an angle \ensuremath{\theta} (0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}/2). For \ensuremath{\theta}\ensuremath{\ll}1, the effective optical-pumping time is shown to increase strongly near the nodes of the standing wave, and the cooling force can be much larger than that for \ensuremath{\theta}=\ensuremath{\pi}/2. Moreover, for \ensuremath{\theta}\ensuremath{\ll}1, it can be shown that the stimulated part of the atomic diffusion is reduced considerably as compared with that for \ensuremath{\theta}=\ensuremath{\pi}/2. As a consequence it is possible to achieve an equilibrium atomic distribution that, for \ensuremath{\theta}\ensuremath{\ll}1, is characterized by a mean kinetic energy that is lower than that predicted to occur for \ensuremath{\theta}=\ensuremath{\pi}/2. The equilibrium velocity distribution is not necessarily Maxwellian, and thus the temperature of the atomic ensemble may not be well defined. The achievable kinetic energy is so small that the cooled atoms may be trapped in the vicinity of the laser-field nodes.
A method of sideband Raman cooling to the vibrational ground state of the m=0m=0m=0 Zeeman sublevel in a far-detuned two-dimensional optical lattice is proposed. In our scheme, the Raman coupling between vibrational manifolds of the adjacent Zeeman sublevels is shifted to the red sideband due to the ac Stark effect induced by a weak pump field. Thus cooling and optical pumping to m=0m=0m=0 are achieved by purely optical means with coplanar cw laser beams. The optical lattice and cooling parameters are estimated in the framework of simple theoretical models. An application of the transverse sideband cooling method to frequency standards is discussed. Coherent population trapping for the sideband Raman transitions between the degenerate vibrational levels is predicted.