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Journal of the Optical Society of America B

Simplest atomic system for sub-Doppler laser cooling

R. Gupta, Sebastião Pádua, Changjian Xie, Herman Batelaan, H. Metcalf

Published Apr 1, 1994• 15 citations
Publisher

Abstract

Sub-Doppler laser cooling requires optical pumping among differently light-shifted ground-state sublevels. We describe a study of the simplest possible angular-momentum configuration that permits all sub-Doppler cooling phenomena. The Jg = 1 ⇒ Je = 0 angular-momentum configuration shows recoil-limited cooling in the two most well-known types of polarization gradient, magnetically induced laser cooling, velocity-selective resonances, transient cooling, and velocity-selective population trapping.

DOI
10.1364/josab.11.000537

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Europhysics Letters (EPL)•Jul 10, 1994•75 citations
Sub-Doppler laser cooling requires optical pumping among differently light-shifted ground-state sublevels. We describe a study of the simplest possible angular-momentum configuration that permits all sub-Doppler cooling phenomena. The Jg = 1 ⇒ Je = 0 angular-momentum configuration shows recoil-limited cooling in the two most well-known types of polarization gradient, magnetically induced laser cooling, velocity-selective resonances, transient cooling, and velocity-selective population trapping.
We describe several one-dimensional sub-Doppler laser-cooling experiments that cool Rb to finite and zero velocities in a magnetic field and polarization gradients. We then present a physical picture that unifies these measurements in terms of coherent two-photon velocity-selective resonances between atomic ground-state sublevels (including Raman resonances). We propose several sub-Doppler cooling schemes without fields or without polarization gradients, based on VSR between nondegenerate ground states.
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.
We have observed a new type of sub-Doppler laser cooling with neither polarization gradients nor magnetic fields. All known sub-Doppler laser cooling methods require one of these two to resdistribute the atomic population among the energy levels. This allows the irreversible processes of optical pumping vels. This allows the irreversible processes of optical pumping (OP) to manipulate the conservative force of light shifts (e.g. resonant exchange between the two beams comprising a standing wave) into a damping force. Our scheme employs stimulated Raman transitions between ground state hyperfine levels of Rb with a bichromatic standing wave, accompanied by a momentum change of {Delta}p = 2{h_bar}k. OP, with {Delta}p = 1{h_bar}k, creates a population imbalance allowing repetition of the Raman process. When the detuning of the light from Raman resonance {delta} is properly chosen, the net momentum exchange damps the atomic motion. Changing {delta} by only {gamma}/6(1 MHz) replaces cooling by heating. This process separates the velocity selective Raman resonance and OP processes differently from others, and helps clarify the role of these different mechanisms.
We present a fully quantum-mechanical analysis of laser cooling of an angular momentum Jg{\mathit{J}}_{\mathit{g}}Jg​=1 to Je{\mathit{J}}_{\mathit{e}}Je​=1 transition in a laser configuration consisting of two counterpropagating linearly polarized laser beams. The essential feature of this configuration is the coexistence of velocity-selective coherent population trapping (VSCPT) and polarization-gradient cooling. The role of polarization-gradient cooling is to provide (i) for short interaction times ``precooling'' of the initial momentum distribution and (ii) in the long-time limit ``confinement of velocities.'' This eventually leads to a larger number of atoms being captured in the dark state when compared with the schme of Aspect et al. [Phys. Rev. Lett. 61, 826 (1988)]. We find that the optimum parameter values for polarization-gradient cooling and VSCPT are in a completely different parameter regime: polarization-gradient cooling works best off resonance and for low intensities, while VSCPT works best on resonance. We can combine the advantages of polarization-gradient cooling and VSCPT in a scheme where we cycle in time between the optimum cooling parameters for both cooling mechanisms.
In Section 8.3.9, we mentioned that the recoil temperature was not the ultimate barrier to cooling. Several mechanisms have been conceived and implemented to concentrate the atomic velocity distribution in a range of values of width less than V R . In contrast to Doppler or Sisyphus cooling, these mechanisms do not appeal to a friction force, but rather to an optical pumping process (see Complement 2B), able to accumulate the atoms in this narrow range of velocities. We now present one such mechanism called ‘velocity-selective coherent population trapping’, considering only the case where the motion occurs in one space direction (the O z -axis). Note, however, that the method generalizes to two or three dimensions. Coherent population trapping Coherent population trapping is a phenomenon that occurs when an atom has a system of three energy levels in the ∧ configuration shown in Figure 8A.1, where each leg of the ∧ interacts with a laser L − or L + . This was discussed in detail in Section 2D.2 of Complement 2D. Here we consider the case where the two ground states g + and L − , have exactly the same energy, and the two lasers have frequencies ω + and ω − , very close to the resonance frequency ω 0 . In this situation, the selectivity of the interactions is obtained via the polarization selection rules (see Complement 2B): if g − , g + and e have magnetic quantum numbers m = −1, +1 and 0, respectively, the laser wave L − is right-circularly polarized (σ + polarization), while the laser wave L + is left-circularly polarized (σ − polarization).
We have theoretically studied a one-dimensional light field configuration which combines velocity-selective coherent-population trapping with the action of a novel kind of sub-Doppler force providing efficient cooling below the recoil limit. The force is based on velocity-induced non-adiabatic passage of atomic population from the non-coupling state to the light-shifted coupling state. We show for 87Rb that within 0.88 ms 35% of an initial distribution of 12k width can be cooled into a 0.5k momentum interval, and that more than 90% of the initial distribution are still confined to 12k width.