Transient laser cooling (TLC) can produce cooling and heating, but often with the opposite detuning from that found in steady state. In TLC the time scale is set by the optical pumping (OP) rate to a state not coupled by the laser field. The combination of such OP processes and the conservative light shift potential U{sub o}sin{sup 2}kz leads to TLC. The average PE of atoms entering a standing wave is U{sub o}/2. They experience the optical force until undergoing OP to an uncoupled state, which is more likely to happen at high light intensity, near an antinode. For {delta} > 0 this means higher PE and thus lower KE, and conversely for {delta} < 0. In TLC there is no final {open_quotes}temperature{close_quotes} resulting from competition between a damping force and diffusive heating. Instead the changes in KE are bounded by U{sub o} so that the signal widths decrease with intensity. This can result in sub-Doppler widths. We have made two independent theoretical studies of these experiments. In a semiclassical calculation we evolve the motion for a calculated OP time and calculate the velocity distribution. We have also performed fully quantum mechanical calculations of the motion of atoms in themore » standing wave whose basis set consists of product states of internal and external atomic coordinates.« less
Transient laser cooling (TLC) can produce cooling and heating, but often with the opposite detuning from that found in steady state. In TLC the time scale is set by the optical pumping (OP) rate to a state not coupled by the laser field. The combination of such OP processes and the conservative light shift potential U{sub o}sin{sup 2}kz leads to TLC. The average PE of atoms entering a standing wave is U{sub o}/2. They experience the optical force until undergoing OP to an uncoupled state, which is more likely to happen at high light intensity, near an antinode. For {delta} > 0 this means higher PE and thus lower KE, and conversely for {delta} < 0. In TLC there is no final {open_quotes}temperature{close_quotes} resulting from competition between a damping force and diffusive heating. Instead the changes in KE are bounded by U{sub o} so that the signal widths decrease with intensity. This can result in sub-Doppler widths. We have made two independent theoretical studies of these experiments. In a semiclassical calculation we evolve the motion for a calculated OP time and calculate the velocity distribution. We have also performed fully quantum mechanical calculations of the motion of atoms in themore » standing wave whose basis set consists of product states of internal and external atomic coordinates.« less
We observed a new type of sub-Doppler cooling that employs neither polarization gradients nor magnetic fields, and involves neither a damping force nor significant diffusive heating. Instead, light shifts combined with optical pumping (OP) to levels not coupled by the laser field gives transient cooling, and steady state is not achieved. The time scale is set by the OP rate. We observe both cooling and heating, but often with the opposite detuning from that of steady state. A semiclassical and a fully quantum mechanical calculation of transient cooling agree very well with one another and with our data.
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 report computational results for the time evolution of the velocity distribution P(V,t) for two-level and multilevel ``Doppler'' laser cooling. We compare results obtained from the semiclassical (SC) Fokker-Planck equation and from generalized optical Bloch equations applied to density matrices over a basis of products of internal and quantized translational states (QDM). Computer memory requirements are optimized to make large-scale QDM calculations feasible. QDM and SC agree well except for two cases: (a) atoms in the wells of the light-shift potential (with kinetic energy less than the well depth, U0), and (b) atoms with recoil energy ER comparable to or greater than the natural linewidth \ensuremath{\Elzxh}\ensuremath{\Gamma}. Transient dips occur in P(V,t) at V=0 in QDM results due to slow cooling of atoms in the light-shift potential wells. Dips in P(V,t) occur at velocity-tuned-resonance (Doppleron) velocities but disappear over long interaction times as atoms accumulate near points where the force is zero. When ER\ensuremath{\approxeq}\ensuremath{\Elzxh}\ensuremath{\Gamma}, sharp peaks occur in P(V,T) at V=\ifmmode\pm\else\textpm\fi{}VR from velocity-selective population quasitrapping not previously found in a two-level transition. Sharp features in P(V,t) occur also for J\ensuremath{\rightarrow}J+1 transitions with J>0, small U0/ER, and sufficiently large detuning, from transitions between individual quantum states in the periodic potential.
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.
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 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.