The setting time of the stationary distribution over translational degrees of freedom of two-level atoms in the field of a one-dimensional standing light wave is studied. The dependences of this time on the problem parameters such as the light wave intensity, frequency detuning, and atom mass are obtained. Calculations are performed on the basis of the quantum-mechanical equation for the atomic density matrix taking completely into account the recoil and spatial localization effects in an arbitrarily intense light field.
The laser cooling of atoms with a narrow-line optical transition, i.e., in regimes of quantum nature of laser-light interactions resulting in a significant recoil effect, is studied. It is demonstrated that a minimum laser-cooling temperature for two-level atoms in a standing wave reached for red detuning close to three recoil frequencies is vastly different from the theory used for a semiclassical description of Doppler cooling. A set of dimensionless parameters uniquely characterizing the time evolution and the steady state of different atoms with narrow-line optical transitions in the laser field is introduced. The results can be used for analysis of optimal conditions for laser cooling of atoms with narrow lines such as Ca, Sr, and Mg, which are of great interest for atomic clocks.
We study the laser cooling of atoms with a narrow-line optical transition in monochromatic laser light, i.e. in regimes of quantum nature of laser-light interactions resulting in a significant recoil effect. It is demonstrated that a minimum laser cooling temperature for two-level atom in standing wave reached for red detuning close to 3 recoil frequency, greatly different from the theory used for a semiclassical description of Doppler cooling. A set of dimensionless parameters uniquely characterizing the time evolution and the steady state of different atoms with narrow-line optical transitions in the laser field is introduced. The results can be used for analysis of optimal conditions for laser cooling of atoms with narrow lines such as Ca, Sr, and Mg, which are of great interest for atomic clocks.
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.
We present a general theoretical description of laser cooling of three-level atoms in a Λ configuration in two standing waves. Detunings, intensity, and spatial phase difference of the two waves are arbitrary. We demonstrate that, for a zero spatial phase shift, sub-Doppler cooling requires equal detunings. The basic mechanism is then coherent population trapping. For different detunings sub-Doppler cooling occurs only when the spatial phases of the two standing waves are different. This effect can be traced back to a mechanism of the Sisyphus type. These schemes of sub-Doppler cooling require neither polarization gradients nor magnetic fields.