Quantum calculations for magnetic field induced laser cooling have shown that cooling is less efficient for atoms near the bottom of the light shift potential wells. Inversion of population among the lowest quantum states is found when the pumping rate is less than the well depth. To see whether this occurs in lin {perpendicular} lin polarization gradient cooling, we are performing quantum density matrix calculations. Here the light shift potential matrix obtained in the weak excitation approximations is not diagonal for J{sub g} {>=} 1. We compute eigenfunctions by Fourier transform methods. The band structure is novel and puzzling. The dispersion relation (E vs. Bloch index {nu}) has 2 branches for either 2 or 3 coupled channels (coupled m{sub F} values). Degeneracies occur at {nu}=0 for 2 channels, and {nu}=1 for 3 channels. We are computing optical excitation and decay rates and the temporal evolution of the density matrix so as to obtain the velocity distribution of the cooled atoms.
Quantum calculations for magnetic field induced laser cooling have shown that cooling is less efficient for atoms near the bottom of the light shift potential wells. Inversion of population among the lowest quantum states is found when the pumping rate is less than the well depth. To see whether this occurs in lin {perpendicular} lin polarization gradient cooling, we are performing quantum density matrix calculations. Here the light shift potential matrix obtained in the weak excitation approximations is not diagonal for J{sub g} {>=} 1. We compute eigenfunctions by Fourier transform methods. The band structure is novel and puzzling. The dispersion relation (E vs. Bloch index {nu}) has 2 branches for either 2 or 3 coupled channels (coupled m{sub F} values). Degeneracies occur at {nu}=0 for 2 channels, and {nu}=1 for 3 channels. We are computing optical excitation and decay rates and the temporal evolution of the density matrix so as to obtain the velocity distribution of the cooled atoms.
Temporal integration of density-matrix equations with quantized translational motion gives alternative results for laser cooling of atoms. For polarization gradient cooling, the average kinetic energy in the cold-atom peak after 1000 radiative lifetimes decreases with increasing Fg, and is 1 recoil energy at low laser intensity. With magnetically induced laser cooling (MILC) and low optical pumping rates, atoms cool slowly within the potential wells, giving minima in the velocity distribution at \ensuremath{\nu}=0. MILC is seen as a cyclic process; optical pumping cools and B-field mixing slightly heats.
We report theoretical velocity distributions for sub-Doppler laser cooling of metastable He*(2{sup 3}S), calculated with the Density Matrix and Monte Carlo Wavefunction approaches. For low-field (B = 50 mG) magnetic-field induced laser cooling on the 2{sup 3}S {yields} (2{sup 3}P, J = 2) transition ({lambda} = 1083 nm), we get a narrow, sub-Doppler structure, consisting of three, {approximately}1 photon recoil wide peaks, spaced {approximately}1 recoil apart. With increasing field, this three-peak structure develops into two velocity-selective resonance (VSR) peaks, each {approximately}2 recoils wide. For the 2{sup 3}S {yields} (3{sup 3}P, J = 2) transition ({lambda} 389 nm), VSR peaks are predicted to appear at low field without the third, central peak, which only develops at higher field (B = 200 mG). Additional computations deal with polarization-gradient cooling. In general, we find that for one-dimensional cooling calculations, the Density Matrix method is more efficient than the Monte Carlo Wavefunction approach. Experiments are currently under way to test the results.
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 describe calculations that predict and analyze distinctive features in the velocity distribution in 1D laser cooling for light shift potential well depths only a few times the recoil energy. These features can be interpreted in terms of populations of energy bands or even Bloch states in the periodic potential. They occur with a ${\mathrm{\ensuremath{\sigma}}}^{+}$ standing wave, with and without a small B field, and for lin\ensuremath{\perp}lin laser cooling. We have observed these features experimentally in a beam of metastable helium atoms cooled on the 23S1\ensuremath{\leftrightarrows}23P2 transition, with velocity resolution \ensuremath{\sim}0.3 recoil.
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.
This dissertation reports on quantum state preparation of cesium atoms in a two-dimensional optical lattice, by resolved-sideband Raman cooling. An optical lattice is a periodic potential produced by the light shift interaction between an atom and light field. Laser cooled atoms can become strongly localized about the bottom of potential wells in an optical lattice, where they occupy a discrete spectrum of bound vibrational energy levels. The distribution over vibrational levels of atoms in the lattice is characterized by the mean vibrational excitation, n . In an optical lattice, absorption and emission of photons from lattice beams causes n to increase in time. This source of heating is always present, but its rate can be greatly reduced in a lattice detuned far from the atomic resonance. Sideband cooling is an efficient means of transferring atoms from higher into lower-lying vibrational levels and, thus, it reduces n for the ensemble. If the sideband cooling rate is much greater than the heating rate, then n approaches zero and virtually all atoms are in the lowest vibrational level in their potential wells. Our sideband cooling scheme involves stimulated Raman transitions between bound states in the potential wells of a pair of magnetic sublevels, followed by optical pumping, for a net loss of one quantum of vibration per cooling cycle. The process accumulates 98% of atoms in the ground vibrational level of a potential well associated with a single Zeeman substate. Each atom in the lattice is then very close to a pure state. For two-dimensional lattice with sideband cooling we find nx≈ny≈0.008 &parl0;16&parr0; . Various issues related to state preparation and sideband cooling are also discussed in the context of a one dimensional lin ⊥ lin optical lattice. These include improvement of laser cooling in a near resonance lattice by application of weak magnetic fields, transfer of atoms from near into far off-resonance lattices, and heating rates in far off-resonance lattices.