This paper derives a general procedure for the numerical solution of the Lindblad equations that govern the coherences arising from multicoloured light interacting with a multilevel system. A systematic approach to finding the conservative and dissipative terms is derived and applied to the laser cooling of gallium. An improved numerical method is developed to solve the time-dependent master equation and results are presented for transient cooling processes. The method is significantly more robust, efficient and accurate than the standard method and can be applied to a broad range of atomic and molecular systems. Radiation pressure forces and the formation of dynamic dark-states are studied in the gallium isotope 66Ga.
We extend the kinetic theory of the laser cooling of atoms to four multilevel atomic schemes: (3+5)-, (5+7)-, (7+9)-, and (9+11)-level atom. In all four atomic schemes the atoms are considered to be excited by two counterpropagating circularly polarized laser waves. A comparison of four multilevel atomic schemes shows that the even-order multiphoton processes are responsible for the narrow structures near zero velocity in the atomic coherences, atomic populations, dipole radiation forces, and the diffusion coefficients. The even-order multiphoton processes in a multilevel atom with a big number of magnetic sublevels are shown to produce the velocity structures, which are much narrower than that produced by the two-photon processes in a (3+5)-level atom. It is found that the multiphoton processes enhance the radiation force at low velocities and the friction produced by the force at a negative detuning. The even-order multiphoton processes caused by the laser waves are identified as the basic physical mechanism responsible for the sub-Doppler laser cooling of atoms. The temperature of laser-cooled atoms is derived for all four models and found to be lower for atomic schemes with a larger number of magnetic sublevels.
Laser cooled atomic gases and atomic beams are widely studied samples in experimental research in atomic and optical physics. For the application of ultra cold gases as model systems for e.g. quantum many particle systems, the atomic species is not very important. Thus this field is dominated by alkaline, earthalkaline elements which are easily accessible with conventional laser sources and have convenient closed cooling transition. On the otherhand, laser cooled atoms may also be interesting for technological applications, for instance for the creation of novel materials by atomic nanofabrication (ANF). There it will be important to use technologically relevant materials. As an example, using group III atoms of the periodical table in ANF may open a route to generate fully 3D structured composite materials. The minimal requirement in such an ANF experiment is the collimation of an atomic beam which is accessible by one dimensional laser cooling. In this dissertation, I describe transverse laser cooling of an Indium atomic beam. For efficient laser cooling on a cycling transition, I have built a tunable, continuous-wave coherent ultraviolet source at 326 nm based on frequency tripling. For this purpose, two independent high power Yb-doped fiber amplifiers for the generation of the fundamental radiation at 977 nm have been constructed. I have observed sub-Doppler transverse laser cooling of an Indium atomic beam on a cycling transition of In by introducing a polarization gradient in the linear-perpendicular-linear configuration. The transverse velocity spread of a laser-cooled In atomic beam at full width at half maximum was achieved to be 13.5 ± 3.8 cm/s yielding a full divergence of only 0.48 ± 0.13 mrad. In addition, nonlinear spectroscopy of a 3-level, Lambda-type level system driven by a pump and a probe beam has been investigated in order to understand the absorption line shapes used as a frequency reference in a previous two-color spectroscopy experiment. For the analysis of this atomic system, I have applied a density matrix theory providing an excellent basis for understanding the observed line shapes.
Deep laser cooling of
24Mg atoms has been theoretically studied. We propose a two-stage sub-Doppler cooling strategy using electrodipole transition $3\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}\ensuremath{\rightarrow}3\phantom{\rule{0.16em}{0ex}}{}^{3}{D}_{3}$ ($\ensuremath{\lambda}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}383.8$ nm). The first stage implies exploiting magneto-optical trap with ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light beams, while at the second stage lin $\ensuremath{\perp}$ lin molasses is used. We focus on achieving a large number of ultracold atoms (${T}_{\mathrm{eff}}<10 \ensuremath{\mu}\mathrm{K}$) in a cold-atomic cloud. The calculations have been based on quantum treatment, taking into full account the recoil effect and beyond many widely used approximations. Steady-state values of average kinetic energy and linear momentum distributions of cold atoms have been analyzed for various light-field intensities and frequency detunings. The results of conducted quantum analysis have been significantly different from the results achieved under a semiclassical approximation based on the Fokker-Planck equation. The second cooling stage allows achieving sufficiently lower kinetic energies of the atomic cloud as well as increased fraction of ultracold atoms at certain conditions compared to the first one. We hope that the obtained results can help in overcoming current experimental problems in deep cooling of
24Mg atoms by means of laser field. Cold magnesium atoms cooled in a large amount to several $\ensuremath{\mu}\mathrm{K}$ are of huge interest to, for example, quantum metrology and to other many-body cold-atoms physics.
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.
Radiation pressure and laser cooling of a moving three-level ladder-type atom in bichromatic travelling fields are considered. The dependence of the force on parameters such as detunings, Rabi frequencies and spontaneous decay rates is calculated numerically and shown graphically and analytical expressions for the force are obtained for some special parameter values. It is shown that the radiation pressure shows Doppler-shifted resonance peaks resulting respectively from one-photon and two-photon transitions. Using the present scheme, Doppler cooling of sodium exploiting the 3 2 S 1/2 –3 2 P 3/2 –3 2 D 5/2 cascade transitions is investigated. It is found that temperatures lower than the Doppler limit can be achieved.