A realistic model of the dipole radiation forces in transverse Doppler cooling (with a s+-s- laser configuration) of an atomic beam of group 13 elements is studied within the quantum-kinetic equation framework. The full energy level sub-structure for such an atom with I = 0 (such as 66Ga) is analysed. Two cooling strategies are investigated; the first involving the 2P3/2 ? 2D5/2 transition and the second a dual laser cooling experiment involving transitions 2P1/2 and 2P3/2 ? 2S1/2. The latter scheme creates a velocity-independent dark-state resonance that inhibits a steady-state dipole cooling force. However, time-dependent calculations show that transient cooling forces are present that could be exploited for laser cooling purposes in pulsed laser fields.
We present a formulation and numerical results for positronium (Ps) laser cooling. The formulation is based on the Lindblad master equation and follows the time evolution of the density matrix of Ps atoms. It therefore accounts for atomic coherence, which is necessary to describe the interaction of Ps with the train of short laser pulses generated by the system developed by Shu
et al. [K. Shu
et al., Phys. Rev. A
109, 043520 (2024)]. Using this formulation, we calculate the time evolution of the populations in each internal and momentum state and thereby quantitatively predict the momentum distribution after laser cooling. We present the representative time evolution of the internal-state populations and momentum distribution, together with a comprehensive scan of the laser parameters used to optimize the cooling efficiency. A prominent feature of the simulated distributions is sub-recoil cooling through velocity-selective coherent population trapping, a coherent effect captured by the quantum-mechanical treatment.
A theoretical discussion of laser cooling of multilevel atomic systems using intense, blue detuned laser beams is given. A method based on matrix continued fractions is presented, which enables the efficient calculation of the semi-classical force on a multilevel system. The method is applied to a three-level system driven by one standing wave and one travelling wave. The force curves obtained exhibit strong cooling features. Cooling of the three-level system is simulated using the fully quantum mechanical Monte Carlo wave function technique. The simulation predicts efficient cooling to sub-Doppler temperatures. The three-level model is related to a multilevel cooling experiment performed on
sp7Li. The experimental results are found to be in reasonable agreement with the three-level model. However, a comparison of the simulation and experiment for a two-level atomic system reveals significant discrepancies, which raises questions about the model and experiment.
Laser cooling of trapped multilevel ions is studied numerically. The ions are assumed to be localized to spatial dimensions smaller than the optical wavelength (Lamb-Dicke regime). A master equation for the center-of-mass motion is used to numerically evaluate cooling rates and final temperatures for arbitrary light field configurations. The results show both well-known cooling mechanisms (Doppler cooling, sideband cooling) and effects introduced by the presence of multiple atomic levels. Quantitative results are given for a trapped
Ba+ ion. The numerical procedure can easily be adapted for all ions used in today's trapping experiments. \textcopyright{} 1996 The American Physical Society.
A theory of deep laser cooling of atoms by counterpropagating circular polarized laser waves in multilevel interaction schemes is developed. Using a (3+5)-level atom as an example, we show that in multilevel interaction schemes two-photon processes are responsible for creating a narrow structure near zero velocity in the ground-state atomic coherence. This structure is in turn responsible for narrow velocity structures in atomic populations and optical coherences. A Fokker-Planck-type kinetic equation is derived for a model of a (3+5)-level interaction scheme. It is found that two-photon coherent processes considerably enhance the radiation force at low velocities and the friction produced by the force at a negative detuning, and considerably decrease the diffusion coefficient. Two-photon processes in multilevel interaction schemes are identified as the basic physical mechanism responsible for deep laser cooling of atoms. The temperature of laser-cooled atoms is derived for a model (3+5)-level atom, and found to be in good agreement with the experimentally observed temperature for laser-cooled cesium atoms.
Using the generalized master equation (GME) formalism, we analyze several approximations for the solutions of Boltzmann or optical Bloch equations. Included in our analysis are the Wilcox-Lamb equations, ordinary master equation (OME), and a new approximation which we designate as the renormalized small-eigenvalue (RSE) approximation. We demonstrate that in multilevel systems, the GME formalism allows direct systematic calculation of radiative-transition coefficients required in the Wilcox-Lamb equations, including all multilevel phase-coherent transitions. However, serious limitations in the applicability of the Wilcox-Lamb approximation are noted both in the high-pressure domain, as an asymptotically exact equation, and for low pressures, as a coarse-grained approximation. The Wilcox-Lamb equations, generally assumed to be valid in a high-pressure domain, are shown to fail in the presence of very efficient inelastic (
T1) relaxation processes regardless of the pressure. Under similar conditions the presence of efficient inelastic processes is also shown to invalidate the use of an OME even when inelastic cross sections are somewhat smaller and the Wilcox-Lamb equations are valid. In particular, we show that when energy losses to the heat bath are severe, an ordinary master equation, traditionally believed to provide a valid description of radiative contributions to level-population evolution when the ratio of Rabi to elastic collision frequency is small, is not valid under any conditions. On this ground we strongly question the recent use of a multilevel OME description to explain the existence of an energy threshold for laser-induced decomposition of S
F6. Finally, we show that for low gas pressures where Rabi oscillations are a prominent feature of the exact solutions, neither the OME nor the Wilcox-Lamb approximation provides an adequate coarse-grained solution. We show that the Wilcox-Lamb solution is in error primarily because of a circumstance not previously recognized, namely, a systematic large error in the way exponential terms contributing to the solution are normalized. A closely related approximation, the RSE approximation, which we present here for the first time, is shown to provide an accurate coarse-grained approximation to the fully coherent GME solutions.