Two distinct lasers are shown to permit controlled cooling of a three-level atomic system to a regime particularly useful for group-II atoms. Alkaline-earth-metal atoms are difficult to laser cool to the micro- or nanokelvin regime, but this technique exhibits encouraging potential to circumvent current roadblocks. Introduction of a sparse-matrix technique permits efficient solution of the master equation for the stationary density matrix, including the quantized atomic momentum. This overcomes long-standing inefficiencies of exact solution methods, and it sidesteps inaccuracies of frequently implemented semiclassical approximations. The realistic theoretical limiting temperatures are optimized over the full parameter space of detunings and intensities. A qualitative interpretation based on the phenomenon of electromagnetically induced transparency reveals dynamical effects due to photon-atom dressing interactions that generate non-Lorentzian line shapes. Through coherent engineering of an asymmetric Fano-type profile, the temperature can be lowered down to the recoil limit range.
Two distinct lasers are shown to permit controlled cooling of a three-level atomic system to a regime particularly useful for group-II atoms. Alkaline-earth-metal atoms are difficult to laser cool to the micro- or nanokelvin regime, but this technique exhibits encouraging potential to circumvent current roadblocks. Introduction of a sparse-matrix technique permits efficient solution of the master equation for the stationary density matrix, including the quantized atomic momentum. This overcomes long-standing inefficiencies of exact solution methods, and it sidesteps inaccuracies of frequently implemented semiclassical approximations. The realistic theoretical limiting temperatures are optimized over the full parameter space of detunings and intensities. A qualitative interpretation based on the phenomenon of electromagnetically induced transparency reveals dynamical effects due to photon-atom dressing interactions that generate non-Lorentzian line shapes. Through coherent engineering of an asymmetric Fano-type profile, the temperature can be lowered down to the recoil limit range.
We analyze the dynamics of atom-laser interactions for atoms having multiple, closely spaced, excited-state hyperfine manifolds. The system is treated fully quantum mechanically, including the atom's center-of-mass degree of freedom, and motion is described in a polarization gradient field created by a three-dimensional laser configuration. We develop the master equation describing this system, and then specialize it to the low-intensity limit by adiabatically eliminating the excited states. We show how this master equation can be simulated using the Monte Carlo wave function technique, and we provide details on the implementation of this procedure. Monte Carlo calculations of steady state atomic momentum distributions for two fermionic alkaline earth isotopes, 25Mg and 87Sr, interacting with a three-dimensional lin-\ensuremath{\perp}-lin laser configuration are presented, providing estimates of experimentally achievable laser-cooling temperatures.
Laser cooling is theoretically investigated in a cascade three-level scheme, where the excited state of a laser-driven transition is coupled by a second laser to a top, more stable level, as for alkaline-earth-metal atoms. The second laser action modifies the atomic scattering cross section and produces temperatures lower than those reached by Doppler cooling on the lower transition. When multiphoton processes due to the second laser are relevant, an electromagnetic-induced transparency modifies the absorption of the first laser, and the final temperature is controlled by the second laser parameters. When the intermediate state is only virtually excited, the dynamics is dominated by the two-photon process and the final temperature is determined by the spontaneous decay rate of the top state.
We employ semiclassical theoretical analysis to study laser cooling of free atoms using three-level cascade transitions, where the upper transition is much weaker than the lower one. This represents an alternate cooling scheme, particularly useful for group II atoms. We find that temperatures below the Doppler limits associated with each of these transitions are expected. The lowest temperatures arise from a remarkable increase in damping and reduced diffusion compared to two-level cooling. They are reached at the two-photon resonance, where there is a crossing between the narrow and the partially dark dressed states, and can be estimated simply by the usual Doppler limit considering the decay rate of the optical coherence between these states.
Summary form only given. The preparation of quantum systems in pure states is a prerequisite for coherent control. In this context laser cooling of trapped particles to the ground state of the confining potential is a powerful tool for preparing e.g. ions for quantum logic. In particular sideband cooling has been demonstrated to be the most efficient technique, allowing to achieve more than 99% of occupation of the ground state of the trap. This cooling technique relies on two conditions: the Lamb-Dicke regime, and the strong confinement regime. This latter condition, which allows the spectral resolution of individual sidebands of the motion, is however a limitation on the cooling time. We propose a model for cooling single ions inside a trap as an alternative to sideband cooling. The scheme uses electromagnetically induced transparency (EIT) in a /spl Lambda/-level scheme, where one of the transitions is dressed by a strong laser field. For detuning of the dressing laser, the absorption spectrum for the transition shows EIT when the cooling (probe) laser has detuning. Then, by tuning the cooling laser on the dark resonance (or EIT), for a suitable set of parameters and in the Lamb-Dicke regime the atoms are cooled to the ground state by the sideband transitions which are resonantly excited. The scheme achieves efficient ground state cooling and fast cooling rates using a continuous driving, instead of a pulsed one as in Raman sideband cooling schemes. An example is illustrated, where the average vibrational number is plotted as a function of the cooling time, and the final probability of occupation is plotted as a function of the vibrational state. This method may also be applied to reduce phase errors in coherent manipulations of trapped ions for quantum logic.
Summary form only given. We consider laser cooling of free atoms with simultaneous two-color excitation of three-level cascade transitions [1], [2], [3], [4], [5], [6] finding theoretically that temperatures below the Doppler limits associated with each one of the individual transitions are obtained. We use standard laser cooling analysis [7], [8] and the dressed state picture in order to identify different cooling regions, and determining optimum parameters for guiding further experiments. These new “sub-Doppler” limits are reached at the two-photon resonance where a significant increase of the damping coefficient and decrease of the diffusion take place. In the dressed state picture, this point corresponds to a crossing of the narrow and a (partially) dark state.Figure 1 shows a plot of temperature (normalized to the Doppler limit for cooling only on the lower transition) as function of single-photon detunings, for the 1S0-1P1-1D2 transition of Magnesium, in which the lower 1S0-1P1 transition is the usual cooling one (λ1 = 2πc/ω1 = 285 nm, λ2 = 2πc/ω2 = 881 nm, γ1 = 2π 78.8 MHz, γ2 = 2π 2.2 MHz). A minimum temperature of 38 μK is predicted. This temperature is lower than the Doppler temperature of the lower and upper transitions, TD = γ/k = 1.9 mK and 49 μK respectively. Due to the asymmetric absorption profile of the dressed atom, there is a remarkable increase in the damping coefficient (α) associated with the narrow transition, in comparison with the broad transition (two-level cooling). The cooling and damping times, inversely proportional to α, are reduced by the same amount. Since the curve for the diffusion coefficient (D) has the same shape as the curve for the absorption coefficient or the population of the intermediate state, D is also reduced with respect to the broad resonance, We analyze situations previously implemented experimentally in alkaline-Earth atoms using cascade transitions, and also discuss prospects for Aand V-type three-level systems.
We present a theoretical analysis of a new one-dimensional laser-cooling scheme that was recently demonstrated on a beam of metastable 4He atoms. Both internal and translational degrees of freedom are treated quantum mechanically. Unlike semiclassical approaches, such a treatment can be applied to situations in which the atomic coherence length is of the same order of or larger than the laser wavelength, which is the case for atoms cooled below the one-photon recoil energy. We introduce families of states that are closed with respect to absorption and stimulated emission, and we establish the generalized optical Bloch equations that are satisfied by the corresponding matrix elements. The existence of velocity-selective trapping states that are linear combinations of states with different internal and translational quantum numbers is demonstrated, and the mechanism of accumulation of atoms in these trapping states by fluorescence cycles is analyzed. From a numerical solution of the generalized optical Bloch equations, we study in detail how the final atomic-momentum distribution depends on the various physical parameters: interaction time, width of the initial distribution, laser detuning, laser power, and imbalance between the two counterpropagating waves. We show that the final temperature decreases when the interaction time increases, so that there is no fundamental limit to the lowest temperature that can be achieved by such a method. Finally, possible extensions of this method to two-dimensional cooling are presented.