We discuss the role of light absorption by pairs of atoms (radiative collisions) in the context of a model for velocity selective coherent population trapping with emphasis on its application to metastable triplet helium. Our main interest is the application of such dark-state cooling schemes to the regime where individual quantum states get multiply occupied, a regime which is sometimes referred to with the term atom laser. We show that, because of radiative collisions, for positive detuning of the driving light fields from an atomic resonance the conditions for proliferation of the occupation numbers of the lowest lying states can only be marginally met. Multiple occupation of these states only occurs if a very efficient sub-Doppler precooling mechanism is operative. In the case of negative frequency detuning the requirements on this sub-Doppler mechanism are less restricting, provided one avoids molecular resonances. \textcopyright{} 1996 The American Physical Society.
We discuss the role of light absorption by pairs of atoms (radiative collisions) in the context of a model for velocity selective coherent population trapping with emphasis on its application to metastable triplet helium. Our main interest is the application of such dark-state cooling schemes to the regime where individual quantum states get multiply occupied, a regime which is sometimes referred to with the term atom laser. We show that, because of radiative collisions, for positive detuning of the driving light fields from an atomic resonance the conditions for proliferation of the occupation numbers of the lowest lying states can only be marginally met. Multiple occupation of these states only occurs if a very efficient sub-Doppler precooling mechanism is operative. In the case of negative frequency detuning the requirements on this sub-Doppler mechanism are less restricting, provided one avoids molecular resonances. \textcopyright{} 1996 The American Physical Society.
When an atom, in a linear superposition of states, absorbs or emits light, interference can occur between two different absorption or emission amplitudes, giving rise to observable physical effects, such as level crossing resonances, quantum beats, and dark states. Early experimental demonstrations of effects of this kind, using an optical detection of the atomic internal state, are briefly reviewed. In fact, such interference effects are still playing a fundamental role in modern developments, such as laser cooling and trapping. We present in this paper a few examples of such applications, including the mechanical Hanle effect, velocity selective resonances for an atom moving in a standing wave and subrecoil laser cooling by Velocity Selective Coherent Population Trapping (VSCPT).
We give a systematic analysis of the extension of the one-dimensional velocity-selective coherent population trapping cooling mechanism to atoms with integer angular momenta F>1 using additional light shifts to compensate for the kinetic energy mismatch between the various Zeeman sublevels contributing to the internally decoupled (i.e., dark) state of the atom. Different configurations to achieve the proper light shifts to obtain a very long lifetime of the velocity-selective dark states are discussed and compared. In addition we show that the maximum occupation probability of the resulting quasidark state and its filling time scale strongly depend on the proper choice of detunings to exploit extra precooling mechanisms involving the Zeeman sublevels not contributing to the dark state. We show that additional cooling can also be implemented on the hyperfine repumping transition. This result should prove important for other schemes involving gray states such as, e.g., dark optical lattices and superlattices as well. As a concrete example we consider cesium including all relevant hyperfine levels.
In Section 8.3.9, we mentioned that the recoil temperature was not the ultimate barrier to cooling. Several mechanisms have been conceived and implemented to concentrate the atomic velocity distribution in a range of values of width less than V R . In contrast to Doppler or Sisyphus cooling, these mechanisms do not appeal to a friction force, but rather to an optical pumping process (see Complement 2B), able to accumulate the atoms in this narrow range of velocities. We now present one such mechanism called ‘velocity-selective coherent population trapping’, considering only the case where the motion occurs in one space direction (the O z -axis). Note, however, that the method generalizes to two or three dimensions. Coherent population trapping Coherent population trapping is a phenomenon that occurs when an atom has a system of three energy levels in the ∧ configuration shown in Figure 8A.1, where each leg of the ∧ interacts with a laser L − or L + . This was discussed in detail in Section 2D.2 of Complement 2D. Here we consider the case where the two ground states g + and L − , have exactly the same energy, and the two lasers have frequencies ω + and ω − , very close to the resonance frequency ω 0 . In this situation, the selectivity of the interactions is obtained via the polarization selection rules (see Complement 2B): if g − , g + and e have magnetic quantum numbers m = −1, +1 and 0, respectively, the laser wave L − is right-circularly polarized (σ + polarization), while the laser wave L + is left-circularly polarized (σ − polarization).
The \ensuremath{\Lambda} system resulting from the interaction of counterpropagating orthogonally polarized beams of light with a Jg=1\ensuremath{\rightarrow}Je=1 transition is known to exhibit laser cooling without the presence of a damping force, through velocity selective coherent population trapping. This occurs independent of the sign of the laser's detuning from the atomic resonance frequency. We present measurements and calculations that show a detuning-dependent transient peak or dip in the ground-state momentum distribution centered at pg=0, however, which is reminiscent of laser cooling by a damping force. We explain this in terms of the character of the quantum-mechanical eigenstates of the total ground-state Hamiltonian of the system, using both analytic expressions and numerical calculations.
We present a new scheme of sub-Doppler laser cooling for atoms used in atomic frequency standards, particularly for 40Ca. We perform calculations concerning optical pumping via a velocity- selective state based upon velocity-selective coherent population trapping. Optical pumping on the Raman transition 41S0- 41P1-31D2 leads to population of the metastable singlet state followed by a decay into the metastable triplet state 4P1. The momentum distribution of atoms in that state (with a half-maximum width of about one corresponding photon recoil momentum) is a direct replica of the distribution of atoms in the 3D2 state.
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.