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arXiv:1605.06464 · Physical Review A

Bichromatic magneto-optical trapping for J→J,J−1 configurations

Anne Cournol, P. Pillet, Hans Lignier, D. Comparat

Published May 24, 2016• 3 citations
arXivHTMLPDF

Abstract

A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$ transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the $J\ensuremath{\rightarrow}J\ensuremath{-}1$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0$) and $J\ensuremath{\rightarrow}J$ case (i.e., ${J}^{\ensuremath{'}\ensuremath{'}}=1/2\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=1/2$). A one-dimensional (1D) model is presented and a complete 3D simulation using rate equations confirms the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the ${\mathrm{C}}_{2}^{\ensuremath{-}}$ molecular anion as a typical example of the interplay between the two simple transitions $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$.

DOI
10.1103/physreva.93.053423

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A magneto-optical trap (MOT) of atoms or molecules is studied when two lasers of different detunings and polarization are used. Especially for J\ensuremath→J,J\ensuremath−1J\ensuremath{\rightarrow}J,J\ensuremath{-}1J\ensuremath→J,J\ensuremath−1 transitions, a scheme using more than one frequency per transition and different polarization is required to create a significant force. Calculations have been performed with the simplest forms of the J\ensuremath→J\ensuremath−1J\ensuremath{\rightarrow}J\ensuremath{-}1J\ensuremath→J\ensuremath−1 case (i.e., J\ensuremath′\ensuremath′=1\ensuremath→J\ensuremath′=0{J}^{\ensuremath{'}\ensuremath{'}}=1\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0J\ensuremath′\ensuremath′=1\ensuremath→J\ensuremath′=0) and J\ensuremath→JJ\ensuremath{\rightarrow}JJ\ensuremath→J case (i.e., J\ensuremath′\ensuremath′=1/2\ensuremath→J\ensuremath′=1/2{J}^{\ensuremath{'}\ensuremath{'}}=1/2\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=1/2J\ensuremath′\ensuremath′=1/2\ensuremath→J\ensuremath′=1/2). A one-dimensional (1D) model is presented and a complete 3D simulation using rate equations confirms the results. Even in the absence of Zeeman effect in the excited state, where no force is expected in the single laser field configuration, we show that efficient cooling and trapping forces are restored in our configuration. We study this mechanism for the C2\ensuremath−{\mathrm{C}}_{2}^{\ensuremath{-}}C2\ensuremath−​ molecular anion as a typical example of the interplay between the two simple transitions J\ensuremath→J,J\ensuremath−1J\ensuremath{\rightarrow}J,J\ensuremath{-}1J\ensuremath→J,J\ensuremath−1.
Abstract We study the forces and optical pumping within grating magneto-optical traps (MOTs) operating on transitions with non-trivial level structure. In contrast to the standard six-beam MOT configuration, rate equation modeling predicts that the asymmetric laser geometry of a grating MOT will produce spin-polarized atomic samples. Furthermore, the Landé g-factors and total angular momenta of the trapping transition strongly influence both the confinement and equilibrium position of the trap. Using the intuition gained from the rate equation model, we realize a grating MOT of fermionic 87Sr and observe that it forms closer to the center of the trap’s quadrupole magnetic field than its bosonic counterpart. We also explore the application of grating MOTs to molecule laser cooling, where the rate equations suggest that dual-frequency operation is necessary, but not sufficient, for stable confinement for type-II level structures. To test our molecule laser cooling models, we create grating MOTs using the D 1 line of 7Li and see that only two of the four possible six-beam polarization configurations operate in the grating geometry. Our results will aid the development of portable atom and molecule traps for time keeping, inertial navigation, and precision measurement.
Realizing a molecular magneto-optical trap has been a dream for cold molecular physicists for a long time. However, due to the complex energy levels and the small effective Lande g -factor of the excited states, the traditional magneto-optical trap (MOT) scheme does not work very well for polar molecules. One way to overcome this problem is the switching MOT, which requires very fast switching of both the magnetic field and the laser polarizations. Switching laser polarizations is relatively easy, but fast switching of the magnetic field is experimentally challenging. Here we propose an alternative approach, the microwave-mediated MOT, which requires a slight change of the current experimental setup to solve the problem. We calculate the MOT force and compare it with the traditional MOT and the switching MOT scheme. The results show that we can operate a good MOT with this simple setup.
In red-detuned magneto-optical traps (MOTs) of molecules, sub-Doppler heating competes with Doppler cooling, resulting in high temperature and low density. A solution is offered by the blue-detuned MOT where sub- Doppler cooling dominates and the cloud is compressed. Several blue-detuned molecular MOTs have been implemented. A recent implementation relies on a pair of orthogonally polarized components whose frequency separation is smaller than the transition linewidth. We identify the trapping force in these MOTs. At a certain magnetic field, there is a state that is dark to the laser propagating in one direction, but not to the counterpropagating one. This Zeeman-induced dark state (ZIDS) sets up an imbalance in the photon scattering rate, leading to a restoring force. We also study the role of the moving lattices generated by the closely spaced frequency components of the light. We show that there is a velocity-dependent force that drives the molecules toward the speeds of these moving lattices, and that over a relevant range of magnetic fields this combines with the ZIDS force to transport molecules toward the center of the MOT. Here, gray molasses cooling, assisted by nonadiabatic transitions driven by the time-varying polarization of the light field, cools the molecules toward zero velocity. We study these mechanisms for model systems with simple level structures and then extend them to molecules with ground-state hyperfine structure.
We demonstrate one- and two-dimensional transverse laser cooling and magneto-optical trapping of the polar molecule yttrium (II) oxide (YO). In a 1D magneto-optical trap (MOT), we characterize the magneto-optical trapping force and decrease the transverse temperature by an order of magnitude, from 25 to 2 mK, limited by interaction time. In a 2D MOT, we enhance the intensity of the YO beam and reduce the transverse temperature in both transverse directions. The approach demonstrated here can be applied to many molecular species and can also be extended to 3D.
Laser cooling and magneto-optical trapping of molecules typically involves multiple transitions driven by several laser frequencies. We analyze how magneto-optical trapping forces depend on the angular momenta, F l and F u , and the g -factors, g l and g u , of the lower and upper states. When the polarizations must be reversed relative to cases where The correct choice of circular polarization depends on the sign of g u but not on the sign of g l . If g u is zero there is no trapping force, and the trapping force is very weak whenever g u is small compared to g l , which it usually is when the cooling transition is the to transition of a molecule. For some molecules, mixing of the excited state with a nearby excited state can greatly increase g u , leading to stronger trapping forces. A strong trapping force can also be produced by rapidly and synchronously reversing both the magnetic field and the laser polarizations. We simulate a recent experiment on magneto-optical trapping of SrF molecules, and suggest that an alternative choice of laser beam polarizations will strengthen the trapping force.
We present a rate equation model to account for the trapping mechanism in the sodium type-II magneto-optical trap (MOT). A key feature of the model is that excitation from the ground F=1 state to both excited states F∣IH{\mathrm{F}}^{|\mathrm{I}\mathrm{H}}F∣IH=1 and F∣IH{\mathrm{F}}^{|\mathrm{I}\mathrm{H}}F∣IH=0---possible in sodium because of the small excited state separation---is confirmed to be crucial in avoiding the optical pumping that otherwise inhibits steady-state trapping. Furthermore, we calculate that the mixed polarization typically present in a three-dimensional trapping arrangement gives substantially better one-dimensional trapping performance than pure circular polarization, and that the active role of repumping in the trapping process is important. The model is also applied to the type-I (F=2 to F∣IH{\mathrm{F}}^{|\mathrm{I}\mathrm{H}}F∣IH=3) MOT and comparisons are made with experiment in both cases. The possibility of blue-detuned Sisyphus cooling in the F=1 to F∣IH{\mathrm{F}}^{|\mathrm{I}\mathrm{H}}F∣IH=1 and 0 transition scheme is considered.