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Physical Review A

Cooling mechanisms in the sodium type-II magneto-optical trap

AnnMarie L. Oien, Iain T McKinnie, P. J. Manson, Weston J. Sandle, D. M. Warrington

Published Jun 1, 1997• 12 citations
Publisher

Abstract

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 ${\mathrm{F}}^{|\mathrm{I}\mathrm{H}}$=1 and ${\mathrm{F}}^{|\mathrm{I}\mathrm{H}}$=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 ${\mathrm{F}}^{|\mathrm{I}\mathrm{H}}$=3) MOT and comparisons are made with experiment in both cases. The possibility of blue-detuned Sisyphus cooling in the F=1 to ${\mathrm{F}}^{|\mathrm{I}\mathrm{H}}$=1 and 0 transition scheme is considered.

DOI
10.1103/physreva.55.4621

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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.
We study several magneto-optical trapping configurations in 87Rb^{87}\mathrm{Rb}87Rb. These unconventional MOTs all use type-II transitions, where the angular momentum of the ground state is greater than or equal to that of the excited state. Some use red-detuned light, and others blue-detuned light. The properties of these MOTs are strongly influenced by the balance between opposing Doppler and Sisyphus forces, and vary widely from one configuration to another. In the blue-detuned MOT, Sisyphus cooling dominates over Doppler heating for all relevant speeds and magnetic fields. We measure the capture velocity of this MOT as a function of intensity and detuning, finding a maximum of $3.8\ifmmode\pm\else\textpm\fi{}0.1$ m/s. Atomic densities are particularly high in the blue-detuned MOT, and its lifetime is limited by collisions between the trapped atoms. We present measurements of the loss rate due to these ultracold collisions as a function of laser intensity and detuning. In the red-detuned MOTs, Sisyphus heating dominates at low speeds and Doppler cooling at higher speeds. Consequently, temperatures in the red-detuned MOTs are up to a thousand times higher than in the blue-detuned MOTs. One MOT forms large ring structures, with no density at the center, showing how atoms driven towards a non-zero equilibrium speed remain trapped by orbiting around the center. Another MOT demonstrates that magnetic mixing of the excited-state hyperfine levels can be an important mechanism in type-II MOTs.
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 $J\ensuremath{\rightarrow}J,J\ensuremath{-}1$.
The role of repumping in the magneto-optical trap (MOT) has often been seen as a necessary evil, requiring the introduction of either an electro-optical modulator or extra laser.1,2 However, repumping can be exploited to improve the performance of the MOT,3 or to study further the behavior of such a trap. We report results of a modified MOT using for repumping the D1 transitions 3S1/2 F = 1 to 3Pl/2 F = 1 and F = 2. Because these wavelengths are well displaced from the usual (D2) repump wavelengths, the direct repump influence on the trapping and cooling laser interaction should be significantly reduced. We also expect further possibilities for cold-atom spectroscopy within the MOT. The possibility of a dark trap with this repumping transition has been suggested.3
In this work we point out a theoretical picture accounting for some unpredicted trapping conditions that have been observed---but not satisfactorily explained---in the past and have been recently confirmed by our experiments. We have realized a sodium magneto-optical trap working on the ${3}^{2}{S}_{1/2}(F=1)\ensuremath{\rightarrow}{3}^{2}{P}_{3/2}{(F}^{\ensuremath{'}}=0)$ transition that, according to the usually accepted model, should not work. Our results, with respect to the previous unexplained observations, support more stringent conclusions because our experimental setup gives us the possibility to repump atoms from the F=2F=2F=2 state using D1{D}_{1}D1​ transitions. This definitely excludes that the repumping frequency may play a role in the trap dynamics. A peculiar perturbation approach allows us to demonstrate that the confinement force originates, in this case, from a magnetically induced level-mixing effect. Moreover, we describe separately the nature of damping and confining forces and we recognize that in this case they are due to different transitions. Trap simulations based on a dynamical three-dimensional model are presented, which quantitatively reproduce our experimental results.
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 present a theoretical study of magneto-optical trapping (MOT) force exerted on magnesium monofluoride (MgF) with three-dimensional rate equations, in which we have considered the complex vibrational and rotational levels and the effects of small internal splittings and degeneracies, including fine and hyperfine structures and the magnetic quantum numbers. We investigate the feasibility of MOT for MgF with a very small excited-state ggg factor $(\phantom{\rule{4pt}{0ex}}{g}_{e}=\ensuremath{-}0.0002)$ and a large radiative decay rate $(\mathrm{\ensuremath{\Gamma}}=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}22\phantom{\rule{0.16em}{0ex}}\mathrm{MHz})$ for the electronic transition of $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ to $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2}$ states. We also optimize the MOT with reference to the three-, four-, and more-frequency component models with various polarization configurations and detunings. By applying the dual-frequency arrangement to more than one hyperfine level, we suggest a configuration of the (3+1)(3+1)(3+1)-frequency components for achieving the MOT of MgF.