Magneto-optical Trap for Polar Molecules

We propose a method for laser cooling and trapping a substantial class of polar molecules and, in particular, titanium (II) oxide (TiO). This method uses pulsed electric fields to nonadiabatically remix the ground-state magnetic sublevels of the molecule, allowing one to build a magneto-optical trap based on a quasicycling $J^{\prime }=J^{\prime \prime }-1$ transition. Monte Carlo simulations of this electrostatically remixed magneto-optical trap demonstrate the feasibility of cooling TiO to a temperature of $10\mu \mathrm{K}$ and trapping it with a radiation-pumping-limited lifetime on the order of 80 ms.

Figure 1

(not to scale) (a) The electronic level structure of TiO and the transitions of interest for laser cooling. The $X^3\Delta$ ground state is split by the spin-orbit interaction into the three $X^3{\Delta }_{1-3}$ sublevels, of which the $X^3{\Delta }_1$ level is the lowest. Each sublevel contains a vibrational ladder, while each vibrational level contains a ladder of rotationally excited states (not shown). ${}^{48}\mathrm{Ti}^{16}\mathrm{O}$ has zero nuclear spin, and thus there is no hyperfine structure. The ground-state $\Lambda$ doublet (not shown) is much less than the natural linewidth of the $E^3\Pi \leftarrow X^3\Delta$ transition. The solid arrow denotes the $v^{\prime }=0\leftarrow v^{\prime \prime }=0$ $P(1)$-branch cooling laser, and the dashed arrows denote the $v^{\prime }=0\leftarrow v^{\prime \prime }=1$ and $v^{\prime }=0\leftarrow v^{\prime \prime }=2$ $P(1)$-branch repump lasers. The squiggly lines depict the dipole-allowed decays, with the associated Franck-Condon factor $q$ [20] next to each decay. (b) The rotational and $\Lambda$-doublet structure of the $E^3{\Pi }_0$ electronic excited manifold. The states are interleaved, as the rotational splitting is smaller than the $\Lambda$-doublet splitting; $a$ and $b$ denote the parity states. Both the cooling and repump lasers address the $J^{\prime }=0$, $a$ state.

Figure 2

(a) The level structure of a traditional MOT. The local magnetic field strength and orientation combined with the Doppler shift enhance the scattering from the laser beam that provides the damping and restoring forces and suppresses scattering from the counterpropagating beam. Since $J^{\prime }>J^{\prime \prime }$, the ground state(s) are always able to scatter from every beam. (b) The level structure of the ER-MOT. The local magnetic field still governs which laser is preferentially scattered, but angular momentum conservation forbids some ground states from interacting with the preferred beam. To overcome this, the ground-state magnetic sublevel populations are remixed by pulsed electric fields, as represented by the dashed lines. (c) A sample ER-MOT design. A pair of electromagnet coils are aligned in anti-Helmholtz fashion to produce a quadrupole field. Six beams of the cooling laser are converged on the center with their polarizations oriented as usual for a MOT, but a set of four open-mesh grids are added. The grids are pulsed in pairs (e.g., first the $X$-axis pair and then the $Y$-axis pair) to produce the dipole electric fields needed to remix the magnetic sublevels. The center is also illuminated by the repump lasers (not shown).

Figure 3

Number (upper, black) and temperature (lower, red) time-of-flight plots for the loading of a molecular packet into a simulated TiO ER-MOT. The initial spike on the number plot is the molecular packet flying through the ER-MOT volume; the broad hump is the actual captured molecules. The decay of the molecule number is due to radiation pumping of the captured population into excited $v^{\prime \prime }\ge 3$ levels and yields an ER-MOT lifetime of $80\pm 5\mathrm{ms}$. Error bars represent statistics over multiple simulation runs.

Figure 4

Fractional capture vs electrostatic remix rate after 160 ms of simulation time for the TiO ER-MOT. Error bars represent statistics over multiple simulation runs. The curve is only a guide to the eye.