Submillikelvin Dipolar Molecules in a Radio-Frequency Magneto-Optical Trap

We demonstrate a scheme for magneto-optically trapping strontium monofluoride (SrF) molecules at temperatures one order of magnitude lower and phase space densities 3 orders of magnitude higher than obtained previously with laser-cooled molecules. In our trap, optical dark states are destabilized by rapidly and synchronously reversing the trapping laser polarizations and the applied magnetic field gradient. The number of molecules and trap lifetime are also significantly improved from previous work by loading the trap with high laser power and then reducing the power for long-term trapping. With this procedure, temperatures as low as $400\mu \mathrm{K}$ are achieved.

Figure 1

(a) rf MOT trapping concept. Excitation by a confining laser (the solid arrows) may lead to decay (the dashed arrows) into dark states. The $B$ field and polarization rapidly reverse such that dark states become bright states; this leads to increased confinement and cooling. (b) LIF from trapped molecules vs relative phase $\varphi$ of the $B$ field and the laser polarization. Molecules are only trapped for $|\varphi |\lesssim 90°$.

Figure 2

Filled markers, microwaves applied; open markers, without. (a) Number of molecules loaded into the MOT vs ${\mathcal{L}}_{00}$ power. The number increases with increasing ${\mathcal{L}}_{00}$ power in all cases. (b) Scattering rate vs ${\mathcal{L}}_{00}$ power. The solid line is a fit of the model described in the text to $f_{\mathrm{MOT}}=1.23\mathrm{MHz}$ data, with $\mathrm{\Delta }$ set to $-2\pi \times 9\mathrm{MHz}$, and fit values ${\mathrm{\Gamma }}_{\text{eff}}=2\pi \times 1.0(1)\mathrm{MHz}$ and $p_{\text{sat}}=1.9(3)\mathrm{mW}$. $R_{\mathrm{sc}}$ is lower for $f_{\mathrm{MOT}}=111\mathrm{kHz}$ than for $f_{\mathrm{MOT}}>1\mathrm{MHz}$. $R_{\mathrm{sc}}$ increases in the absence of repump microwaves by $\sim 40\%$. (c) Trap lifetime ${\tau }_{\mathrm{MOT}}$ vs $R_{\mathrm{sc}}$. ${\tau }_{\mathrm{MOT}}$ as long as 500 ms are achieved for low $R_{\mathrm{sc}}$’s in the rf MOT. For higher $R_{\mathrm{sc}}$’s, ${\tau }_{\mathrm{MOT}}\propto 1/R_{\mathrm{sc}}$ (the dashed line is a $1/R_{\mathrm{sc}}$ trend line), and ${\tau }_{\mathrm{MOT}}$ is much shorter in the absence of repump microwaves. For the ${\mathrm{dc}}^{*}$ MOT, ${\tau }_{\mathrm{MOT}}$ decreases for lower $R_{\mathrm{sc}}$’s. (d) Parity mixing (the curved blue line) due to the coil-induced electric field ${\mathcal{E}}_{\mathrm{rf}}$ causes loss (the wiggly grey lines) from the main cycling transition (the vertical red lines), which is repumped via ${\mathcal{L}}_{00}^{N=2}$ and resonant microwaves (the diagonal green lines).

Figure 3

Filled symbols, microwaves applied; open symbols, without; red line, analytical model fit to $f_{\mathrm{MOT}}=1.23\mathrm{MHz}$ data. Measured (a) spring constant $\overline{\kappa }$ and (b) temperature $\overline{T}$ vs scattering rate $R_{\mathrm{sc}}$. The maximum $\overline{\kappa }$ for the ${\mathrm{dc}}^{*}$ MOT is $\sim 2$ times that of the rf MOT, but it decreases much more rapidly for lower $R_{\mathrm{sc}}$. The analytical model, with ${\mathrm{\Gamma }}_{\text{eff}}$ set to the fit value from $R_{\mathrm{sc}}$ vs $I_{00}$, and $B$-field gradient $\partial B_z/\partial z$ and detuning $\mathrm{\Delta }$ set to experimental values, has ${\mu }_{\text{eff}}$ as the only free parameter. $\overline{T}$ decreases with falling $R_{\mathrm{sc}}$, but at a slower rate than predicted by the analytical model with no free parameters. $\overline{T}$ is lower for $f_{\mathrm{MOT}}>1\mathrm{MHz}$ than for $f_{\mathrm{MOT}}=111\mathrm{kHz}$. The model correctly predicts $\overline{T}\sim T_D$ for a low $R_{\mathrm{sc}}$. The spread in values for a given MOT configuration is indicative of variations between measurements made on the same day, while the representative error bars are standard errors of measurements taken on multiple days under similar conditions. (c) Phase space density $\rho$ vs $R_{\mathrm{sc}}$ after a linear power ramp from full power. Ramping increases $\rho$ by up to 2.5 orders of magnitude in the rf MOT. In the ${\mathrm{dc}}^{*}$ MOT, $\rho$ increases only slightly when $R_{\mathrm{sc}}$ is lowered.