Deep Laser Cooling and Efficient Magnetic Compression of Molecules

We introduce a scheme for deep laser cooling of molecules based on robust dark states at zero velocity. By simulating this scheme, we show it to be a widely applicable method that can reach the recoil limit or below. We demonstrate and characterize the method experimentally, reaching a temperature of $5.4(7)\mu \mathrm{K}$. We solve a general problem of measuring low temperatures for large clouds by rotating the phase-space distribution and then directly imaging the complete velocity distribution. Using the same phase-space rotation method, we rapidly compress the cloud. Applying the cooling method a second time, we compress both the position and velocity distributions.

Figure 1

(a) Hyperfine components of the laser cooling transition in CaF, with three cooling schemes shown: (I) multifrequency; (II) $\mathrm{\Lambda }$ enhanced; (III) single frequency. (b) Steady-state acceleration vs speed and (c) excited-state fraction vs speed, obtained from optical Bloch equation simulations of each scheme. Simulation parameters are (I) total intensity $I=117\mathrm{mW}/{\mathrm{cm}}^2$, detuning $\delta f=20\mathrm{MHz}$; (II) $I=50\mathrm{mW}/{\mathrm{cm}}^2$, $\delta f=30\mathrm{MHz}$; (III) $I=340\mathrm{mW}/{\mathrm{cm}}^2$, $\delta f=8.3\mathrm{MHz}$. Parameters for (I) and (II) are close to those that give the lowest measured temperatures [8, 12].

Figure 2

Phase space rotation in a 1D magnetic trap. (a) Magnitude of effective magnetic field, $|B_{\mathrm{eff}}|=|B|+mgz/{\mu }_B$, vs axial and radial displacements. Weak-field seeking molecules are trapped axially. (b) Magnetic moments $\mu$ of Zeeman sublevels in the $X^2{\mathrm{\Sigma }}^{+}(N=1,F=2)$ state, vs $B$. At large $B$, $\mu \approx {\mu }_B$ for $m_F\in \{-1,0,1,2\}$. (c) Phase space evolution in harmonic trap. After a quarter period, the position distribution is proportional to the initial velocity distribution. (d) Top: fluorescence images of molecules at 5 ms intervals, averaged over 50 shots; $z$ is vertical, and the field of view is 13.5 mm wide. Bottom: rms width in the $z$ direction vs time in trap, ${\sigma }_z(t)$. Error bars include systematic uncertainties. Line is a fit to Eq. (1).

Figure 3

Temperature vs single-frequency molasses parameters. (a) $T$ vs $t_{\mathrm{sfm}}$, when $I=287{\mathrm{mW}\mathrm{cm}}^{-2}$ and $\delta f=164\mathrm{MHz}$. Line: fit to $T=T_0+(T_{\mathrm{i}}-T_0)e^{-t_{\mathrm{sfm}}/\tau }$, giving $\tau =0.52(6)\mathrm{ms}$. (b) $T$ vs $\delta f$ when $t_{\mathrm{sfm}}=5\mathrm{ms}$ and $I=287{\mathrm{mW}\mathrm{cm}}^{-2}$. (c) $T$ vs $I$ when $t_{\mathrm{sfm}}=5\mathrm{ms}$ and $\delta f=164\mathrm{MHz}$. (d) $T$ vs one component of $B$, after optimization of the other two components; $t_{\mathrm{sfm}}=5\mathrm{ms}$, $I=287{\mathrm{mW}\mathrm{cm}}^{-2}$ and $\delta f=164\mathrm{MHz}$. Line: fit to $T=T_0+\alpha B^2$, giving $\alpha =9(1)\times {10}^{-4}\mu \mathrm{K}{\mathrm{mG}}^{-2}$. Points give average and standard error of 50 experimental runs. Error bars are dominated by systematic uncertainties.