Magnetic Trapping and Coherent Control of Laser-Cooled Molecules

We demonstrate coherent microwave control of the rotational, hyperfine, and Zeeman states of ultracold CaF molecules, and the magnetic trapping of these molecules in a single, selectable quantum state. We trap about $5\times {10}^3$ molecules for almost 2 s at a temperature of $70(8)\mu \mathrm{K}$ and a density of $1.2\times {10}^5{\mathrm{cm}}^{-3}$. We measure the state-specific loss rate due to collisions with background helium.

Figure 1

(a) The energy levels (not to scale) of the two lowest-lying rotational states of CaF, $X^2{\mathrm{\Sigma }}^{+}(v=0)$. Hyperfine splittings and magnetic g-factors are given. (b) The timing sequence of the experiment (not to scale), starting from $t=40\mathrm{ms}$, when the first fluorescence image is taken. The MOT light sequence is color coded according to detuning. The MOT is first compressed by ramping up $B^{\prime }$. Then, the molecules are cooled in a blue-detuned molasses, optically pumped into $|1,0,0⟩$, and transferred to $N=0$ with a microwave pulse. A push pulse removes those remaining in $N=1$, then (optionally) another microwave pulse transfers from $N=0$ back to $N=1$. Finally, the magnetic trap is turned on.

Figure 2

The density versus axial magnetic field gradient used for the compressed MOT. Line: fit to $n=a(B^{\prime }{)}^b$.

Figure 3

Microwave transitions between rotational levels. (a),(b) The depletion of $N=1$ population versus microwave frequency: (a) $|1,0,0⟩\to |0,1,0⟩$ transition driven by a $140\mu \mathrm{s}$ $\pi$ pulse; (b) $|1,0,0⟩\to |0,1,1⟩$ transition driven by a $40\mu \mathrm{s}$ $\pi$ pulse. (c) Rabi oscillations driven between $|1,0,0⟩$ and $|0,1,1⟩$. (d) Rabi oscillations between $|0,1,1⟩$ and $|1,2,2⟩$ after a push pulse has removed all molecules in $N=1$. Each point gives the average and standard error of nine experiments. Where not visible, error bars are smaller than points. In (a),(b), lines show fits to the Rabi line shape for a $\pi$ pulse of the known duration, with background, amplitude and central frequency as free parameters. The data have been corrected for a systematic frequency shift of 1.9 kHz in (a) and 4.7 kHz in (b), arising from a drift in microwave frequency when the pulse is applied. In (c),(d), lines show fits to solutions of the optical Bloch equations with time varying detuning and integration over Rabi frequencies (see text).

Figure 4

The magnetic trap loss rate versus the helium flow rate for molecules in states $|0,1,1⟩$ (red) and $|1,2,2⟩$ (blue). Lines: linear fits. Shaded regions: 68% confidence bands. Inset: The percentage recaptured versus the time in the magnetic trap for molecules in $|0,1,1⟩$, when flow rate is 0.6 sccm. Where not visible, error bars are smaller than points.