Continuous all-optical deceleration and single-photon cooling of molecular beams

Ultracold molecular gases are promising as an avenue to rich many-body physics, quantum chemistry, quantum information, and precision measurements. This richness, which flows from the complex internal structure of molecules, makes the creation of ultracold molecular gases using traditional methods (laser plus evaporative cooling) a challenge, in particular due to the spontaneous decay of molecules into dark states. We propose a way to circumvent this key bottleneck using an all-optical method for decelerating molecules using stimulated absorption and emission with a single ultrafast laser. We further describe single-photon cooling of the decelerating molecules that exploits their high dark state pumping rates, turning the principal obstacle to molecular laser cooling into an advantage. Cooling and deceleration may be applied simultaneously and continuously to load molecules into a trap. We discuss implementation details including multilevel numerical simulations of strontium monohydride. These techniques are applicable to a large number of molecular species and atoms with the only requirement being an electric dipole transition that can be accessed with an ultrafast laser.

Figure 1

Single-pulse population transfer fidelity for SrH as a function of the time-averaged laser intensity, $I_{\mathrm{avg}}$, and the gdd applied to a $\tau =7$ $\mathrm{ps}$ (temporal) Gaussian transform-limited pulse. The calculated pulse is composed of 99% $\pi$-polarized light that connects the two sublevels of an $X$-state $J=\frac{1}{2}$ manifold to two sublevels of an $A$-state $J^{\prime }=\frac{1}{2}$ manifold along a $Q$-branch. The hyperfine structure is unresolved and therefore not included in the calculation. The white diamond highlights the maximum intensity realized and the gdd used in the Monte Carlo simulation shown in Fig. 5. The typical Rabi flopping as a function of intensity is realized for $\mathrm{gdd}=0$.

Figure 2

Example schemes for applying ultrafast stimulated slowing to ground-state diatomics. The red lines show the deceleration transition, the blue lines a rotational repump, and the broken black lines indicate the nearest transition that will outcouple molecules from the deceleration cycle if they are significantly within the bandwidth of the pulsed laser. Notable spectroscopically characterized species with these structures include (a) SrO, ThO, (b) AlCl, AlF, (c) SrF, YO, CaF, SrH, and (d) CH, OH, SiF.

Figure 3

The pertinent level structure for ${}^{88}$SrH. A full slowing cycle can be completed along the $Q_1$ branch, pictured as an inset, with Zeeman sublevels, $m_F$, shown driven by $\pi$-polarized light. Occasional decays from the excited state will populate the desired slowing state, along with dark states highlighted in blue, including higher vibrational states, which can be repumped with cw or pulsed lasers.

Figure 4

Molecules emitted from a CBGB source are in their rovibrational ground state. After exiting the nozzle they are slowed by picosecond pulses (shown in purple). A velocity-selective optical-pumping laser (red) drives single-photon cooling and compresses the velocity-space density of the beam.

Figure 5

A Monte Carlo simulation of the deceleration and cooling for SrH. The longitudinal phase-space distribution is shown for the initial distribution (black), ballistic trajectories (gray), the trajectories when the ultrafast laser deceleration force is applied (red), and the trajectories when both the deceleration force and single-photon-cooling lasers are applied (blue). A histogram of longitudinal velocities is shown on the right in a semilogarithmic scale.