Optoelectrical cooling of polar molecules

We present an optoelectrical cooling scheme for polar molecules based on a Sisyphus-type cooling cycle in suitably tailored electric trapping fields. Dissipation is provided by spontaneous vibrational decay in a closed level scheme found in symmetric-top rotors comprising six low-field-seeking rovibrational states. A generic trap design is presented. Suitable molecules are identified with vibrational decay rates on the order of 100 Hz. A simulation of the cooling process shows that the molecular temperature can be reduced from 1 K to 1 mK in approximately 10 s. The molecules remain electrically trapped during this time, indicating that the ultracold regime can be reached in an experimentally feasible scheme.

Figure 1

(Color online) Energy-level and state-transition diagram for the cooling scheme. A molecule in the strong lfs state $|s⟩$ diffuses from the low-field region to the high-field region (1) where it is driven to the weak lfs state $|w⟩$ (2). After moving back to the low-field region (3), the molecule is driven to the excited state $|e⟩$ (4) from which it decays spontaneously to $|s⟩$ (5). The irreversible spontaneous decay makes this cycling process unidirectional.

Figure 2

Design of an electric trap for the cooling scheme. Regions of tunable homogeneous fields are achieved using parallel capacitor plates (a). Collisions with the plate surface are eliminated by alternatingly charged microstructured surface electrodes [15] (b). Transverse confinement is achieved by a high-voltage electrode between the plates around the perimeter of the trap (a). By interrupting the perimeter electrode, an electric-quadrupole guide can be connected to the trap for the injection and extraction of molecules [11] (c).

Figure 3

(Color online) Transition scheme used to simulate cooling of ${\text{CF}}_3\text{H}$. Rotational states are labeled using the notation $|J,K,M⟩$. MW and ir denote the induced microwave and infrared transitions. $\Gamma$ denotes spontaneous decay to the five states with vibrational excitation $\mathrm{v}=0$. The energy levels are obtained by diagonalizing the rigid-rotor Hamiltonian for ${\text{CF}}_3\text{H}$ at field strengths of 5 and 20 kV/cm for the low-field and high-field regions, respectively.

Figure 4

(Color online) Velocity distribution in the weak-field region of the trap after cooling for a time $t$. Velocities are converted to temperatures according to $\frac{m}{2}{v}^2=\frac{3}{2}{k}_{B}T$. Monitoring the population in the excited state during the cooling process shows that on average a molecule spontaneously decays 4.7 times during the first second, 17.0 times during the first 5 s, and 9.0 times during the next 5 s.