Cavity Cooling of Internal Molecular Motion

We predict that it is possible to cool rotational, vibrational, and translational degrees of freedom of molecules by coupling a molecular dipole transition to an optical cavity. The dynamics is numerically simulated for a realistic set of experimental parameters using OH molecules. The results show that the translational motion is cooled to a few $\mu \mathrm{K}$ and the internal state is prepared in one of the two ground states of the two decoupled rotational ladders in a few seconds. Shorter cooling times are expected for molecules with larger polarizability.

Figure 1

(a) A molecular sample interacts with the cavity field and is driven by a laser, inducing Raman transitions cooling the internal and external degrees of freedom. (b) Comb of resonances at which photon emission into the cavity is enhanced. The gray bars symbolize the molecular lines, which in OH extend over several tens of nanometers. The laser frequency (arrow) is varied to sequentially address several anti-Stokes lines.

Figure 2

(a) Simulated Raman spectra for the first nine rotational states of OH, which are relevantly occupied at room temperature. (b) Potential energy surfaces of the $X^2{\Pi }_i$ ground state and of the $A^2{\Sigma }^{+}$ excited state. The coherent Raman process is indicated by the arrows. (c) Rovibrational substructure.

Figure 3

Reduced spectrum of the relevant rotational anti-Stokes transitions: the lines are projected onto a single free-spectral range of the cavity, whose width is indicated by the arrows. The unfolded Raman spectrum spans 15 THz or up to ${10}^3$ cavity modes. The frequencies of the lines are evaluated from quantum chemical calculations, and must be understood as a qualitative picture; high-resolution experimental input is needed to fix the absolute position with kHz accuracy.

Figure 4

Mean rotational quantum number versus time during the cooling process. The manually optimized cooling sequence first empties the levels $J=(2,3)$, thereafter higher levels are addressed. The small figures show the state distributions at time 0, 0.3, and 1.8 s. The cavity length is fine-tuned to address the $J_{2\to 0}$ and the $J_{3\to 1}$ transition simultaneously.