Cavity sideband cooling of trapped molecules

The efficiency of cavity sideband cooling of trapped molecules is theoretically investigated for the case in which the infrared transition between two rovibrational states is used as a cycling transition. The molecules are assumed to be trapped either by a radiofrequency or optical trapping potential, depending on whether they are charged or neutral, and confined inside a high-finesse optical resonator that enhances radiative emission into the cavity mode. Using realistic experimental parameters and COS as a representative molecular example, we show that in this setup, cooling to the trap ground state is feasible.

Figure 1

Schematic representation of the setup. A molecule is confined by an external harmonic potential inside a high-finesse resonator. The transition between two molecular vibrational levels is driven transversally by a laser and scatters photons into a quasiresonant cavity mode. The scattering processes are tailored to enhance the transitions that cool the external motion.

Figure 2

Schematic representation of the scattering process leading to cooling. The molecular vibrational levels are labeled by $v=0,1$, and the phononic trap excitations by $n$. The pump laser at frequency ${\omega }_L$ drives resonantly the red sideband transition $|v=0,n\rangle \to |v=1,n-1\rangle$. The laser photon is scattered into a cavity mode at frequency ${\omega }_c={\omega }_0$, which couples resonantly with the molecular transition. Since the photon is then lost via cavity decay, the molecule is cooled by one phonon.

Figure 3

Contour plots of the cooling rate (left column) and corresponding steady-state occupation (right column) of the motion of a trapped COS molecule driven at the asymmetric stretch vibration (2108  cm${}^{-1}$) as a function of the laser-molecule detuning $\Delta$ and the laser-cavity detuning ${\delta }_c$. The parameters are $g=0.41\nu$, $\eta =0.02$, $\kappa =14\nu$, $\gamma =1.9\times {10}^{-4}\nu$, and ${\Theta }_L={\Theta }_C=\phi =\pi /4$. Subplots (a) and (b) correspond to the results found by applying perturbation theory Eq. (12) and taking $\Omega =0.05\nu$. Subplots (c) and (d) are found for the same parameters as in (a) and (b), but are calculated from the density matrix found by numerical integration of Eq. (1). Subplots (e) and (f) are the same as (c) and (d) but with pump strength $\Omega =0.1\nu$.

Figure 4

Extremal values of the cooling rate (black line) and of the steady-state occupation (gray line) vs the laser Rabi frequency (in units of $\nu$). The other parameters are the same as in Fig. 3.