Deceleration of molecules in a supersonic beam by the optical field in a low-finesse cavity

We study the dynamics of a supersonic molecular beam in a low-finesse optical cavity and demonstrate that most molecules in the beam can be decelerated to zero central velocity by the intracavity optical field in a process analogous to electrostatic Stark deceleration. We show that the rapid switching of the optical field for slowing the molecules is automatically generated by the cavity-induced dynamics. We further show that $~$1% of the molecules can be optically trapped at a few millikelvin in the same cavity.

Figure 1

(a) Schematic of an optical cavity-based decelerator. (b) Transition lines of CaF around 606.5 nm, the $R$(0) line: ${}^2{\Pi }_{1/2}({\upsilon }^{\text{'}}=0,N^{\text{'}}=1,J^{\text{'}}=3/2)\to X^2{\Sigma }^{+}({\upsilon }^{\text{'}\text{'}}=0,N^{\text{'}\text{'}}=0,J^{\text{'}\text{'}}=1/2)$ and $Q$(0) line: ${}^2{\Pi }_{1/2}({\upsilon }^{\text{'}}=0,N^{\text{'}}=1,J^{\text{'}}=1/2)\to X^2{\Sigma }^{+}({\upsilon }^{\text{'}\text{'}}=0,N^{\text{'}\text{'}}=0,J^{\text{'}\text{'}}=1/2$).

Figure 2

Position-velocity distributions of the molecules at the initial stage (a) and after spatial self-organization (b). (c) Rapidly switching optical field intensity in the cavity as the molecular beam travels along the cavity axis, the insert shows the evolution of the intensity for the initial period. The parameters used are $g=240\hspace{0.5em}\mathrm{MHz}$ (the mode value $V=3\times {10}^{-6}\hspace{0.5em}{\mathrm{mm}}^3$), ${\Delta }_A=-2\times {10}^3\hspace{0.5em}\mathrm{GHz}$, ${\Delta }_c=-10\hspace{0.5em}\mathrm{GHz}$, ${\Gamma }_0=0$, $\kappa =1\hspace{0.5em}\mathrm{GHz}$, $\eta =2\times {10}^4$ GHz and $N={10}^4$.

Figure 3

Phase space plot of a traveling molecular beam at different times, traces (a)–(e), the intracavity field intensities of which are marked in Fig. 2c. The parameters are the same as in Fig. 2.

Figure 4

Velocity distributions of the molecules corresponding to trace (a)–(e) in Fig. 3. Traces (f) and (g) show the initial and final distributions of trapped molecules in the cavity. The parameters used are the same as in Fig. 2.

Figure 5

The theoretical (green) and simulation (black) results of the percentage of the molecules and their temperatures in the cavity.

Figure 6

Scaling with respect to (a) $N$ and $V$ (or $1/g^2$) (${\mathit{Ng}}^2=5.76\times {10}^8$ MHz${}^2$ fixed), where ${\Delta }_A=-2\times {10}^3\hspace{0.5em}\mathrm{GHz}$ and ${\sigma }_0=30$ m/s, (b)${\Delta }_A$ and $\sqrt{N}$ (${\Delta }_A/\sqrt{N}=-200$ GHz fixed), where $g=240\hspace{0.5em}\mathrm{MHz}$ and ${\sigma }_0=30$ m/s, and (c) ${\sigma }_0$, where ${\Delta }_A=-2\times {10}^3\hspace{0.5em}\mathrm{GHz}$ and $N={10}^4$. Other parameters are $\kappa =10$ GHz, ${\Delta }_c=-100\hspace{0.5em}\mathrm{GHz}$ and $v_0=300\hspace{0.5em}\mathrm{m}/\mathrm{s}$.