$C_6$ coefficients for interacting Rydberg atoms and alkali-metal dimers

We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure ($n^2{L}_j$; $L\le 2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X{}^1\mathrm{\Sigma }^{+}$; $v=0, J=0$). We compute the associated $C_6$ dispersion coefficients of atom-molecule pairs involving ${}^{133}\mathrm{Cs}$ and ${}^{85}\mathrm{Rb}$ atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial $O\left(n^7\right)$ over the range of principal quantum numbers $40\le n\le 150$. For all atom-molecule pairs considered, Rydberg states $n{}^{2}S_j$ and $n{}^{2}P_j$ result in attractive $1/R^6$ potentials. In contrast, $n{}^{2}D_j$ states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as $n^{-5}$ for $n>40$. For intermediate values of $n\lesssim 40$, both repulsive and attractive interaction energies of the order of 10–$1000\mu \mathrm{K}$ can be achieved with specific atomic and molecular species. The accuracy of the reported $C_6$ coefficients is limited by the quality of the atomic quantum defects, with relative errors $\mathrm{\Delta }{C}_6/C_6$ estimated to be no greater than 1% on average.

Figure 1

$C_6$ dispersion coefficients as a function the atomic principal quantum number $n$ for the Cs-LiCs collision pair. Results are shown for several atomic Rydberg states $n^2{L}_j$. LiCs is in the electronic and rovibrational ground state. Panels show results for different total angular momentum projections $\mathrm{\Omega }=m+M$: (a) $\left|\mathrm{\Omega }\right|=1/2$, (b) $\left|\mathrm{\Omega }\right|=3/2$, (c) $\left|\mathrm{\Omega }\right|=5/2$. Solid lines correspond to a fitted $n^7$ scaling.

Figure 2

$C_6$ dispersion coefficients as a function of the atomic principal quantum number $n$ for the Rb-KRb collision pair. Results are shown for several atomic Rydberg states $n^2{L}_j$. KRb is in the electronic and rovibrational ground state. Panels show results for different total angular momentum projections $\mathrm{\Omega }=m+M$: (a) $\left|\mathrm{\Omega }\right|=1/2$, (b) $\left|\mathrm{\Omega }\right|=3/2$, (c) $\left|\mathrm{\Omega }\right|=5/2$. Solid lines correspond to a fitted $n^7$ scaling.

Figure 3

Molecular polarizability function at imaginary frequency ${\alpha }_{00}\left(i\omega \right)$ for selected alkali-metal dimers in the electronic and rovibrational ground state $X{}^1\mathrm{\Sigma }^{+}, \nu =J=M=0$.

Figure 4

Dynamic polarizability function at imaginary frequencies ($i\omega$) for (a) ${}^{85}\mathrm{Rb}$ and (b) ${}^{133}\mathrm{Cs}$, for selected $n^2{L}_j$ states with $n=80$.

Figure 5

Static polarizability of ${}^{133}\mathrm{Cs}$ atoms in selected angular momentum states (in units of $a_0^3$), as a function of the principal quantum number $n$, for ${}^{133}\mathrm{Cs}$ atoms in selected angular momentum states: (a) ${\alpha }_{00}$ component for ${}^{2}S_{1/2}$, (b) ${\alpha }_{00}$ component for ${}^{2}D_{5/2}, m=5/2$, (c) ${\alpha }_{00}, {\alpha }_{11}$, and ${\alpha }_{-1-1}$ components for ${}^{2}D_{3/2}m=1/2$. Results for ${\alpha }_{00}$ from Ref. [49] are also shown.

Figure 6

Static polarizability of ${}^{85}\mathrm{Rb}$ atoms in selected angular momentum states (in units of $a_0^3$), as a function of the principal quantum number $n$: (a) ${\alpha }_{00}$ component for ${}^{2}S_{1/2}$, (b) ${\alpha }_{00}$ component for ${}^{2}D_{5/2}, m=5/2$, (c) ${\alpha }_{00}, {\alpha }_{11}$, and ${\alpha }_{-1-1}$ components for ${}^{2}D_{3/2}m=1/2$. Results for ${\alpha }_{00}$ from Ref. [49] are also shown.

Figure 7

Bar plots ${\log }_{10}\left|C_6\right|$ for $n=15,50,80$ for atom-molecule pairs involving ${}^{85}\mathrm{Rb}$ atoms in the $n{}^{2}P_{1/2}$ state with KRb, RbCs, and LiRb molecules in the rovibrational ground state. The permanent dipole moment of each molecule is shown in parentheses on the horizontal axis [48].