Observation of Dipole-Quadrupole Interaction in an Ultracold Gas of Rydberg Atoms

We observe the direct excitation of pairs of Cs atoms from the ground state to molecular states correlating asymptotically to $ns{n}^{\prime }f$ asymptotes. The molecular resonances are interpreted as originating from the dipole-quadrupole interaction between the $ns{n}^{\prime }f$ pair states and close-by $npnp$ asymptotes ($22\le n\le 32$). This interpretation is supported by Stark spectroscopy of the pair states and a detailed modeling of the interaction potentials. The dipole-quadrupole interaction mixes electronic states of opposite parity and, thus, requires a coupling between electronic and nuclear motion to conserve the total parity of the system. This non-Born-Oppenheimer coupling is facilitated by the near-degeneracy of even- and odd-$L$ partial waves in the atom-atom scattering which have opposite parity.

Figure 1

Comparison of experimental spectra (thick lines) with simulated line profiles (dashed lines). The asymptotic pair energies of the $n{s}_{1/2}(n-3)f_J$ ($J=5/2$, 7/2) and $(n+1)s_{1/2}(n-4)f_J$ states are indicated by vertical dotted and dashed-dotted lines, respectively. Experimental and simulated spectra have been scaled separately for each $n$ to optimize the visibility of spectral features. The $n$ dependence of the asymptotic pair energies is visualized by gray bands connecting their positions. The features in the traces for $30\le n\le 32$ marked by asterisks originate from $ns(n+1)s$ pair states.

Figure 2

Experimental spectra of the $22s_{1/2}19f_J$ and $23s_{1/2}18f_J$ pair states at different electric fields (left and right black traces, respectively) and corresponding calculated positions of the atomic asymptotes (blue and red curves corresponding to $s_{1/2}{f}_{5/2}$ and $s_{1/2}{f}_{7/2}$, respectively). The experimental spectra are offset by the respective electric field value in $\mathrm{V}/\mathrm{cm}$ (marked by the solid base line of each spectrum).

Figure 3

(a) Calculated potential-energy curves for $n=22$ and $\mathrm{\Omega }=0$, 1, 2, 3 (black, red, blue, and green curves, respectively). The intensity of the color codifies the value of $\overline{p_{\mathrm{\Psi }}}$ as defined in the text (gray corresponding to zero, full color to more than 5% overlap with the excited atomic state). (b) Simulated excitation profile using Eq. (3). Dotted lines indicate the asymptotic pair energies.