Experimental Characterization of Singlet Scattering Channels in Long-Range Rydberg Molecules

We observe the formation of long-range ${\mathrm{Cs}}_2$ Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near $6s_{1/2}(F=3,4)\to n{p}_{3/2}$ resonances ($n=26–34$). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet $s$-wave scattering with binding energies ranging from 400 MHz at $n=26$ to 80 MHz at $n=34$, and states bound by mixed singlet-triplet $s$-wave scattering with smaller and $F$-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including $s$-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet $s$-wave scattering length for low-energy-electron–Cs collisions.

Figure 1

Potential-energy curves (black lines) and vibrational wave functions (colored lines) for ${}^3\mathrm{\Sigma }$ states dissociating to the $26p_{3/2},6s_{1/2}(F=3,4)$ asymptotes (left panel), and the ${}^{1,3}\mathrm{\Sigma }$ states dissociating to the $26p_{3/2},6s_{1/2}(F=3)$ asymptote (middle panel) and $26p_{3/2},6s_{1/2}(F=4)$ asymptote (right panel). Vertical dashed lines mark the positions where the semiclassical Rydberg-electron energy equals the energy of the ${}^3{P}_0$ Cs-$e^{-}$ scattering resonance (see text).

Figure 2

Detected ${\mathrm{Cs}}_2^{+}$ ions as a function of laser frequency relative to the $n{p}_{3/2},6s_{1/2}(F=3,4)$ asymptotes. Solid (dashed) red lines mark the calculated positions of the $v=0$ levels of ${}^3\mathrm{\Sigma }$ (${}^{1,3}\mathrm{\Sigma }$) states. Calculated positions of higher vibrational levels are also shown (full and open triangles, respectively). The strongly saturated atomic transitions correspond to the gray areas.

Figure 3

Comparison of experimental (full symbols) and calculated (open symbols) binding energies of the ${}^3\mathrm{\Sigma }(v=0)$ and ${}^{1,3}\mathrm{\Sigma }(v=0)$ levels. The solid and dashed lines are fits of a ${(n^{*})}^s$ scaling law to the experimental binding energies to guide the eye. Black and red symbols designate states with the ground-state atoms prepared in the $F=4$ and $F=3$ hyperfine level, respectively.