Photoassociation of Long-Range $nD$ Rydberg Molecules

We observe long-range homonuclear diatomic $nD$ Rydberg molecules photoassociated out of an ultracold gas of ${}^{87}\mathrm{Rb}$ atoms for $34\le n\le 40$. The measured ground-state binding energies of ${}^{87}\mathrm{Rb}(nD+5S_{1/2})$ molecular states are larger than those of their ${}^{87}\mathrm{Rb}(nS+5S_{1/2})$ counterparts, which shows the dependence of the molecular bond on the angular momentum of the Rydberg atom. We exhibit the transition of ${}^{87}\mathrm{Rb}(nD+5S_{1/2})$ molecules from a molecular-binding-dominant regime at low $n$ to a fine-structure-dominant regime at high $n$ [akin to Hund’s cases (a) and (c), respectively]. In the analysis, the fine structure of the $nD$ Rydberg atom and the hyperfine structure of the $5S_{1/2}$ atom are included.

Figure 1

Spectrum centered on the $35D_{5/2}$ atomic Rydberg line showing the ${}^{87}\mathrm{Rb}(35D_{5/2}+5S_{1/2})(\nu =0)$ molecular line at $-38\pm 3\mathrm{MHz}$. The vertical error bars are the standard error of three sets of 55 individual experiments at each frequency step. The error in the binding energy is equal to the average long-term frequency drift observed over one full scan.

Figure 2

(a) Right: Spectra centered on $n{D}_{5/2}$ atomic Rydberg lines for the indicated values of $n$ and identified molecular lines (squares). Left: Selected spectra from the plot on the right for states with identified molecular lines. Error bars are obtained as in Fig. 1. (b) Binding energies obtained from Gaussian fits to the molecular lines identified in (a) vs $n$. An allometric fit (solid curve) to the experimental binding energies yields a $n^{-5.9\pm 0.4}$ scaling. Also shown are theoretical binding energies for the ${}^{87}\mathrm{Rb}(n{D}_{5/2}+5S_{1/2})(\nu =0)$ molecular states with $a_{s0}=-14a_0$ (hollow circles and dotted curve). (c) Peak number of detected ions on the $n{D}_{5/2}$ atomic Rydberg line (solid diamonds, left axis) and ratio of molecular and atomic line strengths (hollow diamonds, right axis) vs $n$.

Figure 3

Spectra centered on the $37D_j$ atomic Rydberg lines for $j=3/2$ (left) and $j=5/2$ (right; the same as in Fig. 2). ${}^{87}\mathrm{Rb}(37D_j+5S_{1/2})(\nu =0)$ molecular signals are indicated by vertical dashed lines and squares.

Figure 4

(a),(b) Deep (solid lines) and shallow (dashed lines) potentials for $35D_{3/2}$ and $35D_{5/2}$-type molecules, for $a_{s0}=-14a_0$, and vibrational wave functions for $\nu =0$, 1 in the deep potentials. (c),(d) Energy levels for $\nu =0$, 1 in the deep (triangles) and shallow (circles) potentials vs $n$.

Figure 5

(a) $\nu =0$ binding energies in the deep molecular potentials for $n{D}_{5/2}$ (filled triangles), $n{D}_{3/2}$ (open triangles), and the $D$ fine structure splitting (dashed line) vs the effective quantum number. Solid lines are fits. The $D_{3/2}$ energies are fit well by $84.2\mathrm{GHz}/n_{\text{eff}}^{6.13}$. The $D_{5/2}$ energies do not exhibit a global scaling; at low $n$ they tend to scale as $23\mathrm{MHz}/n_{\text{eff}}^{3.6}$. (b) Electric dipole moments for $\nu =0$ vs $n$ for the deep (triangles) and shallow (circles) $V_{\text{ad}}(Z)$ for $j=3/2$ (open) and $j=5/2$ (filled). (c) Magnetic dipole moments for the same states as in (b).