Photoassociation spectroscopy of ${}^{88}\mathrm{Sr}$: Reconstruction of the wave function near the last node

We have investigated photoassociation (PA) spectra of ultracold ${}^{88}\mathrm{Sr}$ atoms near the $5s^2{}^{1}S_0+5s5p{}^{1}P_1$ atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose last nodal point was determined to be $r_0=3.78\left(18\right)\mathrm{nm}$. The PA lines also determined a precise lifetime of the ${}^{1}P_1$ state to be $5.263\left(4\right)\mathrm{ns}$.

Figure 1

Relevant ${\mathrm{Sr}}_2$ molecular energy levels: The ${}^1\Sigma _g^{+}$ ground state and the attractive ${}^1\Sigma _u^{+}$ molecular states near the $5s^2{}^{1}S_0+5s5p{}^{1}P_1$ atomic asymptote are shown by dashed lines. At the Condon radius $r_C$, the PA laser excites an atom pair in the ground state to the $v\text{th}$ vibrational levels of the ${}^1\Sigma _u^{+}$ state with a binding energy of $h\Delta$. The PA signal intensity, as schematically depicted in the left panel, probes the squared amplitude of the scattering wave function $u_g\left(r\right)$ (solid line) to determine its nodal point of $r_0$.

Figure 2

PA resonances $\mid {\Delta }_{\mathrm{PA}}\left(v\right)\mid$ as a function of the vibrational quantum numbers $v$ plotted on a log-log scale are shown in the lower panel. The solid line is the fit $\mid \Delta \left(v\right)\mid$ by the semiclassical formula given in Eq. (5). The inset shows a typical PA line; atom loss fraction $\kappa$ as a function of detuning $\Delta$. The residuals of the fit, $\delta \left(v\right)={\Delta }_{\mathrm{PA}}\left(v\right)-\Delta \left(v\right)$, are plotted in the middle panel. The upper panel shows the PA linewidth ${\gamma }_{\mathrm{PA}}$.

Figure 3

The squared ground-state wave function ${\mid u_g\left(r\right)\mid }^2$ as a function of the interatomic distance $r$. Filled squares indicate reconstructed wave function from the PA signals. The inset is the enlarged view around the node, where the data points were used to be fit by ${\mid u_g\left(r\right)\mid }^2=A{(r-r_0)}^2$ (solid line) to determine the node to be $r_0=(3.78\pm 0.18)\mathrm{nm}$.