Hyperfine-Structure-Induced Purely Long-Range Molecules

We have experimentally observed and theoretically identified a novel class of purely long-range molecules. This novel purely long-range state is formed due to a very weak hyperfine interaction that is usually treated only as a small perturbation in molecular spectra. Photoassociation spectroscopy of ultracold ytterbium (${}^{171}\mathrm{Yb}$) atoms with the ${}^{1}S_0\mathrm{\text{−}}{}^{3}P_1$ intercombination transition presents clear identification of molecular states and the shallowest molecular potential depth of about 750 MHz among the purely long-range molecules ever observed.

Figure 1

Potentials for PLR states of various atoms. The potential curves for alkali-metal atoms correlate to the ${}^{2}S_{1/2}+{}^{2}P_{3/2}$ atomic states, and that for helium correlates to the ${}^{3}S_1+{}^{3}P_0$ state. Except ${}^{171}\mathrm{Yb}$, only the resonant dipole interaction and the fine-structure splitting are taken into account to calculate these potentials. The potentials of heavy alkali-metal atoms (Cs, Rb), which are not shown here, have deeper wells than those of K and Na.

Figure 2

Adiabatic potentials near the ${}^{1}S_0+{}^{3}P_1$ dissociation limit obtained from Eq. (4). (a),(b) The potentials for the states composed of the basis sets $|\alpha ⟩$ and $|\beta ⟩$, respectively. The nuclear spin $i$ of ${}^{171}\mathrm{Yb}$ is $1/2$. The value of $C_{6e}$ is set to be 2810 a.u., as discussed later. The potentials are labeled by $|{\Phi }_e|$, and the $\pm$ superscript indicates the reflection symmetry with respect to a plane containing the molecular axis.

Figure 3

PA spectra of ${}^{171}\mathrm{Yb}$ atoms at $2\mu \mathrm{K}$. The fraction of atoms remaining is plotted against the detuning from the ${}^{1}S_0+{}^{3}P_1(f=3/2)$ asymptote. The lines are fitted Lorentzian profiles to guide the eye. The labels show the intensities and the duration times of the PA laser.

Figure 4

PA spectra of ${}^{171}\mathrm{Yb}$ atoms at $25\mu \mathrm{K}$. The fraction of atoms remaining is plotted against the detuning from the ${}^{1}S_0+{}^{3}P_1(f=3/2)$ asymptote. The lines are fitted Lorentzian profiles to guide the eye. The intensities and the duration times of the PA laser are written below the spectra. The bars above the graph show peak positions of the PA lines. The symbols $S$, $P$, and $L$ denote the transitions from the $s$-wave state, from the $p$-wave state, and to the PLR state from the $p$-wave state, respectively. The numbers indicate the values of $T_e$. The insets show the spectra observed at about $15\mu \mathrm{K}$.