Two-photon photoassociation spectroscopy of the ${}^2\mathrm{\Sigma }^{+}$ YbLi molecular ground state

We report on measurements of the binding energies of several weakly bound vibrational states of the paramagnetic ${}^{174}\mathrm{Yb}{}^6\mathrm{Li}$ molecule in the electronic ground state using two-photon spectroscopy in an ultracold atomic mixture confined in an optical dipole trap. We theoretically analyze the experimental spectrum to obtain an accurate description of the long-range potential of the ground-state molecule. Based on the measured binding energies, we arrive at an improved value of the interspecies $s$-wave scattering length $a_{s0}=30a_0$. Employing coherent two-photon spectroscopy we also observe the creation of “dark” atom-molecule superposition states in the heteronuclear Yb-Li system. This paper is an important step towards the efficient production of ultracold YbLi molecules via association from an ultracold atomic mixture.

Figure 1

A plot of the relevant interatomic potentials with a schematic representation of two-photon spectroscopy. The potentials are plotted to scale while the locations of the bound states are exaggerated for clarity. ${\omega }_{\text{FB}}$ and ${\omega }_{\text{BB}}$ are the angular frequencies of the free-bound and bound-bound lasers, respectively. ${\delta }_{\text{FB}}$ and ${\delta }_{\text{BB}}$ are the one-photon detunings from the free-bound and bound-bound PA resonances, respectively.

Figure 2

(a) A representative one-photon PA loss resonance of $v^{*}=-2$ with a binding energy of 15.9 GHz relative to the Yb ${}^{1}S_0+\mathrm{Li}{}^{2}P_{1/2}$ free-atom energy. The solid line is a Lorentzian fit. (b) Evolution of the Li atom number in the presence of resonant (blue circles) and off-resonant (red triangles) PA light. In the resonant case the FB laser is locked to the $v^{*}=-2$ resonance. In the off-resonant case it is locked to $2\pi \times 1\mathrm{GHz}$ to the red of resonance. The off-resonant data are fit with an exponential and the on-resonant data are fit with a biexponential for which one of the time constants is fixed to that of the fit to the off-resonant data. (c) A representative two-photon PA resonance of $v=-3$ with binding energy 123.96 GHz relative to the Yb ${}^{1}S_0+\mathrm{Li}{}^{2}S_{1/2}$ free-atom energy. The solid line is a Lorentzian fit. All error bars are statistical.

Figure 3

The magnetic moment of the shallowest bound state of $X^2{\mathrm{\Sigma }}^{+}$ for ${}^{174}\mathrm{Yb}{}^6\mathrm{Li}$ is determined by measuring its binding energy at various magnetic fields using two-photon PA spectroscopy. At each field, the well-known Zeeman shift of the atomic state is subtracted from the apparent shift in the binding energy to give the Zeeman shift of the molecule.

Figure 4

The long-range shape of the $X^2{\mathrm{\Sigma }}^{+}$ potential of YbLi and the measured weakly bound rovibrational states labeled by horizontal dashed lines.

Figure 5

${\chi }^2$ as a function of the $C_6$ and $C_8$ parameters. The rotational quantum number $l$, the $b$ parameter, and the depth of the potential well are all used to minimize ${\chi }^2$ for a specific set of $C_6$ and $C_8$. Panel (a) shows the initial search with a coarse grid. The color is coded to the total rotation number $\lambda$ defined in Eq. (5) according to the color bar. The left side of the color bar corresponds to smaller $\lambda$ and the right side corresponds to larger $\lambda$, with $\lambda =0$ specifically coded in deep orange. According to Eq. (5), we divide the color bar of $\lambda$ into three sections. The one on the left corresponds to $l_{v=-1}=0$, the one in the middle corresponds to $l_{v=-1}=1$, and the one on the right corresponds to $l_{v=-1}=2$. The point with the lowest ${\chi }^2$ is magnified and the dashed arrow points to its location on the two-dimensional grid of $C_6$ and $C_8$. Panel (b) shows the second step of the search with a much finer grid in the adjacent area of the minimum of the initial search. The three-dimensional surface of ${\chi }^2$ as well as its contours are color coded with the value of ${\chi }^2$. Red indicates smaller values while light blue indicates larger values.

Figure 6

The total and first five partial elastic-scattering cross sections as functions of collision energy. The solid red line corresponds to the total cross section. The dashed lines correspond to partial cross sections with $l=0$ to 4, which are labeled as $s$ to $g$ wave. Note that not all partial wave cross sections that contribute significantly to the total cross section are shown here.

Figure 7

Representative coherent two-photon spectrum in which the ground $v=-1$ state is observed as the narrow atom-molecule dark state feature within a broad loss resonance. For these data, the BB laser was fixed at the $v^{*}=-2\leftrightarrow v=-1$ resonance while the FB laser was varied across the $v^{*}=-2$ one-photon PA resonance. The solid line is a sum of two Lorentzians fit to the data. The error bars are statistical.