Optical Production of Stable Ultracold ${}^{88}\mathrm{Sr}_2$ Molecules

We have produced large samples of stable ultracold ${}^{88}\mathrm{Sr}_2$ molecules in the electronic ground state in an optical lattice. The fast, all-optical method of molecule creation involves a near-intercombination-line photoassociation pulse followed by spontaneous emission with a near-unity Franck-Condon factor. The detection uses excitation to a weakly bound electronically excited vibrational level corresponding to a very large dimer and yields a high-$Q$ molecular vibronic resonance. This is the first of two steps needed to create deeply bound ${}^{88}\mathrm{Sr}_2$ for frequency metrology and ultracold chemistry.

Figure 1

(a) Long-range ${}^{88}\mathrm{Sr}_2$ potential energies versus internuclear separation. The two curves relevant to this work are the ground state potential $X^1{\Sigma }_g^{+}$ and the excited state potential $(1)0_u^{+}$ that dissociate to the ${}^{1}S_0+{}^{1}S_0$ and ${}^{1}S_0+{}^{3}P_1$ (689 nm) atomic limits, respectively. Several vibrational energy levels $v,v^{\prime }$, with the total molecular angular momenta $(J,J^{\prime })=(0,1)$, are shown, along with their binding energies; the primed values refer to the excited potential. The negative $v,v^{\prime }$ values refer to counting from the dissociation limit, with $-1$ corresponding to the highest-lying level. The natural line widths of the shown $v^{\prime }$ levels are $\sim 20\mathrm{kHz}$. The horizontal dashed line represents the thermal continuum for the $\mu \mathrm{K}$ atoms. The vertical solid arrows indicate one-photon optical pathways used for molecule creation and atom recovery. The vertical dashed arrows indicate decay pathways completing the molecule creation and recovery; these rely on the unusually large FCF and optical length, respectively. (b) The large value of the FCF $f_{v{v}^{\prime }}=f_{(-2,-5)}\approx 0.8$ results from an excellent agreement of the outer turning points, as illustrated by the wave function plots for these vibrational levels.

Figure 2

Autler-Townes doublets emerge when the $L_{\mathrm{BB}}$ frequency is fixed near a molecular resonance while $L_{\mathrm{FB}}$ is scanned. (a) Autler-Townes peak positions, along with their separation ${\Omega }^{\prime }$ fitted to Eq. (1), for $(v,v^{\prime })=(-2,-5)$. The dashed line indicates the on-resonance Rabi frequency $\Omega$ at the indicated $L_{\mathrm{BB}}$ power. (b) The same as (a), for $(v,v^{\prime })=(-3,-4)$. The $L_{\mathrm{BB}}$ power is $60\times$ larger, while $\Omega$ is $4.4\times$ smaller, resulting in $f_{(-3,-4)}/f_{(-2,-5)}=0.9\times {10}^{-3}$. The inset shows a representative atom loss curve with an Autler-Townes doublet corresponding to the circled data points.

Figure 3

(a) Solid line: Fraction of the atom cloud detected after a molecule producing PA pulse followed by an atom clearing pulse and an atom recovery pulse. The data are scaled to the calculation; the lowest bound on the peak atom-molecule conversion fraction is 3%. Dashed line: Calculated fraction of the atom cloud converted to $v=-2$ molecules after the PA pulse. The curve parameters were measured independently, with the exception of the molecule lifetime, which was fixed at 3 ms to best match the data. The inset shows denser data in the first millisecond. (b) Fraction of the atom cloud detected after a 1 ms PA pulse followed by the atom clearing and $20\mu \mathrm{W}$ atom recovery pulses, as a function of the $L_{\mathrm{BB}}$ frequency. The sharp peak corresponds to the bound-bound transition from $v=-2$ to $v^{\prime }=-1$. Its fitted Lorentzian full width of 32(4) kHz corresponds to a quality factor $Q=1.4\times {10}^{10}$, the highest reported for a molecular vibronic transition. (c) The same as (b), at the higher $380\mu \mathrm{W}$ atom recovery pulse power. In this high power regime, atoms are also recovered via the ${}^{1}S_0+{}^{3}P_1$ thermal continuum, which is only 0.4 MHz away from $v^{\prime }=-1$.