Feshbach-Resonance-Enhanced Coherent Atom-Molecule Conversion with Ultranarrow Photoassociation Resonance

We reveal the existence of high-density Feshbach resonances in the collision between the ground and metastable states of ${}^{171}\mathrm{Yb}$ and coherently produce the associated Feshbach molecules by photoassociation. The extremely small transition rate is overcome by the enhanced Franck-Condon factor of the weakly bound Feshbach molecule, allowing us to observe Rabi oscillations with long decay time between an atom pair and a molecule in an optical lattice. We also perform the precision measurement of the binding energies, which characterizes the observed resonances. The ultranarrow photoassociation will be a basis for practical implementation of optical Feshbach resonances.

Figure 1

(a) Low-lying energy level diagram of ${}^{171}\mathrm{Yb}$. (b)–(d) Observation of FRs (marked with rectangles) in a mixture of $|g_{\uparrow }⟩\text{−}|g_{\downarrow }⟩\text{−}|e⟩$, $|g_{\uparrow }⟩\text{−}|e⟩$ and $|g_{\downarrow }⟩\text{−}|e⟩$, respectively. Trap loss spectra at temperature of (b) 1.1 and (b),(c) $1.8\mu \mathrm{K}$ are shown. Pink points in (b) represents the data for a sample containing $|e⟩$ atoms only. Red dashed line in (c) highlights the existence of a broad resonance at 6.6 G.

Figure 2

(a) ${{}^{1}S}_0\leftrightarrow {{}^{3}P}_2$ laser spectroscopy at $B=6.2\mathrm{G}$. The PA resonance to the Feshbach molecule associated with the 6.6 G broadest FR is visible at $-38\mathrm{kHz}$ from the atomic resonance. The PA laser pulse has a duration 20 ms and intensity $2.3\mathrm{W}/{\mathrm{cm}}^2$. (b) Binding energy of the Feshbach molecule associated with resonances at $B=6.0$ and 6.6 G. The solid lines are the result of the coupled two-channel calculation. Two dashed lines indicate the bare closed channel molecule and the shallowest bound state of the open channel. The dot-dashed line is the prediction of the universal relation $E_b=-{\hslash }^2/(m{a}^2)$. (c) Detailed behavior near the anti level crossing at 6 G.

Figure 3

(a) Spectrum on the ${{}^{1}S}_0\leftrightarrow {{}^{3}P}_2$ transition in an optical lattice with the depth of $14.7E_R$. (b) Magnetic field dependence of the scattering length $a_{g\uparrow ,e}$ determined by spectroscopy in an optical lattice.

Figure 4

(a) Rabi oscillations of isolated atoms (top) and atom pairs $\leftrightarrow$ molecules at various magnetic field (bottom) in an optical lattice. The laser intensity is fixed to $58\mathrm{W}/{\mathrm{cm}}^2$. For the atomic transition, the Rabi frequency is 11.8 kHz. (b) The atom-molecule Rabi frequency $\mathrm{\Omega }$ as a function of the magnetic field. Symbols (circles, squares) distinguish the different branches of the anticrossing at 6 G. The solid line shows the prediction from the wave function overlap (see text).