Molecules of Fermionic Atoms in an Optical Lattice

We create molecules from fermionic atoms in a three-dimensional optical lattice using a Feshbach resonance. In the limit of low tunneling, the individual wells can be regarded as independent three-dimensional harmonic oscillators. The measured binding energies for varying scattering length agree excellently with the theoretical prediction for two interacting atoms in a harmonic oscillator. We demonstrate that the formation of molecules can be used to measure the occupancy of the lattice and perform thermometry.

Figure 1

(a) Illustration of the rf spectroscopy between two bound states within a single well of the optical lattice. The atoms in the initial states $|-7/2⟩$ and $|-9/2⟩$ are converted into a bound dimer by sweeping across a Feshbach resonance. Subsequently we drive an rf transition $|-7/2⟩\to |-5/2⟩$ to dissociate the molecule. (b) rf spectrum taken at $B=202.9\mathrm{G}$, i.e., for $a<0$. (c) rf spectrum taken at $B=202.0\mathrm{G}$, i.e., for $a>0$. All data are taken for a lattice depth of $22E_r$. The lines are Lorentzian fits to the data.

Figure 2

The measured binding energy of molecules in a three-dimensional optical lattice. The data are taken for several potential depths of the optical lattice of $6E_r$ (triangles), $10E_r$ (stars), $15E_r$ (circles), and $22E_r$ (squares). The solid lines correspond to the theory of Ref. 13 with no free parameters; the dashed lines use an energy-dependent pseudopotential according to Ref. 14. At the position of the Feshbach resonance ($a\to \pm \infty$) the binding energy takes the value $E=-\hslash \omega$.

Figure 3

The fraction of molecules detected by rf spectroscopy at a potential depth of $15E_r$. For weakly bound molecules ($a_{\mathrm{ho}}/a<-1$) the dissociation works well since the overlap between the molecular and the atomic wave functions is large. For deeply bound molecules $a_{\mathrm{ho}}/a>0$ the detected molecular fraction is suppressed due to the vanishing overlap between the wave functions. The solid line shows the theoretical expectation for a constant molecular fraction of 43%.