Observation of Efimov Molecules Created from a Resonantly Interacting Bose Gas

We convert a strongly interacting ultracold Bose gas into a mixture of atoms and molecules by sweeping the interactions from resonant to weak. By analyzing the decay dynamics of the molecular gas, we show that in addition to Feshbach dimers it contains Efimov trimers. Typically around 8% of the total atomic population is bound into trimers, identified by their density-independent lifetime of about $100\mu \mathrm{s}$. The lifetime of the Feshbach dimers shows a density dependence due to inelastic atom-dimer collisions, in agreement with theoretical calculations. We also vary the density of the gas across a factor of 250 and investigate the corresponding atom loss rate at the interaction resonance.

Figure 1

(a) The solid green line shows the two-body scattering length near the Feshbach resonance centered at 155.04 G. The solid red line is the calculated energy of the ground state Efimov trimer, $E_T^{(0)}$ [27]. The solid blue and dashed red lines show the calculated molecular energies of the Feshbach dimer, $E_b$, and first excited Efimov trimer, $E_T^{(1)}$, respectively. We populate molecular states by sweeping our gas from 155.04 G to $B>158.6\mathrm{G}$. With a microwave pulse, we then transfer either atomic or molecular population to the $|3,-3⟩$ state for absorption imaging; the experimental points in (b) are population transfer. The green line is a delta function free-atom transition broadened by experimental resolution. The blue line is a calculated Frank-Condon factor for dimer dissociation [26]. The red line shows the expected shape of the trimer dissociation yield, but the difference between $E_T^{(1)}$ and $E_b$ is exaggerated for clarity.

Figure 2

The number of molecules, normalized by the initial atom number, as a function of hold time at $a=700(7)a_0$ for initial BEC densities $n_0=1.3(1)\times {10}^{12}{\mathrm{cm}}^{-3}$ (dark triangles) and $n_0=0.20(1)\times {10}^{12}{\mathrm{cm}}^{-3}$ (light circles). The solid lines show a two component exponential decay. At high and low densities the time for the initial fast loss ($t_1$) does not significantly change, being 97(23) and $125(36)\mu \mathrm{s}$, respectively; we identify this loss as decay of the trimers. The time scales for the slower loss ($t_2$) are 1240(80) and $2200(100)\mu \mathrm{s}$; as discussed in the text, this is consistent with a combination of dipole relaxation and collisional loss in the population of dimers [see Eq. (3)]. For higher density data, the number of trimers is $A_1=2000(200)$ and dimers $A_2=4500(200)$. This corresponds to 6000 atoms that were swept into the trimer state, roughly 8% of the initial sample. The inset shows the normalized number of molecules as a function of inverse ramp rate for $n_0=5.5(2)\times {10}^{12}{\mathrm{cm}}^{-3}$ (dark squares) and $n_0=0.18\times {10}^{12}{\mathrm{cm}}^{-3}$ (light circles); the solid lines are guides for the eye.

Figure 3

(a) The lifetime of the Feshbach dimers for various densities as a function of the scattering length, $a$. The solid lines represent the predicted dimer lifetime for the respective densities. The dashed line represents the predicted dimer lifetime considering only spin relaxation. While our lowest density molecules live somewhat longer than the inelastic spin relaxation model predicts, we see good agreement with previous measurements of dimer lifetimes from Ref. [30] for $n_0=0.26\times {10}^{12}{\mathrm{cm}}^{-3}$ (open circle). (b) Over a factor of 30 range in density, the lifetime of the Efimov trimers at $a=700(7)a_0$ averages to $114(16)\mu \mathrm{s}$ (dashed line), and shows no significant variation.

Figure 4

$(1-N/N_0)/{\tau }_{\text{evolve}}$ is the perceived atom loss rate. We measure the number of atoms that return to weak interactions after ${\tau }_{\text{evolve}}\approx t_n$. The solid line goes as $n^{2/3}$. The dashed line goes as $n^2$, the expected three-body loss rate in the mean-field regime.