Quantitative analysis of losses close to a $d$-wave open-channel Feshbach resonance in ${}^{39}\mathrm{K}$

We study atom losses associated to a previously unreported magnetic Feshbach resonance in ${}^{39}\mathrm{K}$. This resonance is peculiar in that it presents $d$-wave character both in the open and closed channels, directly coupled by the dominant spin-exchange interaction. The losses associated to a $d$-wave open-channel resonance present specific signatures such as strong temperature dependance and anisotropic line shapes. The resonance strength and position depend on the axial projection of the orbital angular momentum of the system and are extracted from rigorous multichannel calculations. A two-step model, with an intermediate collision complex being ejected from the trap after collisions with free atoms, permits us to reproduce the observed dependance of the loss rate as a function of temperature and magnetic field.

Figure 1

Normalized number of atoms remaining in the trap after a waiting time of 1 s at different magnetic fields. The shape of the loss curve is asymmetric and its width increases with the temperature.

Figure 2

Decay of the number of atoms for a trapped gas at 140 $\mu \mathrm{K}$ for two different magnetic fields. Experimental points are crosses and stars; fits are solid lines.

Figure 3

Measured three-body loss rate $\mathrm{K}{}_3$ as a function of the magnetic field. The plotted error bars are the uncertainties estimated from the loss curve fit quality. They do not take into account the uncertainties related to the initial densities which may effect the absolute values of $K_3$ up to a factor of $\sim 2.5$. Ratios of $K_3$ at different temperatures are better controlled with an uncertainty of $\sim 40\%$. The continuous lines are fits according to the model described in the text. The fitted values of $C$ are $0,2.7\times {10}^{-17},6.6\times {10}^{-17},\text{and}7.3\times {10}^{-17}$ $\mathrm{m}{}^3$ $\mathrm{s}{}^{-1}$ for the sample with temperatures ranging from 22 to $180\mu \mathrm{K}$.

Figure 4

Partial decay widths of a $l=2$ resonance to the $\{{\alpha }_{in},l=2\}$ (dashed blue line), $\{{\alpha }_{in},l=0\}$ (dash-dotted red line) elastic collision channels as a function of the resonance position. The total inelastic width (dotted green line) and the full width (full black line) are also shown (see text for details). Calculation is for total magnetic quantum number $M=-2$.