Feshbach resonances in ultracold ${}^{85}$Rb

We present 17 experimentally confirmed Feshbach resonances in optically trapped ${}^{85}$Rb. Seven of the resonances are in the ground-state channel $(f,m_f)=(2,+2)+(2,+2)$ and nine are in the excited-state channel $(2,-2)+(2,-2)$. We find a wide resonance at high field in each of the two channels, offering possibilities for the formation of larger ${}^{85}$Rb condensates and studies of few-body physics. A detailed coupled-channel analysis is presented to characterize the resonances and also provides an understanding of the inelastic losses observed in the excited-state channel. In addition we have confirmed the existence of one narrow resonance in a $(2,+2)+(3,+3)$ spin mixture.

Figure 1

Top panel: Calculated $s$-wave scattering length in the $\mathrm{aa}$ channel of ${}^{85}$Rb${}_2$, with resonances marked with lines whose color depends on their $M_F$ value (see legend); the length of each line is proportional to the logarithm of the width of the resonance. Bottom panel: Energies of weakly bound molecular states, relative to the aa threshold, $(2,+2)+(2,+2)$ channel. All calculations in this figure are for $M_{\mathrm{tot}}=4$, corresponding to $s$-wave scattering in the aa channel.

Figure 2

Top two panels: Real and imaginary parts of the $s$-wave scattering length in the ee channel of ${}^{85}$Rb${}_2$. Each resonance is indicated by a colored vertical line that indicates its $M_F$ value (see legend); for polelike resonances, the length of the line is proportional to the logarithm of the width of the resonance. Inelastically dominated resonances are not always evident in $\alpha$, but appear as peaks in $\beta$ and are indicated by dashed vertical lines. Bottom panel: Energies of weakly bound molecular states, relative to the ee threshold, $(2,-2)+(2,-2)$ channel. Only states with no continuum interference ($M_F\le -4$) are shown in the bound-state map, but all resonances are included in the scattering length. All calculations in this figure are for $M_{\mathrm{tot}}=-4$, corresponding to $s$-wave scattering in the ee channel.

Figure 3

Narrow resonances in ${}^{85}$Rb, with fitted width $\delta <0.2$ G, observed as loss features in the atom number due to an enhancement in inelastic collisions near the resonance. (a) A resonance in the $(2,-2)$ state at 248.64(1) G. (b) A resonance in the $(2,+2)$ state at 770.81(1) G. The error bars show the standard deviation for multiple control shots at specific magnetic fields.

Figure 4

Broad resonances in ${}^{85}$Rb, with width $\Delta >1$ G, observed as features in the atom number. (a) A resonance in the $(2,-2)$ state at 532.3(3) G. (b) A resonance in the $(2,+2)$ state at 852.3(3) G. The experimental widths are determined by the difference between the positions of the minima and maxima in the atom number marked with solid lines in both plots. The error bars show the standard deviation for multiple control shots at specific magnetic fields.

Figure 5

The two inelastically dominated features observed in the $(2,-2)$ state. (a) and (b) show the atom number while (c) and (d) show temperature. Error bars show the standard deviation for multiple control shots at specific magnetic fields. (e) and (f) show the calculated rate coefficient for two-body loss $K_{\mathrm{loss}}$.

Figure 6

Resonance measured between the $(2,+2)$ and $(3,+3)$ spin states in ${}^{85}$Rb at 817.45(5) G. On resonance the increased inelastic collision rate in the mixture results in a loss feature in the $(2,+2)$ atom number as a function of magnetic field. The error bars show the standard deviation for multiple control shots at a specific magnetic field.

Figure 7

Rate coefficient for two-body loss $K_{\mathrm{loss}}$ (red solid lines), which is proportional to the imaginary part of the scattering length, and the corresponding real part of the scattering length (dashed lines) for the two resonances with $\Delta >1$ G in the $\mathrm{ee}$ channel. Note the dip in $K_{\mathrm{loss}}$ on the high-field side of the 532 G resonance.