Ultracold three-body collisions near narrow Feshbach resonances

We study ultracold three-body collisions of bosons and fermions when the interatomic interaction is tuned near a narrow Feshbach resonance. We show that the width of the resonance has a substantial impact on the collisional properties of ultracold gases in the strongly interacting regime. From our numerical and analytical analyses, we identify universal features dependent on the resonance width. Remarkably, we find that all inelastic processes near narrow resonances leading to deeply bound states in bosonic systems are suppressed, while those for fermionic systems are enhanced. As a result, narrow resonances present a scenario that is the reverse of that found for broad resonances, opening up the possibility of creating stable samples of ultracold bosonic gases with large scattering lengths.

Figure 1

Schematic comparison of (a) a Feshbach resonance and (b) a shape resonance. On resonance, the short-range ($r<r_0$), bound component is similar in both cases, and the long-range ($r>r_0$) wave function is the same. The double-headed arrows indicate the coupling.

Figure 2

Ultracold three-body recombination rates for identical bosons ($a>0$). The vertical dashed lines indicate the position of the first Efimov feature predicted in Refs. [23, 24]. The solid triangles are experimental data for the 907 G Feshbach resonance in a Na Bose-Einstein condensate [55]. Here we show $K_3$ with one or more two-body $s$-wave bound states (BS), including the analytical result from [23] scaled to match our data (thick solid line). In the bottom panel we show the recombination rates calculated by using two different two-body potentials: the potentials defined in Eqs. (3) and (4). Here $r_0=50$ a.u.

Figure 3

Ultracold three-body recombination rates ($a<0$) for identical bosons. The solid lines through the numerical data points are to guide the eye, while the dashed lines are the analytical results from Eq. (21), using the $\alpha$ and $\beta$ indicated from a fit in the limit $\left|r_{\mathrm{eff}}\right|\to \infty$. Here $r_0$ $=$ 50 a.u.

Figure 4

Ultracold three-body relaxation rates ($a>0$) for identical bosons. The solid lines through the numerical data points are to guide the eye, while the dashed lines are the analytical results from Eq. (16), using the $\alpha$ and $\beta$ indicated from a fit in the limit $\left|r_{\mathrm{eff}}\right|\to \infty$. Here $r_0=50$ a.u.

Figure 5

Schematic $W_{\nu \nu }(R)$ used to derive Eqs. (16) and (21) with $r_0\ll \left|r_{\mathrm{eff}}\right|\ll \left|a\right|$. The difference in the potentials between the recombination ($a<0$) and relaxation ($a>0$) is only in the asymptotic region. In the “Coulomb-like” region, the potential shown with the dashed line is attractive only when there is one or two two-body bound states in the system. The short-range region is shaded to indicate strong coupling between the initial and final channels, where inelastic transition occurs dominantly.

Figure 6

Adiabatic hyperspherical potentials near a narrow Feshbach resonance. Numerical $W_{\nu \nu }(R)$ is multiplied by 2$\mu R^2$ with $r_{\mathrm{eff}}=-5000$ a.u. and $\left|a\right|=\infty$. The lower curve is from the calculations with a single $2+1$ $s$-wave bound channel, and the upper one is from the calculations with three $2+1$ $s$-wave bound channels.

Figure 7

Relaxation rates for mixed-spin fermions with $a>0$ and large $\left|r_{\mathrm{eff}}\right|$. The relaxation rate for small $\left|r_{\mathrm{eff}}\right|$ is also plotted, showing the same scaling with $a$ but not with $\left|r_{\mathrm{eff}}\right|$ since it is not in the universal limit.