Three-Body Recombination at Vanishing Scattering Lengths in an Ultracold Bose Gas

We report on measurements of three-body recombination loss rates in an ultracold gas of ${}^7\mathrm{Li}$ atoms in the extremely nonuniversal regime where the two-body scattering length vanishes. We show that the loss rate coefficient is well defined and can be described by two-body parameters only: the scattering length $a$ and the effective range $R_e$. We find the rate to be energy independent, and, by connecting our results with previously reported measurements in the universal limit, we cover the behavior of the three-body recombination rate in the whole range from weak to strong two-body interactions. We identify a nontrivial magnetic field value in the nonuniversal regime where the rate should be suppressed.

Figure 1

Scattering length $a$ (green solid line), effective range $R_e$ (blue dotted line) and effective length $L_e^{\prime }$ (pink dashed line) in units of Bohr radius $a_0$ as a function of the magnetic field $B$ as obtained from our most up-to-date coupled channels analysis [21]. (a) Region of the high field zero crossing with $a=0$ at 850.1 G. $a$ diverges at the positions of Feshbach resonances at 845.5 G and 894 G. $R_e$ diverges when $a\to 0$. (b) Region of the low field zero crossing with $a=0$ at 575.9 G. The absolute value of $L_e^{\prime }$ is shown to emphasize the $L_e^{\prime }=0$ point at 744.15 G, where $R_e$ (not shown) rapidly changes sign.

Figure 2

Temperature at the end of fast evaporation cycle as a function of the magnetic field $B$. Maximal temperature corresponds to minimum in the collisional cross section. The red solid line is the finite temperature theory model described in text. The fitted position of the scattering length’s zero crossing is 849.92(25) G. The dashed line represents the model which excludes energy dependence of the cross section and disagrees with data.

Figure 3

Measurements of the three-body recombination length $L_m$ at $2.5\mu \mathrm{K}$ (black circles) and $10\mu \mathrm{K}$ (red open circles). Blue dashed-dotted line represents the effective recombination length $L_e$ and pink dashed line shows the modified effective length $L_e^{\prime }$ that includes $a^3$ term correction [see Eq. (6)]. Green solid line represents the modulus of the scattering length $|a|$. For comparison, the van der Waals length for ${}^7\mathrm{Li}$ atoms is $r_{\text{VDW}}=32.5a_0$.