Lifetime of the Bose Gas with Resonant Interactions

We study the lifetime of a Bose gas at and around unitarity using a Feshbach resonance in lithium 7. At unitarity, we measure the temperature dependence of the three-body decay coefficient $L_3$. Our data follow a $L_3={\lambda }_3/T^2$ law with ${\lambda }_3=2.5(3{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}\times {10}^{-20}(\mu \mathrm{K}{)}^2{\mathrm{cm}}^6{\mathrm{s}}^{-1}$ and are in good agreement with our analytical result based on zero-range theory. Varying the scattering length $a$ at fixed temperature, we investigate the crossover between the finite-temperature unitary region and the previously studied regime where $|a|$ is smaller than the thermal wavelength. We find that $L_3$ is continuous across the resonance, and over the whole $a<0$ range our data quantitatively agree with our calculation.

Figure 1

Time dependence of the atom number (a) and temperature (b) for $U=\eta k_{B}T$, with $T=5.2(4)\mu \mathrm{K}$, $\eta =7.4$, and (uncorrected) $L_3=1.2(2{)}_{\mathrm{stat}}\times {10}^{-21}{\mathrm{cm}}^6{\mathrm{s}}^{-1}$. The dotted line shows the long time $t^{-1/2}$ dependence of the number of atoms.

Figure 2

Temperature dependence of the three-body loss rate $L_3$. Filled circles, experimental data; green dashed line, best fit to the data $L_3(T)={\lambda }_3/T^2$ with ${\lambda }_3=2.5(3{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}\times {10}^{-20}(\mu \mathrm{K}{)}^2{\mathrm{cm}}^6{\mathrm{s}}^{-1}$; the shaded green band shows the $1\sigma$ quadrature sum of uncertainties. Solid line, prediction from Eq. (5), ${\lambda }_3=1.52\times {10}^{-20}(\mu \mathrm{K}{)}^2{\mathrm{cm}}^6{\mathrm{s}}^{-1}$ with ${\eta }_{*}=0.21$ from Refs. 30, 39.

Figure 3

(a) ${}^7\mathrm{Li}$ scattering-length dependence of the three-body rate constant $L_3(a)$ for constant $T=5.9(6)\mu \mathrm{K}$ (filled and open circles). For small positive $a$, $L_3(a)$ for a low-temperature condensate is also shown (green squares). The solid blue line corresponds to our theoretical prediction Eq. (4) for $T=5.9\mu \mathrm{K}$. The blue range is the same theory for 5.3 to $6.5\mu \mathrm{K}$. The dashed lines show the zero-temperature prediction for $L_3(a)$ [20] fitted to the measurements in Refs. 30, 39 with the parameters ${\eta }_{*}=0.21$ and $R_0=270a_0$. The vertical dotted lines correspond to $|a|/{\lambda }_{\mathrm{th}}=1$. The open circles in the range $1500a_0<a<5000a_0$ are not corrected for residual evaporation as our model is not applicable. (b) Logarithmic plot of the $a<0$ side, displaying the two Efimov loss resonances.