Stability of a Unitary Bose Gas

We study the stability of a thermal ${}^{39}\mathrm{K}$ Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length $a$ exceeds the thermal wavelength $\lambda$. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive $a\ll \lambda$ we find agreement with three-body theory. However, for $a<0$ and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, $L_3\propto {\lambda }^4$, is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes ${}^{39}\mathrm{K}$ particularly promising for studies of many-body physics in a unitary Bose gas.

Figure 1

Particle loss and heating in a resonantly interacting Bose gas ($\lambda /a=0$). Each point is an average of 5 measurements and error bars show standard statistical errors. Solid red lines are fits based on Eqs. (5, 3).

Figure 2

Heating exponent $\beta$, as defined in Eq. (3). The red dashed line is a result of nonunitary three-body theory, while the red star indicates the predicted value of 1.8 at unitarity. Open symbols indicate the region where four-body decay is significant (see text and Fig 3). Note that $\lambda \approx 5\times {10}^3{a}_0$ and horizontal error bars reflect its variation during a measurement sequence at a fixed $a$. Vertical error bars show fitting uncertainties. Inset: Log-log plots of $N$ vs $T$ (scaled to their values at $t=0$) for the data series at $\lambda /a\approx -5.3$ (open) and 8.5 (solid).

Figure 3

Three- vs four-body decay for $a<0$ (away from unitarity). $N$ decay at $a=-850a_0$ is fitted to a model including both three- and four-body losses (green solid line), as well as to pure three- and four-body models (red dashed and black dot-dashed line, respectively). Inset: For comparison, at $a=700a_0$, the solid green and the dashed red lines are indistinguishable, showing that four-body decay does not play a detectable role.

Figure 4

Particle-loss exponent $\nu$, as defined in Eq. (5). The red dashed line shows the nonunitary theory, $\nu =3+3/\beta$, assuming nonunitary $\beta$ values. The red star shows the unitary prediction, $\nu =3+5/\beta$, corresponding to $L_3\propto 1/T^2$ and the measured $\beta$. Error bars are analogous to those in Fig. 2.

Figure 5

Three-body loss coefficient. Main panel: $(L_3/L_3^{\mathrm{M}}{)}^{-1/4}$ (see text) at $T=1.1\mu \mathrm{K}$. Horizontal green line marks the theoretical upper bound on $L_3$, while the red dashed line is a guide to the eye showing the $L_3\propto a^4$ nonunitary scaling. At unitarity, $L_3/L_3^{\mathrm{M}}\approx 0.27$. Inset: $L_3$ at $1.1\mu \mathrm{K}$ (open symbols) and $1.7\mu \mathrm{K}$ (solid symbols). The expected ratio between the two unitary plateaux is indicated by the green vertical bar.