Momentum Distribution of a Dilute Unitary Bose Gas with Three-Body Losses

Using a combination of Boltzmann’s equation and virial expansion, we study the effect of three-body losses and interactions on the momentum distribution of a homogeneous unitary Bose gas in the dilute limit where quantum correlations are negligible. The comparison of our results to the recent measurement made at JILA on a unitary gas of ${}^{85}\mathrm{Rb}$ allows us to determine an experimental fugacity $z=0.5(1)$.

Figure 1

Deformation of the momentum distribution of a unitary Bose gas due to three-body losses. From top to bottom: $n{\lambda }_{\text{th}}^3(1-e^{-4\eta })=0$ (blue, Boltzmann gas), $n{\lambda }_{\text{th}}^3(1-e^{-4\eta })=0.05$ (orange), and $n{\lambda }_{\text{th}}^3(1-e^{-4\eta })=0.1$ (red).

Figure 2

Correction to the Boltzmann gas: Three-body losses vs interactions. The correction to Boltzmann’s distribution is plotted for maximal three-body losses ($\eta =\infty$, red dashed line), $\eta =0.2$, corresponding to ${}^7\mathrm{Li}$ (orange dotted line). The blue solid line corresponds to the correction, Eq. (19), due to Bose statistics and two-body interactions.

Figure 3

The dimensionless momentum occupation number for the unitary Bose gas in a semilog scale. $\kappa =p/\hslash k_n$ with $k_n\equiv {(6{\pi }^2⟨n⟩)}^{1/3}$ and $⟨n⟩$ the spatially averaged density ($⟨n⟩=5.5\times 10^{12}{\mathrm{cm}}^{-3}$ and $⟨n⟩=1.6\times 10^{12}{\mathrm{cm}}^{-3}$). The occupation number is normalized so that $\int n(\kappa )4\pi \kappa d\kappa =8{\pi }^3$. The continuous line is the experimental result from Ref. [18] , the dashed line is the result of Eq. (19) averaged over the initial density profile for $z=0.6$, and the dotted line includes the effect of three-body losses. The fit is restricted to $\kappa >0.5$ since for lower momenta, the momentum distribution never equilibrates.