Two-Body and Three-Body Contacts for Identical Bosons near Unitarity

In a recent experiment with ultracold trapped Rb-85 atoms, Makotyn et al. studied a quantum-degenerate Bose gas in the unitary limit where its scattering length is infinitely large. We show that the observed momentum distributions are compatible with a universal relation that expresses the high-momentum tail in terms of the two-body contact C-2 and the three-body contact C-3. We determine the contact densities for the unitary Bose gas with number density n to be C-2 approximate to 20n(4/3) and C-3 approximate to 2n(5/3). We also show that the observed atom loss rate is compatible with that from 3-atom inelastic collisions, which gives a contribution proportional to C-3, but the loss rate is not compatible with that from 2-atom inelastic collisions, which gives a contribution proportional to C-2. We point out that the contacts C-2 and C-3 could be measured independently by using the virial theorem near and at unitarity, respectively.