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

Abstract

In a recent experiment with ultracold trapped [superscript 85]Rb 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[subscript 2] and the three-body contact C[subscript 3]. We determine the contact densities for the unitary Bose gas with number density n to be C[subscript 2] ≈ 20n[superscript 4/3] and C[subscript 3] ≈ 2n[superscript 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[subscript 3], but the loss rate is not compatible with that from 2-atom inelastic collisions, which gives a contribution proportional to C[subscript 2]. We point out that the contacts C[subscript 2] and C[subscript 3] could be measured independently by using the virial theorem near and at unitarity, respectively.