Abstract
The two- and three-body contacts are central to a set of univeral relations between microscopic few-body physics within an ultracold Bose gas and its thermodynamical properties. They may also be defined in trapped few-particle systems, which is the subject of this work. In this work, we focus on the unitary three-body problem in a trap, where interactions are as strong as allowed by quantum mechanics. We derive analytic results for the two- and three-body contacts in this regime and compare them with existing limiting expressions and previous numerical studies.
Highlights
As the s-wave scattering length approaches unitarity | a| → ∞, properties of both macroscopic and microscopic strongly-interacting ultracold quantum systems can be described effectively by a reduced set of remaining finite quantities
For three trapped bosonic alkali atoms at unitarity, physics in the unitary regime is parametrized solely by the range of the potential, captured by the van der Waals length rvdW [1], and the trap length aho = (h/mω )1/2, with frequency ω and single-particle mass m. These scales parametrize the two and three-body contacts, respectively, that are central to many relevant observables in the system including the tail of the single-particle density, short-distance behavior of correlation functions, high-frequency tail of the rf transition rate, virial theorem, and total energy of the system [2,3]
Any one of the universal relations involving the contacts can be used as a starting point; we choose to obtain them through the limiting behavior of few-body correlation functions [2,3]
Summary
As the s-wave scattering length approaches unitarity | a| → ∞, properties of both macroscopic and microscopic strongly-interacting ultracold quantum systems can be described effectively by a reduced set of remaining finite quantities. For three trapped bosonic alkali atoms at unitarity, physics in the unitary regime is parametrized solely by the range of the potential, captured by the van der Waals length rvdW [1], and the trap length aho = (h/mω )1/2 , with frequency ω and single-particle mass m These scales parametrize the two and three-body contacts, respectively, that are central to many relevant observables in the system including the tail of the single-particle density, short-distance behavior of correlation functions, high-frequency tail of the rf transition rate, virial theorem, and total energy of the system [2,3]. We find generally excellent agreement with the available results of that work
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