Universal few-body physics in a harmonic trap

Abstract

Few-body systems with resonant short-range interactions display universal properties that do not depend on the details of their structure or their interactions at short distances. In the three-body system, these properties include the existence of a geometric spectrum of three-body Efimov states and a discrete scaling symmetry. Similar universal properties appear in 4-body and possibly higher-body systems as well. We set up an effective theory for few-body systems in a harmonic trap and study the modification of universal physics for 3- and 4-particle systems in external confinement. In particular, we focus on systems where the Efimov effect can occur and investigate the dependence of the 4-body spectrum on the experimental tuning parameters.Comment: 20 pages, 10 figures, final version, new references adde

Convergence properties of the effective theory for trapped bosons

“…In this paper, we have extended our previous work on universal few-body physics in harmonic confinement [26]. We investigated A-body systems with up to six particles using genuine and smeared contact interactions at leading order in the large scattering length.…”

“…use contact interactions and extrapolate in 1/ N + (A − 1)3/2 as in our previous work [26], and 2. use smeared contact interactions and extrapolate the converged results in N linearly in the width parameter ǫ.…”

“…In Ref. [26], we published results for a 4-boson system with contact interactions. Here we revisit these calculations using smeared interactions.…”

“…In our previous work, we found that the convergence to the results in the full Hilbert space is slow due to the irregularity of the δ-distribution in the parametrization of the genuine contact interactions [26]. For the cutoff dependence to become insignificant, values for 1/ √ N of order 0.1 or smaller have to be reached.…”

“…The effective interactions were defined within a finite model space with a cutoff N on the basis functions. In previous work [26], we have performed a systematic study of the spectra of three-and four-body systems in the vicinity of the unitary limit at leading order in the effective theory. In this paper, we extend our calculations to six bodies.…”