Abstract
The stationary states of a few bosons in a one-dimensional harmonic trap are investigated throughout the crossover from weak to strongly attractive interactions. For sufficient attraction, three different classes of states emerge: (i) N-body bound states, (ii) bound states of smaller fragments and (iii) gas-like states that fermionize, that is, map to ideal fermions in the limit of infinite attraction. The two-body correlations and momentum spectra characteristic of the three classes are discussed, and the results are illustrated using the soluble two-particle model.
Highlights
In recent years, ultracold atoms have become a flexible tool for the simulation of fundamental quantum systems [1, 2, 3]
III B), the diagonal {x1 = x2} “damps out” more and more. The fact that it persists even for couplings as large as g = −10 underscores the notion of the super-Tonks gas being more strongly correlated than its repulsive counterpart [20]. This in turn relates to the picture that, due to a positive 1D scattering length a = −2/g, a small region is excluded from the scattering zone, so that the hard core effectively extends to a nonzero volume
We have brought together the subjects of attractive, one-dimensional Bose gases—which currently are of great interest and experimentally relevant—and the binding properties of few-body systems
Summary
Ultracold atoms have become a flexible tool for the simulation of fundamental quantum systems [1, 2, 3]. The case of repulsive interactions has long received considerable attention, mostly for the striking feature that, in the hard-core limit of infinite repulsion between the bosons, the system maps to an ideal Fermi gas [6]. In this fermionization limit, the bosons become impenetrable, which has a similar effect as Pauli’s exclusion principle for identical fermions. We study the entire crossover from the noninteracting to the strongly attractive limit for few bosons in a harmonic trap
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