Expansion of harmonically trapped interacting particles and time dependence of the contact

Abstract

We study the expansion of an interacting atomic system at zero temperature, following its release from an isotropic three-dimensional harmonic trap and calculate the time dependence of its density and momentum distribution, with special focus on the behavior of the contact parameter. We consider different quantum systems, including the unitary Fermi gas of infinite scattering length, the weakly interacting Bose gas, and two interacting particles with highly asymmetric mass imbalance. In all cases analytic results can be obtained, which show that the initial value of the contact, fixing the 1/k 4 tail of the momentum distribution, disappears for large expansion times. Our results raise the problem of understanding the recent experiment of Chang et al. [Phys. Rev. Lett. 117, 235303 (2016)] carried out on a weakly interacting Bose gas of metastable 4 He atoms, where a 1/r 4 tail in the density distribution was observed after a large expansion time, implying the existence of the 1/k 4 tail in the asymptotic momentum distribution.

Entropy of a Turbulent Bose-Einstein Condensate

“…For example, in Ref. [ 26 ] the authors studied the expansion of a weakly interacting Bose gas at zero temperature, following its release from an isotropic three-dimensional harmonic trap. They calculated the time dependence of the momentum distribution with a special focus on the behavior of the contact parameter, which depends on the tail of the distribution.…”

Momentum distribution and coherence of a weakly interacting Bose gas after a quench

“…In particular, in a quasi-one-dimensional (1D) regime, we show how the degree of coherence and the prethermalization are affected by the speed of the quench and by the initial interaction parameter. We note here that considering a uniform gas is a simplifying assumption which can be overcome [33,38] but already yields interesting qualitative results. Furthermore, it corresponds to realistic platforms since uniform quantum gases are also being engineered in the laboratory [8,37,53].…”

Effective self-similar expansion of a Bose-Einstein condensate: Free space versus confined geometries

“…Manifestly, the above formulas in Eqs. (14), (15), and (17) interpolate between the noninteracting (λ −3 terms) and TF (λ −4 term) regimes. The behavior of the coefficients A and B as a function of the interaction strengthg, see Fig.…”

“…Recently, motivated by the experiment reported in Ref. [14], scaling transformations have been employed for understanding how the momentum distribution is affected by the expansion in an interacting quantum system [15], and the conditions for the breaking of scale invariance have also been investigated [16].…”