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 \textit{et al.} [Phys. Rev. Lett. \textbf{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.

published version, 9 pages, 5 figures

References in corpus (13)

• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Verification of universal relations in a strongly interacting Fermi gas
• Number of closed-channel molecules in the BEC-BCS crossover
• Universal Properties of the Ultra-Cold Fermi Gas
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Precise determination of the structure factor and contact in a unitary Fermi gas
• Momentum Distribution and Contact of the Unitary Fermi gas
• Momentum-resolved observation of thermal and quantum depletion in an interacting Bose gas
• Universal contact of strongly interacting fermions at finite temperatures
• Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas
• Bound-state signatures in quenched Bose-Einstein condensates
• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

Cited by in corpus (6)

• Quantum depletion of a homogeneous Bose-Einstein condensate
• Observation of $1/k^4$-tails after expansion of Bose-Einstein Condensates with impurities
• Tailoring Dynamical Fermionization: Delta kick cooling of a Tonks-Girardeau gas
• Entropy of a Turbulent Bose-Einstein Condensate
• Condensate and superfluid fraction of homogeneous Bose gases in a self-consistent Popov approximation
• Dynamic virial theorem at nonequilibrium and applications