Multiple-scale approach for the expansion scaling of superfluid quantum gases

Abstract

We present a general method, based on a multiple-scale approach, for deriving the perturbative solutions of the scaling equations governing the expansion of superfluid ultracold quantum gases released from elongated harmonic traps. We discuss how to treat the secular terms appearing in the usual naive expansion in the trap asymmetry parameter and calculate the next-to-leading correction for the asymptotic aspect ratio, with significant improvement over the previous proposals.

Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving

“…Typically, nonlinear ("quantum") systems are described by effective evolution equations derived within a mean-field approach. A prominent example is the description of Bose-Einstein condensates, where scale-invariant dynamics is of great relevance to time-of-flight measurements [57][58][59]. The dynamics is described by the time-dependent Gross-Pitaevskii equation (TDGPE) governing the (normalized) wavefunction Ψ(q, t) of a Bose-Einstein condensate…”

Effective self-similar expansion for the Gross-Pitaevskii equation

“…In this case, the dynamical equations for a d-dimensional system are replaced by d ordinary differential equations (with respect to time) for the scaling parameters. This approach has been successfully employed for describing the collective excitations and the free expansion of Bose-Einstein condensates of interacting atomic gases in different geometries (for which exact solutions exists both in the noninteracting limit and in the Thomas-Fermi regime, where interactions dominate over the kinetic energy) [1][2][3][4][5][6][7], the expansion of a one-dimensional Bose gas (in the deep Thomas-Fermi regime and in the Tonks-Girardeau regime of impenetrable bosons) [8], of a superfluid Fermi gas [7,9,10], and of a thermal cloud [11].…”

Effective Scaling Approach to Frictionless Quantum Quenches in Trapped Bose Gases

“…In most cases of classical hydrodynamics [3] or scaling transformations [4,5], exact analytical solution can be found for the collective dynamics and free expansion of BECs in time-dependent harmonic traps, both in the noninteracting limit and the Thomas-Fermi (TF) regime [2]. In this vein, symmetries give birth to an intriguing property of self-similarity, which allows to utilize the scaling approach for describing the dynamics of ultracold atomic systems, for instance, the atomic gases in the non-interacting and the hydrodynamic regimes [6,7], Tonks-Girardeau (TG) gas of impenetrable bosons [8,9], superfluid Fermi gas [7,10], and thermal cloud [11] in different geometries.…”