Hydrodynamic versus collisionless dynamics of a one-dimensional harmonically trapped Bose gas

Abstract

By using a sum rule approach we investigate the transition between the hydrodynamic and the collisionless regime of the collective modes in a 1D harmonically trapped Bose gas. Both the weakly interacting gas and the Tonks-Girardeau limits are considered. We predict that the excitation of the dipole compression mode is characterized, in the high temperature collisionless regime, by a beating signal of two different frequencies (ωz and 3ωz) while, in the high temperature collisional regime, the excitation consists of a single frequency ( √ 7ωz). This behaviour differs from the case of the lowest breathing mode whose excitation consists of a single frequency (2ωz) in both regimes. Our predictions for the dipole compression mode open promising perspectives for the experimental investigation of collisional effects in 1D configurations.PACS numbers: PACS numbers arXiv:1608.08417v2 [cond-mat.quant-gas]

Generalized Hydrodynamics on an Atom Chip

“…To do so, we measure the in situ density profiles of a time-evolving 1d atomic cloud trapped on an atom chip, and compare the data with predictions from GHD. We contrast those predictions with the ones of the conventional hydrodynamic (CHD) approach-based on the assumption of local thermal equilibrium [33]-that has been frequently used [34][35][36][37][38][39]. Starting from a cloud at thermal equilibrium in a longitudinal potential V (x), dynamics is triggered by suddenly quenching V (x).…”

Solvable Hydrodynamics of Quantum Integrable Systems

“…This allows us to make novel and detailed physical predictions for finite-time dynamics in a wide range of physical systems. For example, we obtain the first practical hydrodynamic technique for the one-dimensional Bose gas [27][28][29][30][31][32] that applies to arbitrary local GGE initial conditions and takes into account the higher conservation laws of the underlying quantum system. This allows us to obtain detailed profiles for the evolution of the Lieb-Liniger gas from collision type initial conditions, which could, in principle, be tested in the laboratory.…”

Collective many-body bounce in the breathing-mode oscillations of a Tonks-Girardeau gas

“…These frequencies, depending on trap configurations, can vary significantly from those of ideal (noninteracting) gases. For example, in a weakly interacting one-dimensional (1D) Bose gas at sufficiently low temperatures, the breathing-mode oscillations of the in situ density occur at a frequency of ω B √ 3ω (where ω is the frequency of the trap) [5,18,19,[22][23][24][25][26][27][28], whereas in an ideal Bose gas the breathing-mode frequency is ω B = 2ω. An even more dramatic qualitative departure from the ideal gas behavior was observed recently in the dynamics of the momentum distribution of a weakly interacting 1D quasicondensate [5,28]: For sufficiently low temperatures, the momentum distribution was oscillating at a frequency of 2ω B , i.e., at twice the rate of the fundamental breathing-mode frequency of the in situ density profile ω B √ 3ω.…”