Macroscopic Excitations in Confined Bose–Einstein Condensates, Searching for Quantum Turbulence

Abstract

We present a survey of macroscopic excitations of harmonically confined Bose-Einstein condensates (BEC), described by Gross-Pitaevskii (GP) equation, in search of routes to develop quantum turbulence. These excitations can all be created by phase imprinting techniques on an otherwise equilibrium BoseEinstein condensate. We analyze two crossed vortices, two parallel anti-vortices, a vortex ring, a vortex with topological charge Q = 2, and a tangle of 4 vortices. Since GP equation is time-reversal invariant, we are careful to distinguish time intervals in which this symmetry is preserved and those in which rounding errors play a role. We find that the system tends to reach stationary states that may be widely classified as having either an array of vortices with collective excitations at different length scales or an agitated state composed mainly of Bogoliubov phonons.

Skyrmions with arbitrary topological charges in spinor Bose–Einstein condensates

“…Some of our cases, as mentioned above, have already been shown to be stable in [47]. Moreover, we also expect the topological defects to be quite stable, as shown in [53], where it is observed that non-stationary vortex states evolve in time, with the vortices precessing in the cloud, without dissipating into other structures. Finally, we discuss the feasibility of experimentally observing these defects.…”

Neutron stars in the laboratory

“…(185). While this power-law behaviour has also emerged in numerical BEC simulations, 275,278 it has not yet been confirmed experimentally. Another feature of superfluid turbulence that has been recreated numerically is the non-classical distribution of the small-scale velocity field, which has already been detected in helium experiments.…”

Quantum turbulence in trapped atomic Bose–Einstein condensates

“…2.4 and 2.5) it results that in a trapped BEC Vinen ultraquantum turbulence is more likely to emerge. It has been recently demonstrated [44] that in the case of only two vortices initially in an orthogonal configuration, or even in the case of one doubly-charged vortex precessing and decaying in a spherically symmetric T = 0 trapped gas, there appear Kolmogorov-like spectra of the energy in the momentum space, but only over a wavenumber range of one decade. Numerical calculations based on the Gross-Pitaevskii equation [45] suggest that Kolmogorov scaling should emerge from the dynamics of vortices in a trapped Bose gas, but there is no experimental verification of the effect yet.…”