The authors theoretically study the development of turbulence in a Bose-Einstein condensate trapped and shaken in a box potential. They identify two distinct turbulence regimes with different scalings for weak and strong forces.
Weakly interacting, dilute atomic Bose-Einstein condensates (BECs) have proved to be an attractive context for the study of nonlinear dynamics and quantum effects at the macroscopic scale. Recently, weakly interacting, dilute atomic BECs have been used to investigate quantum turbulence both experimentally and theoretically, stimulated largely by the high degree of control which is available within these quantum gases. In this article we motivate the use of weakly interacting, dilute atomic BECs for the study of turbulence, discuss the characteristic regimes of turbulence which are accessible, and briefly review some selected investigations of quantum turbulence and recent results. We focus on three stages of turbulence – the generation of turbulence, its steady state and its decay – and highlight some fundamental questions regarding our understanding in each of these regimes.
Weakly interacting, dilute atomic Bose-Einstein condensates (BECs) have proved to be an attractive context for the study of nonlinear dynamics and quantum effects at the macroscopic scale. Recently, weakly interacting, dilute atomic BECs have been used to investigate quantum turbulence both experimentally and theoretically, stimulated largely by the high degree of control which is available within these quantum gases. In this article we motivate the use of weakly interacting, dilute atomic BECs for the study of turbulence, discuss the characteristic regimes of turbulence which are accessible, and briefly review some selected investigations of quantum turbulence and recent results. We focus on three stages of turbulence- the generation of turbulence, its steady state and its decay- and highlight some fundamental questions regarding our understanding in each of these regimes. 1.
A variety of turbulent regimes have been observed in quantum fluids, some being analagous to classical fluids and others being uniquely quantum in behaviour. The development of optical box-traps for atomic condensates means that this turbulence is more straightforward to analyse than in harmonic trapping-potentials. In several recent publications, weak-wave turbulence (WWT) has been observed in otherwise uniform systems with hard-wall confinement. In each case with slightly different scaling-laws and different arguments as to the underlying turbulence mechanism. This thesis explores steady turbulence in optical box-traps numerically. We perform simulations of turbulence from the ground state through to a quasi-steady state, over a wide range of forcing amplitudes. In doing so we observe both ordinary WWT with k−3 scaling, and the steeper k−3.5 scaling which has been observed in recent experiments. Using a recent reformulation of energy spectral densities, we show that this k−3.5 scaling is a unique regime to ordinary WWT. The steeper scaling is potentially driven by less weakly nonlinear wave interactions, and does not seem to be directly due to vortices as previously suggested. We also demonstrate that accounting for quantum phase is essential when calculating energy spectral densities.
By combining experiments and numerical simulations which model the dynamics of shaken atomic Bose-Einstein condensates, we reveal the surprising nature of quantum turbulence in these systems. Unlike the tangles of vortex lines described in the superfluid helium literature, we find that our turbulent atomic condensate contains a mixture of strong fragmented density fluctuations and small random vortex loops which are not homogeneously distributed. This unusual form of turbulence, with its own properties and scaling behavior, which we call strong quantum turbulence, is significantly different from the turbulence which is observed in either classical or other quantum systems, thus posing a new challenge in turbulence research.