Intra-scales energy transfer during the evolution of turbulence in a trapped Bose-Einstein condensate

Abstract

In turbulence phenomena, including the quantum turbulence in superfluids, an energy flux flows from large to small length scales, composing a cascade of energy. It is a well-known fact that for multi-scale energy flow, dissipation can be scale-dependent. In particular, the existence of a range of scales where there is no energy accumulation, the inertial range, is an indication of universal behavior in turbulence. There are intrinsic difficulties associated with the measurement of the energy flux during the time evolution of turbulence. Here we present a procedure to measure the energy flux during the time evolution of turbulence in a sample of a trapped Bose-Einstein condensate. The energy flux is evaluated using the energy spectrum and the continuity equation. We identified intervals of momentum where the flux is constant using two different procedures. The identification of a region with constant flux in turbulent BECs is a manifestation of the universal character of turbulence in these quantum systems. These measurements pave the way for studies of energy conservation and dissipation in a scale-dependent manner in trapped atomic superfluids, and also analogies with the related processes that take place in ordinary fluids.

Entropy of a Turbulent Bose-Einstein Condensate

“…Hence, approaches other than the power-law behavior have been employed to overcome these issues. Energy and particle fluxes have been used in simulations [ 7 , 8 ] and experiments [ 9 , 10 ] as alternative methods to investigate and characterize quantum turbulence.…”

Characteristic Length Scale during the Time Evolution of a Turbulent Bose-Einstein Condensate

“…We found that the turbulent state can be identified and characterized in terms of the energy flux regardless of whether we employ the whole cloud or just a region close to the major axis of the expanded cloud. We should note that the axial trapping frequencies of this work and of Reference [11] are very close; however, in this work, we employ a radial trapping frequency that is ≈0.7 smaller than the one used in Reference [11]. Thus, the BECs in this work are much less elongated and closer to a spherical shape than the ones in Reference [11].…”

“…This is because such large-scale inhomogeneities affect only regions in Fourier space up to the order of k ∼ 2π/L min , where L min is the smaller linear size of the cigar-shaped cloud. In a previous work [11], we studied the impact of anisotropy in the energy transfer during the evolution of turbulence in a trapped BEC. Like the integral length scale, the energy flux can also be computed from the kinetic energy spectrum.…”

“…Hence, strategies other than the power law identification have been employed to identify and characterize QT. Energy and particle fluxes have been used in simulations [8,9] and experiments [10,11] to overcome some of these difficulties. Since turbulence and disorder are intimately related, an approach based on the entropy of turbulent BECs has also been successfully applied [12] as an alternative method to investigate and characterize quantum turbulence.…”

Cold Atoms Beyond Atomic Physics

“…There are some inherent challenges in determining and characterizing the turbulent state in these systems [14,15]. Hence, different approaches have been used to clarify aspects of quantum turbulence [114][115][116]. What we showed in Section 3 can be used to look at the phenomena from a different perspective, which is of paramount importance when dealing with quantum turbulence.…”