Entropy of a Turbulent Bose-Einstein Condensate

Quantum turbulence deals with the phenomenon of turbulence in quantum fluids, such as superfluid helium and trapped Bose-Einstein condensates (BECs). Although much progress has been made in understanding quantum turbulence, several fundamental questions remain to be answered. In this work, we investigated the entropy of a trapped BEC in several regimes, including equilibrium, small excitations, the onset of turbulence, and a turbulent state. We considered the time evolution when the system is perturbed and let to evolve after the external excitation is turned off. We derived an expression for the entropy consistent with the accessible experimental data, that is, using the assumption that the momentum distribution is well-known. We related the excitation amplitude to different stages of the perturbed system, and we found distinct features of the entropy in each of them. In particular, we observed a sudden increase in the entropy following the establishment of a particle cascade. We argue that entropy and related quantities can be used to investigate and characterize quantum turbulence.Comment: 14 pages, 5 figure

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

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose-Einstein condensate. We present an alternative way of exploring this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. We reconstruct the three-dimensional momentum distributions with the inverse Abel transform, as we have done successfully in other works. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to intuitively visualize the time evolution of the turbulent state

Energy cascade in a far-from-equilibrium inhomogeneous trapped Bose gas obtained by power spectrum analysis

We characterize the energy spectrum in far-from-equilibrium inhomogeneously trapped Bose-Einstein condensate using the power spectrum technique. We demonstrate that pseudo-momentum fluctuations can be used to characterize turbulence and we compare the obtained exponents to one measured by well established techniques such as the momentum distribution in time of flight. The power spectrum of pseudo-momentum fluctuations and the momentum distribution reveals a power-law dependence into the inertial range of momentum for the turbulent out-of-equilibrium system. We analyze the evolution of the power-law exponent for different far-from-equilibrium regimes and both methods show that the power-law exponent reaches the same stationary value when the cloud is in the developed turbulent regime. These results provide a better understanding of out-of-equilibrium states, which is a new frontier in the study of cold trapped atoms