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.