Direct and Inverse Cascades in Turbulent Bose-Einstein Condensates

Quantum (wave) turbulence in a trapped BEC


When a Bose-Einstein condensate (BEC) is driven out of equilibrium, density waves interact non-linearly and trigger the emergence of turbulent cascades. In a turbulent BEC, energy is transferred towards small scales by a direct cascade, whereas the number of particles displays an inverse cascade toward large scales. In this work, we study analytically and numerically the direct and inverse cascades in wave-turbulent BECs. We analytically derive the Kolmogorov-Zakharov spectra, including the universal pre-factor constants and the log-correction to the direct cascade scaling. We test and corroborate our predictions using high-resolution numerical simulations of the forced-dissipated Gross-Pitaevskii model in a periodic box and the corresponding wave-kinetic equation. Theoretical predictions and data are in excellent agreement, without adjustable parameters. Moreover, in order to connect with experiments, we successfully test our theoretical predictions using the Gross-Pitaevskii model with a cubic trap. Our results explain previous experimental observations and suggest new experimental settings for future studies.

Phys. Rev. Lett. 130, 133001 (2023) Selected for the PRL’s Cover

The figure above show the results of Gross-Pitaevskii simulations of a three-dimensional turbulent BEC. In (a) we see an snapshot of the turbulent BEC and the trap that confines it. Figure (b) show the wave-action spectrum (occupation number) in the inverse and direct cascades settings. The dashed lines display our theoretical predictions without any adjustable parameter.