Strong and weak wave turbulence regimes in Bose-Einstein condensates

Abstract

When a turbulent Bose-Einstein condensate is driven out-of-equilibrium at a scale much smaller than the system size, nonlinear wave interactions transfer particles towards large scales in an inverse cascade process. In this work, we study numerically wave turbulence in a three-dimensional Bose-Einstein condensate in forced and dissipated inverse cascade settings. We observe that when the forcing rate increases, thereby increasing the particle flux, the turbulence spectrum gradually transitions from the weak-wave Kolmogorov-Zakharov cascade to a critical balance state characterized by a range of scales with balanced linear and nonlinear dynamic timescales. Further forcing increases lead to a coherent condensate component superimposed with Bogoliubov-type acoustic turbulence. The role of vortices in such a strongly forced state is marginal, which makes this new state very different from the strongly turbulent state composed of a tangle of quantized vortex lines. We then use our predictions and numerical data to formulate a new out-of-equilibrium equation of state for the 3D inverse cascade.

Figures (6)

• Figure 1: (a) Stationary spectra for different strengths. of the particle flux $|Q_0|$ (b) Same spectra compensated by the KZ prediction.
• Figure 2: (a)--(c): Representative STFT spectra for the weak, intermediate and strong fluxes; the dashed-dotted vertical lines are at $k=1/\xi$. (d): nonlinear frequency broadening as a function of $k$ for the cases shown in (a)--(c), (the straight line is $\delta\omega=\omega_k$. (e) Strong flux case: spectrum decomposition into the condensate and thermal components.
• Figure 3: (a): Percentages of energy components in terms of flux for the incompressible kinetic energy $E_{\rm kinI}$, compressible kinetic energy $E_{\rm kinC}$, quantum energy $E_{\rm q}$, and internal energy $E_{\rm int}$, respectively; (b): "Equation of state" plot covering the weak, intermediate, and strong flux regimes.
• Figure S1: Spectra flux $|Q(k)|$. The particle flux $|Q_0|$ is measured in the inertial ranges with quasi-constant values.
• Figure S2: Fitting spectra of the thermal components for case 9 and case 10: (a) Spectra compensated by the expected power-law solution (Bologliubov spectrum $n_{\rm B} \sim k^{-2}$); (b) Original spectra with the power-law fits superposed.