Turbulence in a matter-wave supersolid

Quantum turbulence associated with wave and vortex dynamics is numerically investigated for a two-dimensional trapped atomic Rydberg-dressed Bose-Einstein condensate (BEC). When the coupling constant of the soft-core interaction is over a critical value, the superfluid (SF) system can transition into a hexagonal supersolid (SS) state. Based on the Gross-Pitaevskii equation approach, we have discovered a new characteristic k(−13/3) scaling law for wave turbulence in the SS state, that coexists with the waveaction k(−1/3) and energy k(−1) cascades commonly existing in a SF BEC. The new k(−13/3) scaling law implies that the SS system exhibits a negative, minus-one power energy dispersion (E ~ k(−1)) at the wavevector consistent with the radius of the SS droplet. For vortex turbulence, in addition to the presence of the Kolmogorov energy k(−5/3) and Saffman enstrophy k(−4) cascades, it is found that large amount of independent vortices and antivortices pinned to the interior of the oscillating SS results in a strong k(−1) scaling at the wavevector consistent with the SS lattice constant.