Abstract
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.
Highlights
Quantum turbulence associated with wave and vortex dynamics is numerically investigated for a twodimensional trapped atomic Rydberg-dressed Bose-Einstein condensate (BEC)
The main theme of this paper is to investigate how the wave turbulence (WT) and vortex turbulence (VT) behave in a SS state
In addition to the Kolmogorov k−5/3 and Saffman k−4 scaling laws commonly seen in VT for a 2D SF BEC, we identify a strong k−1 scaling law that covers almost a decade of the k range in the infrared regime
Summary
This explains why the lower bound of the new k−13/3 scaling law coincides with kR. Substitution of D = 2, N = 4, and the identified power y = −13/3 into the second equation of (3) gives α = −1 This indicates that the wave which causes the new WT −13/3 scaling law has an effective dispersion with a minus-one power at the relevant scales: ωk ∼ λk−1. As displayed a minus-one by the black line in power dispersion, The low-energy gapless k−1 elementary excitation does not have a direct relation to the new −13/3 WT scaling law though. The ultraviolet waves will conform to the droplets with an onset wavevector kR
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