Formation of Quantum Turbulence from Dark Solitons in Atomic Bose-Einstein Condensates

We theoretically propose a new method of making quantum turbulence from many dark solitons in atomic Bose-Einstein condensates. We solve numerically the two-dimensional Gross-Pitaevskii equation. We set initially many solitons so that they can form a square grid. A dark soliton is known to be stable in one-dimensional systems, but unstable in two- or three-dimensional systems and decay to vortices. Our simulation shows that these solitons decay to a lot of vortices which move around in the system and eventually lead to two-dimensional quantum turbulence. The probability distribution function of the superfluid velocity obeys a Gaussian distribution in the low-velocity region and a power-law distribution in the high-velocity region. The decay of the total number of vortices obeys a power-law for a relatively long period. This scenario may be experimentally realized through interference of Bose-Einstein condensates in a trap potential.