Spin turbulence with small spin magnitude in spin-1 spinor Bose-Einstein condensates

Abstract

We theoretically and numerically study spin turbulence (ST) with small spin magnitude in spin-1 spinor Bose-Einstein condensates by using the spin-1 spinor Gross-Pitaevskii (GP) equations. This kind of ST is realized in two cases: (i) with antiferromagnetic interaction and (ii) with ferromagnetic interaction under a static magnetic field. The ST with small spin magnitude can exhibit two characteristic power laws in the spectrum of the spin-dependent interaction energy: $-1$ and $-7/3$ power laws in the low- and high-wave-number regions, respectively. These power laws are derived from a Kolmogorov-type dimensional scaling analysis for the equations of motion of the spin vector and nematic tensor. To confirm these power laws, we perform a numerical calculation of the spin-1 spinor GP equations in a two-dimensional uniform system. In case (i), the $-7/3$ power law tends to appear in the high-wave-number region, but the spectrum in the low-wave-number region deviates from the $-1$ power law. In contrast, both the $-1$ and $-7/3$ power laws tend to appear in case (ii). DOI: http://dx.doi.org/10.1103/PhysRevA.88.063628 ©2013 American Physical Society