The generation of mesoscopic Bell states via collisions of distinguishable bright solitons has been suggested in Phys. Rev. Lett. 111, 100406 (2013). Here, we extend our former proposal to two hyperfine states of 85Rb instead of two different atomic
species, thus simplifying possible experimental realisations. A calculation of the $s$-wave scattering lengths for the hyperfine states $(f,m_f)=(2,+2)$ and $(3,+2)$ identifies parameter regimes suitable for the creation of Bell states with an advantageously broad Feshbach resonance. We show the generation of Bell states using the truncated Wigner method for the solitons centre of mass and demonstrate the validity of this approach by a comparison to a mathematically rigorous effective potential treatment of the quantum many-particle problem.
Despite the prominence of Onsagers point-vortex model as a statistical description of 2D classical turbulence, a first-principles development of the model for a realistic superfluid has remained an open problem. Here we develop a mapping of a system
of quantum vortices described by the homogeneous 2D Gross-Pitaevskii equation (GPE) to the point-vortex model, enabling Monte-Carlo sampling of the vortex microcanonical ensemble. We use this approach to survey the full range of vortex states in a 2D superfluid, from the vortex-dipole gas at positive temperature to negative-temperature states exhibiting both macroscopic vortex clustering and kinetic energy condensation, which we term an Onsager-Kraichnan condensate (OKC). Damped GPE simulations reveal that such OKC states can emerge dynamically, via aggregation of small-scale clusters into giant OKC-clusters, as the end states of decaying 2D quantum turbulence in a compressible, finite-temperature superfluid. These statistical equilibrium states should be accessible in atomic Bose-Einstein condensate experiments.
We demonstrate an inverse energy cascade in a minimal model of forced 2D quantum vortex turbulence. We simulate the Gross-Pitaevskii equation for a moving superfluid subject to forcing by a stationary grid of obstacle potentials, and damping by a sta
tionary thermal cloud. The forcing injects large amounts of vortex energy into the system at the scale of a few healing lengths. A regime of forcing and damping is identified where vortex energy is efficiently transported to large length scales via an inverse energy cascade associated with the growth of clusters of same-circulation vortices, a Kolmogorov scaling law in the kinetic energy spectrum over a substantial inertial range, and spectral condensation of kinetic energy at the scale of the system size. Our results provide clear evidence that the inverse energy cascade phenomenon, previously observed in a diverse range of classical systems, can also occur in quantum fluids.
