Unitary qubit lattice simulations of complex vortex structures

Abstract

A quantum vortex is a topological singularity with quantized circulation, unlike a classical vortex with its continuous circulation strength. Quantum turbulence, envisaged as strong tangle of quantum vortices, of a Bose–Einstein condensate is examined by developing a unitary qubit lattice algorithm for the solution of the Gross–Pitaevskii equation. Earlier, it was shown that a certain class of initial conditions had a very short Poincare recurrence time for this Hamiltonian system. Here it is shown quantitatively that increasing the internal energy of the initial state leads to a systematic degradation of this class of solutions. Coupled Bose–Einstein condensate systems are investigated for a Hopf link class of initial conditions in which a vortex ring core is threaded by a linear vortex core that then closes toroidal around the vortex ring. These states are known as skyrmions and play a role in particle physics, astrophysics and condensed matter physics.