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Radiation effects and defects in solids

Qubit unitary lattice algorithm for spin-2 Bose-Einstein condensates: II - vortex reconnection simulations and non-Abelain vortices

George Vahala, Min Soe, Linda L. Vahala

Published Jan 2, 2020• 8 citations
Publisher

Abstract

Using the qubit unitary algorithm developed in the previous paper, quantum reconnection of non-Abelian quantum vortices is simulated and rung-like vortices are seen during the reconnection. Vortices in two of the four tetrahedral symmetry group are examined. Moreover, the algorithm performs exceptionally on classical supercomputers, as shown on timings on the IBM-Q supercomputer MIRA. It is expected that one should see the exponential speedup on a quantum computer since quantum entanglement is crucial for the qubit algorithm to recover the Gross-Pitaevskii equations for spin-2 systems.Keywords : spin-2 BECs, non-Abeliam vortices

DOI
10.1080/10420150.2020.1718136

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Using the qubit unitary algorithm developed in the previous paper, quantum reconnection of non-Abelian quantum vortices is simulated and rung-like vortices are seen during the reconnection. Vortices in two of the four tetrahedral symmetry group are examined. Moreover, the algorithm performs exceptionally on classical supercomputers, as shown on timings on the IBM-Q supercomputer MIRA. It is expected that one should see the exponential speedup on a quantum computer since quantum entanglement is crucial for the qubit algorithm to recover the Gross-Pitaevskii equations for spin-2 systems.Keywords : spin-2 BECs, non-Abeliam vortices
The ground state wave function for a Bose Einstein condensate is well described by the Gross-Pitaevskii equation. A Type-II quantum algorithm is devised that is ideally parallelized even on a classical computer. Only 2 qubits are required per spatial node. With unitary local collisions, streaming of entangled states and a spatially inhomogeneous unitary gauge rotation one recovers the Gross-Pitaevskii equation. Quantum vortex reconnection is simulated - even without any viscosity or resistivity (which are needed in classical vortex reconnection).
A wide order-parameter manifolds of Bose-Einstein condensates (BECs) with spin degrees of freedom enables various kinds of topological defects which never appear in conventional scalar BECs. In this paper, we focus on the characteristic example of them; non-Abelian vortices and their dynamics in the cyclic phase of a spin-2 BEC. Non-Abelian vortices shows the unique effect in their collision dynamics, i.e. unlike Abelian vortices, they do neither reconnect themselves nor pass through each other but create a rung vortex between them.
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.
The dynamics of vortex solitons is studied in a BEC superfluid. A quantum lattice-gas algorithm (measurementbased quantum computation) is employed to examine the dynamical behavior vortex soliton solutions of the Gross-Pitaevskii equation (ø4 interaction nonlinear Schroedinger equation). Quantum turbulence is studied in large grid numerical simulations: Kolmogorov spectrum associated with a Richardson energy cascade occurs on large flow scales. At intermediate scales, a new k-6 power law emerges, due to vortex filamentary reconnections associated with Kelvin wave instabilities (vortex twisting) coupling to sound modes and the exchange of intermediate vortex rings. Finally, at very small spatial scales a k-3power law emerges, characterizing fluid dynamics occurring within the scale size of the vortex cores themselves. Poincaré recurrence is studied: in the free non-interacting system, a fast Poincaré recurrence occurs for regular arrays of line vortices. The recurrence period is used to demarcate dynamics driving a nonlinear quantum fluid towards turbulence, since fast recurrence is an approximate symmetry of the nonlinear quantum fluid at early times. This class of quantum algorithms is useful for studying BEC superfluid dynamics and, without modification, should allow for higher resolution simulations (with many components) on future quantum computers.