Quantum algorithm for Bose-Einstein condensate quantum fluid dynamics

TL;DR

This paper introduces a quantum lattice-gas algorithm to simulate Bose-Einstein condensate superfluid dynamics, revealing turbulence spectra and vortex behaviors across multiple scales, advancing quantum fluid simulation methods.

Contribution

It presents a novel quantum algorithm for simulating BEC superfluid dynamics, capturing turbulence spectra and vortex interactions across different scales.

Findings

Kolmogorov spectrum observed at large scales

Power law k^{-6} at intermediate scales

Kelvin wave cascade with k^{-3} spectrum at small scales

Abstract

The dynamics of vortex solitons in a BEC superfluid is studied. A quantum lattice-gas algorithm (localization-based quantum computation) is employed to examine the dynamical behavior of vortex soliton solutions of the Gross-Pitaevskii equation (phi^4 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 k^{-6} power law emerges, in a classical-quantum transition from vortex filament reconnections to Kelvin wave-acoustic wave coupling. The spontaneous exchange of intermediate vortex rings is observed. Finally, at very small spatial scales a k^{-3} power law emerges, characterizing fluid dynamics occurring within the scale size of the vortex cores themselves, a characteristic Kelvin wave cascade region. Poincare recurrence is studied: in the free non-interacting system, a fast Poincare recurrence occurs for regular arrays of line vortices. The recurrence period is used to demarcate dynamics driving the 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 over a broad range of wave numbers, from quantum flow to a pseudo-classical inviscid flow regime to a Kolmogorov inertial subrange.