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.
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.
Using a set of interleaved unitary collision-stream operators, a three-dimensional (3D) quantum lattice gas algorithm is devised which, on taking moments, recovers the Gross-Pitaevskii (GP) equation. If a zero-temperature Bose-Einstein condensate (BEC) is trapped in an a magnetic well, the evolution of the ground-state wave function satisfies the scalar GP equation, while if the BEC is trapped in an optical trap the ground-state wave function satisfies spin or GP equations. Quantum turbulence is studied in a scalar GP system on 5,7603 grid yielding not only the classical Kolmogorov k-5/3 cascade but also the quantum vortex k-3 spectrum. For a certain class of initial conditions, one finds an intermittent loss of tangled quantum vortices as the vortex cores attain minimal size, and thus prevent the Kelvin wave cascade (due to helical wave-wave coupling on the vortex). A coupled set of GP equations are solved for spin or BEC. Skrymions, which describe topologically-linked quantum vortices, are examined. One finds, for certain initial conditions that the incompressible kinetic energy spectrum for the condensate component of a vortex ring core rapidly departs from the k-3 linear quantum vortex spectrum.
Quantum vortex structures and energy cascades are examined for two-dimensional quantum turbulence (2D QT) at zero temperature. A special unitary evolution algorithm, the quantum lattice algorithm, is employed to simulate the Bose-Einstein condensate governed by the Gross-Pitaevskii (GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is a short Poincaré recurrence time. It is demonstrated that such short recurrence times are destroyed by stronger nonlinear interaction. The similar loss of Poincaré recurrence is also seen in the 3D GP equation. Various initial conditions are considered in an attempt to discern if 2D QT exhibits inverse cascades as is seen in 2D classical turbulence (CT). In our simulation parameter regimes, no dual cascade spectra were observed for 2D QT-unlike that seen in 2D CT.
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.
A unitary qubit lattice algorithm, which scales almost perfectly to the full number of cores available (e.g., 216000 cores on a CRAY XT5), is used to examine quantum turbulence and its interrelationship to classical turbulence with production runs on grids up to 57603. The maximal grids achievable by conventional CFD for quantum turbulence is just 20483, and artificial dissipation had to be introduced. Our unitary algorithms preserve the Hamiltonian structure of the Gross-Pitaevskii equation which describes quantum turbulence in a zero-temperature Bose-Einstein condensate (BEC). As a result, parameter regimes have been uncovered which exhibit very short Poincare recurrence time, as well as a strong triple cascade structure in the kinetic energy spectrum. Moreover, a detailed examination of the incompressible kinetic energy spectrum has revealed for the first time within a turbulence simulation the κ−17/5 quantum Kelvin wave cascade. By generalizing the unitary entanglement operators on the 2 qubits, a finite temperature BEC system is examined. These unitary qubit lattice algorithms are directly applicable to quantum computers as they become available.
Quantum vortex structures and energy cascades are examined for two dimensional quantum turbulence (2D QT) using a special unitary evolution algorithm. The qubit lattice gas (QLG) algorithm, is employed to simulate the weakly-coupled Bose-Einstein condensate (BEC) governed by the Gross-Pitaevskii (GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is a very short Poincare recurrence time. This short recurrence time is destroyed as the nonlinear interaction energy is increased. Energy cascades for 2D QT are considered to examine whether 2D QT exhibits the inverse cascades of 2D classical turbulence. In the parameter regime considered, the spectra analysis reveals no such dual cascades---dual cascades being a hallmark of 2D classical turbulence.
We examine the energy cascades and quantum vortex structures in two-dimensional quantum turbulence through a special unitary time evolution algorithm. An early attempt at using the Lattice Boltzmann Method proved successful in correctly representing some features of the Nonlinear Schrodinger System (NLS), such as the phase shift following the one-dimensional soliton-soliton collision, as well as the two-dimentional modulation instability. However, to accurately evaluate NLS, the implicit Euler method is required to resolve the time evolution, which is computationally expensive. A more accurate and efficient method, the Quantum Lattice Gas model is employed to simulate the quantum turbulence governed by the Gross-Pitaevskii equation, an equaiton that describes the evolution of the ground state wave function for a Bose-Einstein condensate (BEC). It is discovered that when the ratio of the internal energy to the kinetic energy is below 0.05, an unexpected short Poincare recurrence occurs independent of the initial profile of the wave function. It is demonstrated that this short recurrence is destroyed as the internal energy is strengthened. to compare the two-dimensional quantum turbulence with its classical counterpart, the incompressible energy spectra of quantum turbulence is analyzed. However, the result reveals no sign of dual cascades which is a hallmark of the classical incompressible two-dimensional fluid (inverse energy cascade to large scales with a direct cascade of enstrophy to small scales). It is the spectra of the compressible energy that can exhibits multiple cascades, but this is strongly dependent on the initial condition.