arXiv subjects

Thomas P. Billam

Publications and source records attributed to Thomas P. Billam.

25 records · Page 2Linked to original sources

arXiv2014

Onsager-Kraichnan Condensation in Decaying Two-Dimensional Quantum Turbulence

Despite the prominence of Onsager's 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.

cond-mat.quant-gas↗

arXiv2014

Signatures of Coherent Vortex Structures in a Disordered 2D Quantum Fluid

The emergence of coherent rotating structures is a phenomenon characteristic of both classical and quantum 2D turbulence. In this work we show theoretically that the coherent vortex structures that emerge in decaying 2D quantum turbulence can approach quasi-classical rigid-body rotation, obeying the Feynman rule of constant average areal vortex density while remaining spatially disordered. By developing a rigorous link between the velocity probability distribution and the quantum kinetic energy spectrum over wavenumber $k$, we show that the coherent vortex structures are associated with a $k^3$ power law in the infrared region of the spectrum, and a well-defined spectral peak that is a physical manifestation of the largest structures. We discuss the possibility of realizing coherent structures in Bose--Einstein condensate experiments and present Gross-Pitaevskii simulations showing that this phenomenon, and its associated spectral signatures, can emerge dynamically from feasible initial vortex configurations.

cond-mat.quant-gas↗

arXiv2014

Entangling two distinguishable quantum bright solitons via collisions

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 soliton's 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.

cond-mat.quant-gas↗

arXiv2013

Generating mesoscopic Bell states via collisions of distinguishable quantum bright solitons

We investigate numerically the collisions of two distinguishable quantum matter-wave bright solitons in a one-dimensional harmonic trap. We show that such collisions can be used to generate mesoscopic Bell states which can reliably be distinguished from statistical mixtures. Calculation of the relevant s-wave scattering lengths predicts that such states could potentially be realized in quantum-degenerate mixtures of 85Rb and 133Cs. In addition to fully quantum simulations for two distinguishable two-particle solitons, we use a mean-field description supplemented by a stochastic treatment of quantum fluctuations in the soliton's center of mass: We demonstrate the validity of this approach by comparison to a mathematically rigorous effective potential treatment of the quantum many-particle problem.

cond-mat.quant-gas↗

arXiv2013

Inverse Energy Cascade in Forced 2D Quantum Turbulence

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 stationary 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.

cond-mat.quant-gas↗

arXiv2012

Scattering bright solitons: quantum versus mean-field behavior

We investigate scattering bright solitons off a potential using both analytical and numerical methods. Our paper focuses on low kinetic energies for which differences between the mean-field description via the Gross-Pitaevskii equation (GPE) and the quantum behavior are particularly large. On the N-particle quantum level, adding an additional harmonic confinement leads to a simple signature to distinguish quantum superpositions from statistical mixtures. While the non-linear character of the GPE does not allow quantum superpositions, the splitting of GPE-solitons takes place only partially. When the potential strength is increased, the fraction of the soliton which is transmitted or reflected jumps non-continuously. We explain these jumps via energy-conservation and interpret them as indications for quantum superpositions on the N-particle level. On the GPE-level, we also investigate the transition from this stepwise behavior to the continuous case.

cond-mat.quant-gas↗

arXiv2012

Bright matter-wave soliton collisions at narrow barriers

We study fast-moving bright solitons in the focusing nonlinear Schrödinger equation perturbed by a narrow Gaussian potential barrier. In particular, we present a general and comprehensive analysis of the case where two fast-moving bright solitons collide at the location of the barrier. In the limiting case of a delta-function barrier, we use a quasi-analytic method to show that the relative norms of the outgoing waves depends sinusoidally on the relative phase of the incoming waves, and to determine whether one, or both, of the outgoing waves are bright solitons. We show using numerical simulations that this quasi-analytic result is valid in the high velocity limit: outside this limit nonlinear effects introduce a skew to the phase-dependence, which we quantify. Finally, we numerically explore the effects of introducing a finite-width Gaussian barrier. Our results are particularly relevant, as they can be used to describe a range of interferometry experiments using bright solitary matter-waves.

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