8 research outputs found
Spontaneous vortices in the formation of Bose-Einstein condensates
Phase transitions are ubiquitous in nature, ranging from protein folding and
denaturisation, to the superconductor-insulator quantum phase transition, to
the decoupling of forces in the early universe. Remarkably, phase transitions
can be arranged into universality classes, where systems having unrelated
microscopic physics exhibit identical scaling behaviour near the critical
point. Here we present an experimental and theoretical study of the
Bose-Einstein condensation phase transition of an atomic gas, focusing on one
prominent universal element of phase transition dynamics: the spontaneous
formation of topological defects during a quench through the transition. While
the microscopic dynamics of defect formation in phase transitions are generally
difficult to investigate, particularly for superfluid phase transitions,
Bose-Einstein condensates (BECs) offer unique experimental and theoretical
opportunities for probing such details. Although spontaneously formed vortices
in the condensation transition have been previously predicted to occur, our
results encompass the first experimental observations and statistical
characterisation of spontaneous vortex formation in the condensation
transition. Using microscopic theories that incorporate atomic interactions and
quantum and thermal fluctuations of a finite-temperature Bose gas, we simulate
condensation and observe vortex formation in close quantitative agreement with
our experimental results. Our studies provide further understanding of the
development of coherence in superfluids, and may allow for direct investigation
of universal phase-transition dynamics.Comment: 14 pages, 6 figures. Accepted for publication in Nature.
Supplementary movie files are available at
http://www.physics.uq.edu.au/people/mdavis/spontaneous_vortice
A note on the propagation of quantized vortex rings through a quantum turbulence tangle:energy transport or energy dissipation?
We investigate quantum vortex ring dynamics at scales smaller than the inter-vortex spacing in quantum turbulence. Through geometrical arguments and high-resolution numerical simulations, we examine the validity of simple estimates for the mean free path and the structure of vortex rings post-reconnection. We find that a large proportion of vortex rings remain coherent objects where approximately 75% of their energy is preserved. This leads us to consider the effectiveness of energy transport in turbulent tangles. Moreover, we show that in low density tangles, appropriate for the ultra-quantum regime, ring emission cannot be ruled out as an important mechanism for energy dissipation. However at higher vortex line densities, typically associated with the quasi-classical regime, loop emission is expected to make a negligible contribution to energy dissipation, even allowing for the fact that our work shows rings can survive multiple reconnection events. Hence the Kelvin wave cascade seems the most plausible mechanism leading to energy dissipatio
Beyond Gross-Pitaevskii Mean Field Theory
A large number of effects related to the phenomenon of Bose-Einstein
Condensation (BEC) can be understood in terms of lowest order mean field
theory, whereby the entire system is assumed to be condensed, with thermal and
quantum fluctuations completely ignored. Such a treatment leads to the
Gross-Pitaevskii Equation (GPE) used extensively throughout this book. Although
this theory works remarkably well for a broad range of experimental parameters,
a more complete treatment is required for understanding various experiments,
including experiments with solitons and vortices. Such treatments should
include the dynamical coupling of the condensate to the thermal cloud, the
effect of dimensionality, the role of quantum fluctuations, and should also
describe the critical regime, including the process of condensate formation.
The aim of this Chapter is to give a brief but insightful overview of various
recent theories, which extend beyond the GPE. To keep the discussion brief,
only the main notions and conclusions will be presented. This Chapter
generalizes the presentation of Chapter 1, by explicitly maintaining
fluctuations around the condensate order parameter. While the theoretical
arguments outlined here are generic, the emphasis is on approaches suitable for
describing single weakly-interacting atomic Bose gases in harmonic traps.
Interesting effects arising when condensates are trapped in double-well
potentials and optical lattices, as well as the cases of spinor condensates,
and atomic-molecular coupling, along with the modified or alternative theories
needed to describe them, will not be covered here.Comment: Review Article (19 Pages) - To appear in 'Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment', Edited by
P.G. Kevrekidis, D.J. Frantzeskakis and R. Carretero-Gonzalez (Springer
Verlag
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Solutions of the two-dimensional hubbard model: Benchmarks and results from a wide range of numerical algorithms
Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods