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Charge flipping vortices in the discrete nonlinear Schrodinger trimer and hexamer
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, The Institute of Technology.
Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-6708-1560
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 91, no 2, 022910- p.Article in journal (Refereed) Published
Abstract [en]

We examine the existence and properties of charge flipping vortices (CFVs), vortices which periodically flip the topological charge, in three-site (trimer) and six-site (hexamer) discrete nonlinear Schrodinger lattices. We demonstrate numerically that CFVs exist as exact quasiperiodic solutions in continuous families which connect two different stationary solutions without topological charge, and that it is possible to interpret the dynamics of certain CFVs as the result of perturbations of these stationary solutions. The CFVs are calculated with high numerical accuracy and we may therefore accurately determine many of their properties, such as their energy and linear stability, and the CFVs are found to be stable over large parameter regimes. We also show that, like in earlier studies for lattices with a multiple of four sites, trimer and hexamer CFVs can be obtained by perturbing stationary constant amplitude vortices with certain linear eigenmodes. However, in contrast to the former case where the perturbation could be infinitesimal, the magnitude of the perturbations for trimers and hexamers must overcome a quite large threshold value. These CFVs may be interpreted as exact quasiperiodic CFVs, with a small perturbation applied. The concept of a charge flipping energy barrier is introduced and discussed.

Place, publisher, year, edition, pages
American Physical Society , 2015. Vol. 91, no 2, 022910- p.
National Category
Physical Sciences
URN: urn:nbn:se:liu:diva-117256DOI: 10.1103/PhysRevE.91.022910ISI: 000351205700005OAI: diva2:807076

Funding Agencies|Swedish Research Council

Available from: 2015-04-22 Created: 2015-04-21 Last updated: 2016-08-22
In thesis
1. Theoretical studies of Bose-Hubbard and discrete nonlinear Schrödinger models: Localization, vortices, and quantum-classical correspondence
Open this publication in new window or tab >>Theoretical studies of Bose-Hubbard and discrete nonlinear Schrödinger models: Localization, vortices, and quantum-classical correspondence
2016 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is mainly concerned with theoretical studies of two types of models:  quantum mechanical Bose-Hubbard models and (semi-)classical discrete nonlinear Schrödinger (DNLS) models.

Bose-Hubbard models have in the last few decades been widely used to describe Bose-Einstein condensates placed in periodic optical potentials, a hot research topic with promising future applications within quantum computations and quantum simulations. The Bose-Hubbard model, in its simplest form, describes the competition between tunneling of particles between neighboring potential wells (`sites') and their on-site interactions (can be either repulsive or attractive). We will also consider extensions of the basic models, with additional interactions and tunneling processes.

While Bose-Hubbard models describe the behavior of a collection of particles in a lattice, the DNLS description is in terms of a classical field on each site. DNLS models can also be applicable for Bose-Einstein condensates in periodic potentials, but in the limit of many bosons per site, where quantum fluctuations are negligible and a description in terms of average values is valid. The particle interactions of the Bose-Hubbard models become  nonlinearities in the DNLS models, so that the DNLS model, in its simplest form, describes a competition between on-site nonlinearity and tunneling to neighboring sites. DNLS models are however also applicable for several other physical systems, most notably for nonlinear waveguide arrays, another rapidly evolving research field.

The research presented in this thesis can be roughly divided into two parts:

1) We have studied certain families of solutions to the DNLS model.

First, we have considered charge flipping vortices in DNLS trimers and hexamers. Vortices represent a rotational flow of energy, and a charge flipping vortex is one where the rotational direction (repeatedly) changes. We have found that charge flipping vortices indeed exist in these systems, and that they belong to continuous families of solutions located between two stationary solutions.

Second, we have studied discrete breathers, which are spatially localized and time-periodic solutions, in a DNLS models with the geometry of a ring coupled to an additional, central site. We found under which parameter values these solutions exist, and also studied the properties of their continuous solution families. We found that these families undergo different bifurcations, and that, for example, the discrete breathers which have a peak on one and two (neighboring) sites, respectively, belong to the same family below a critical value of the ring-to-central-site coupling, but to separate families for values above it.

2) Since Bose-Hubbard models can be approximated with DNLS models in the limit of a large number of bosons per site, we studied signatures of certain classical solutions and structures of DNLS models in the corresponding Bose-Hubbard models.

These studies have partly focused on quantum lattice compactons. The corresponding classical lattice compactons are solutions to an extended DNLS model, and consist of a cluster of excited sites, with the rest of the sites exactly zero (generally localized solutions have nonzero `tails'). We find that only one-site classical lattice compactons remain compact for the Bose-Hubbard model, while for several-site classical compactons there are nonzero probabilities to find particles spread out over more sites in the quantum model. We have furthermore studied the dynamics, with emphasize on mobility, of quantum states that correspond to the classical lattice compactons. The main result is that it indeed is possible to see signatures of the  classical compactons' good mobility, but that it is then necessary to give the quantum state a `hard kick' (corresponding to a large phase gradient). Otherwise, the time scales for quantum fluctuations and for the compacton to travel one site become of the same order.

We have also studied the quantum signatures of a certain type of instability (oscillatory) which a specific solution to the DNLS trimer experiences in a parameter regime. We have been able to identify signatures in the quantum energy spectrum, where in the unstable parameter regime the relevant eigenstates undergo many avoided crossings, giving a strong mixing between the eigenstates. We also introduced several measures, which either drop or increase significantly in the regime of instability.

Finally, we have studied quantum signatures of the charge flipping vortices mentioned above, and found several such, for example when considering the correlation of currents between different sites.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2016
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1775
National Category
Physical Sciences
urn:nbn:se:liu:diva-129564 (URN)10.3384/diss.diva-129564 (DOI)978-91-7685-735-9 (Print) (ISBN)
Public defence
2016-09-02, Hörsal Planck, Fysikhuset, Campus Valla, Linköping, 10:15 (English)
Available from: 2016-08-22 Created: 2016-06-21 Last updated: 2016-08-22Bibliographically approved

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