Change search
ReferencesLink to record
Permanent link

Direct link
Bose-Einstein condensates under a spatially modulated transverse confinement
Dipartimento di Fisica “Galileo Galilei,” Università di Padova, Via Marzolo 8, 35131 Padova, Italy.
Umeå University, Faculty of Science and Technology, Department of Physics.
Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.
Dipartimento di Fisica “Galileo Galilei,” Università di Padova, Via Marzolo 8, 35131 Padova, Italy.
Show others and affiliations
2007 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 76, 013623- p.Article in journal (Refereed) Published
Abstract [en]

We derive an effective nonpolynomial Schrödinger equation (NPSE) for self-repulsive or attractive BEC in the nearly one-dimensional cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. In addition to the usual linear cigar-shaped trap, where the periodic modulation emulates the action of an optical lattice (OL), the model may be also relevant to toroidal traps, where an ordinary OL cannot be created. For either sign of the nonlinearity, extended and localized states are found, in the numerical form [using both the effective NPSE and the full three-dimensional (3D) Gross-Pitaevskii equation] and by means of the variational approximation (VA). The latter is applied to construct ground-state solitons and predict the collapse threshold in the case of self-attraction. It is shown that numerical solutions provided by the one-dimensional NPSE are always very close to full 3D solutions, and the VA yields quite reasonable results too. The transition from delocalized states to gap solitons, in the first finite bandgap of the linear spectrum, is examined in detail, for the repulsive and attractive nonlinearities alike.

Place, publisher, year, edition, pages
2007. Vol. 76, 013623- p.
URN: urn:nbn:se:umu:diva-38888DOI: 10.1103/PhysRevA.76.013623OAI: diva2:384311
Available from: 2011-01-10 Created: 2011-01-08 Last updated: 2011-01-11Bibliographically approved
In thesis
1. Excitations in Superfluids: From solitons to gravitational waves
Open this publication in new window or tab >>Excitations in Superfluids: From solitons to gravitational waves
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In 1995 two different research groups observed for the first time the Bose-Einstein condensation (BEC) in ultracold gases. When the confining magnetic trap was turned off the gas was left free to expand, and the velocity of the particles showed a clear peak: most of the particles were occupying the same single particle state, the one of lowest energy. The Bose-Einstein condensation had been predicted in 1925 by Einstein, written by inspiration of a work on the statistic of the photons by Bose (1924). In this work Bose described the behavior of an ensemble of photons, treating them as massless particles, with no number conservation associated. Einstein extended this approach to particles with a mass and with fixed number, creating what is now called the Bose-Einstein distribution. The particles that follow such a description are called ``bosons'', as opposed to the ``fermions'' of the Fermi-Dirac statistics. Einstein predicted that in a gas of bosons - under a critical temperature - a finite fraction of the total number of particles would have been in the ground state, and act as a single entity.


This amusing theoretical discovery found its utility a few years later. In the late thirties, new techniques allowed to cool Helium-4 at few Kelvins above the absolute zero. The properties of the resulting liquid were a puzzlement to the scientific community: among others, it could flow without experiencing friction. The liquid was called a ``superfluid''. A first explanation was given by London in 1938, which linked the superfluid behavior to the presence of a BEC among the bosonic Helium particles. The fermions cannot condense by themselves. On the other hand, they can form bound pairs and act as bosons, as it happens in a metal at low temperature. Using this approach, in 1957 Bardeen, Cooper and Schrieffer created a successful model of superconductivity by describing a superconductor as a superfluid in a charged system.


During the course of these years we explored the superfluid properties of Bosons and Fermions in different settings. The original contributions of the thesis are described starting from the third chapter, where we speak about the generation and stability of solitons in a periodic optical lattices, both fixed or in motion. In the fourth chapter we study the generation of giant vortices in cold fermions, by using a generalized hydrodynamical approach. In chapter 5 we study the effect of a quasiperiodic lattice and the glassy phase it produces on a gas of bosons. Finally, we study the interaction of normal matter and superfluids with gravitational waves. While this interaction is seen to be extremely small, we believe that the resulting formalism is interesting by itself.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, Institutionen för fysik, 2011. 92 p.
urn:nbn:se:umu:diva-38914 (URN)978-91-7459-129-3 (ISBN)
Public defence
2011-02-03, Biologihuset, BiA 201, Umeå universitet, Umeå, 10:00 (Swedish)
Available from: 2011-01-10 Created: 2011-01-10 Last updated: 2011-01-21Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Cetoli, Alberto
By organisation
Department of Physics
In the same journal
Physical Review A. Atomic, Molecular, and Optical Physics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 29 hits
ReferencesLink to record
Permanent link

Direct link