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Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices
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.
2007 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 75, 013623- p.Article in journal (Refereed) Published
Abstract [en]

Within the framework of a mean-field description, we investigate atomic Bose-Einstein condensates, with attraction between atoms, under the action of a strong transverse confinement and periodic [optical-lattice (OL)] axial potential. Using a combination of the variational approximation, one-dimensional (1D) nonpolynomial Schrödinger equation, and direct numerical solutions of the underlying 3D Gross-Pitaevskii equation, we show that the ground state of the condensate is a soliton belonging to the semi-infinite band gap of the periodic potential. The soliton may be confined to a single cell of the lattice or extended to several cells, depending on the effective self-attraction strength g (which is proportional to the number of atoms bound in the soliton) and depth of the potential, V0, the increase of V0 leading to strong compression of the soliton. We demonstrate that the OL is an effective tool to control the soliton’s shape. It is found that, due to the 3D character of the underlying setting, the ground-state soliton collapses at a critical value of the strength, g=gc, which gradually decreases with the increase of V0; under typical experimental conditions, the corresponding maximum number of 7Li atoms in the soliton, Nmax, ranges between 8000 and 4000. Examples of stable multipeaked solitons are also found in the first finite band gap of the lattice spectrum. The respective critical value gc again slowly decreases with the increase of V0, corresponding to Nmax≃5000.

Place, publisher, year, edition, pages
APS , 2007. Vol. 75, 013623- p.
URN: urn:nbn:se:umu:diva-38886DOI: 10.1103/PhysRevA.75.033622OAI: diva2:384309
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

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