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Excitations in Superfluids: From solitons to gravitational waves
Umeå University, Faculty of Science and Technology, Department of Physics.
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.
Identifiers
URN: urn:nbn:se:umu:diva-38914ISBN: 978-91-7459-129-3 (print)OAI: oai:DiVA.org:umu-38914DiVA: diva2:384482
Public defence
2011-02-03, Biologihuset, BiA 201, Umeå universitet, Umeå, 10:00 (Swedish)
Opponent
Supervisors
Available from: 2011-01-10 Created: 2011-01-10 Last updated: 2011-01-21Bibliographically approved
List of papers
1. Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices
Open this publication in new window or tab >>Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices
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
Identifiers
urn:nbn:se:umu:diva-38886 (URN)10.1103/PhysRevA.75.033622 (DOI)
Available from: 2011-01-10 Created: 2011-01-08 Last updated: 2017-12-11Bibliographically approved
2. Bose-Einstein condensates under a spatially modulated transverse confinement
Open this publication in new window or tab >>Bose-Einstein condensates under a spatially modulated transverse confinement
Show others...
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.

Identifiers
urn:nbn:se:umu:diva-38888 (URN)10.1103/PhysRevA.76.013623 (DOI)
Available from: 2011-01-10 Created: 2011-01-08 Last updated: 2017-12-11Bibliographically approved
3. Dynamics of kicked matter-wave solitons in an optical lattice
Open this publication in new window or tab >>Dynamics of kicked matter-wave solitons in an optical lattice
2009 (English)In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 238, no 15, 1388-1393 p.Article in journal (Refereed) Published
Abstract [en]

We investigate effects of the application of a kick to one-dimensional matter-wave solitons in a self-attractive Bose–Einstein condensate trapped in an optical lattice. The resulting soliton’s dynamics is studied within the framework of the time-dependent nonpolynomial Schrödinger equation. The crossover from the pinning to quasi-free motion crucially depends on the size of the kick, strength of the self-attraction, and parameters of the optical lattice.

Place, publisher, year, edition, pages
Elsevier, 2009
Identifiers
urn:nbn:se:umu:diva-38889 (URN)10.1016/j.physd.2008.07.010 (DOI)
Available from: 2011-01-10 Created: 2011-01-08 Last updated: 2017-12-11Bibliographically approved
4. Hydrodynamic theory of giant vortices in trapped unitary Fermi gases
Open this publication in new window or tab >>Hydrodynamic theory of giant vortices in trapped unitary Fermi gases
2009 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 80, no 2, 023610- p.Article in journal (Refereed) Published
Abstract [en]

The rotational properties are studied for a unitary superfluid gas of fermions at zero temperature. Using a hydrodynamic approach, the conditions for the formation of a giant vortex are discussed. It is found that in the present approximation, an anharmonic addition to the usual harmonic-oscillator type of trap potential is necessary for the energetic stability of a giant vortex. To determine the conditions quantitatively, a Thomas-Fermi approach is compared with numerical solutions in three dimensions.

Place, publisher, year, edition, pages
APS, 2009
Identifiers
urn:nbn:se:umu:diva-38890 (URN)10.1103/PhysRevA.80.023610 (DOI)
Available from: 2011-01-10 Created: 2011-01-08 Last updated: 2017-12-11Bibliographically approved
5. Re-entrant transition of bosons in a quasiperiodic potential
Open this publication in new window or tab >>Re-entrant transition of bosons in a quasiperiodic potential
2010 (English)In: European Physics Letters, Vol. 90, no 4, 46001-46005 p.Article in journal (Refereed) Published
Abstract [en]

We investigate the behavior of a two-dimensional array of Bose-Einstein condensate tubes described by means of a Bose-Hubbard Hamiltonian. Using a Wannier function expansion for the wave function in each tube, we compute the Bose-Hubbard parameters related to two different longitudinal potentials, periodic and quasiperiodic. We predict that—upon increasing the external potential strength along the direction of the tubes—the system can experience a re-entrant transition between a Mott insulating phase and the superfluid one.

Identifiers
urn:nbn:se:umu:diva-38892 (URN)10.1209/0295-5075/90/46001 (DOI)000279119200017 ()
Available from: 2011-01-10 Created: 2011-01-08 Last updated: 2011-01-11Bibliographically approved
6. Correlations and superfluidity of a one-dimensional Bose gas in a quasiperiodic potential
Open this publication in new window or tab >>Correlations and superfluidity of a one-dimensional Bose gas in a quasiperiodic potential
2010 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 81, no 6, 063635-063642 p.Article in journal (Refereed) Published
Abstract [en]

We consider the correlations and superfluid properties of a Bose gas in an external potential. Using a Bogoliubov scheme, we obtain expressions for the correlation function and the superfluid density in an arbitrary external potential. These expressions are applied to a one-dimensional system at zero temperature subject to a quasiperiodic modulation. The critical parameters for the Bose glass transition are obtained using two different criteria and the results are compared. The Lifshitz glass is seen to be the limiting case for vanishing interactions.

Place, publisher, year, edition, pages
American Physical Society, 2010
Identifiers
urn:nbn:se:umu:diva-38894 (URN)10.1103/PhysRevA.81.063635 (DOI)000279262800001 ()
Available from: 2011-01-10 Created: 2011-01-08 Last updated: 2017-12-11Bibliographically approved
7. Interaction of gravitational waves with normal and superconducting matter
Open this publication in new window or tab >>Interaction of gravitational waves with normal and superconducting matter
2012 (English)In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 85, no 6, 064036- p.Article in journal (Other academic) Published
Abstract [en]

We develop a unified formalism for describing the interaction of gravitational waves with matterthat clearly separates the effects of general relativity from those due to interactions in the matter.This allows one to take into account the microscopic character of the matter, and we derive a generalexpression for the dispersion of gravitational waves in matter in terms of correlation functions forthe matter in flat spacetime. The formalism enables one to derive simply previous results for thedispersion of gravitational waves in astrophysical plasmas. We also consider metals and show that,while simple estimates indicate that contributions of electrons to the stress tensor could be large,screening of the Coulomb interaction reduces these effects considerably. We consider both normaland superconducting metals, and show that in both cases, electrons and ions are locked togetherunder the influence of a gravitational wave with a frequency much less than the plasma frequencyand, consequently, charge separation has little effect on gravitational waves.

Place, publisher, year, edition, pages
American Physical Society, 2012
Keyword
Astronomy & Astrophysics, Physics, Particles & Fields
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:umu:diva-38895 (URN)10.1103/PhysRevD.85.064036 (DOI)
Available from: 2011-01-10 Created: 2011-01-08 Last updated: 2017-12-11Bibliographically approved

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