Ring Dark Solitons in Toroidal Bose-Einstein Condensates
Toikka, Lauri (2014-06-18)
Ring Dark Solitons in Toroidal Bose-Einstein Condensates
Toikka, Lauri
(18.06.2014)
Turun yliopisto Annales Universitatis Turkuensis A I 489
Julkaisun pysyvä osoite on:
https://urn.fi/URN:ISBN:978-951-29-5739-2
https://urn.fi/URN:ISBN:978-951-29-5739-2
Kuvaus
Siirretty Doriasta
Tiivistelmä
In this Thesis, we study various aspects of ring dark solitons (RDSs) in quasi-two-dimensional toroidally trapped Bose-Einstein condensates, focussing on atomic realisations thereof.
Unlike the well-known planar dark solitons, exact analytic expressions for RDSs are not known. We address this problem by presenting exact localized soliton-like solutions to the radial Gross-Pitaevskii equation. To date, RDSs have not been experimentally observed in cold atomic gases, either. To this end, we propose two protocols for their creation in experiments.
It is also currently well known that in dimensions higher than one, (ring) dark solitons are susceptible, in general, to an irreversible decay into vortex-antivortex pairs through the snake instability. We show that the snake instability is caused by an unbalanced quantum pressure across the soliton's notch, linking the instability to the Bogoliubov-de Gennes spectrum. In particular, if the angular symmetry is maintained (or the toroidal trapping is restrictive enough), we show that the RDS is stable (long-lived with a lifetime of order seconds) in two dimensions. Furthermore, when the decay does take place, we show that the snake instability can in fact be reversible, and predict a previously unknown revival phenomenon for the original (many-)RDS system: the soliton structure is recovered and all the point-phase singularities (i.e. vortices) disappear. Eventually, however, the decay leads to an example of quantum turbulence; a quantum example of the laminar-to-turbulent type of transition. Tässä työssä käsitellään pimeitä rengassolitoneja litteissä kaksiulotteisissa atomisissa Bosen-Einsteinin kondensaateissa. Toisin kuin suorat pimeät solitonit, pimeälle rengassolitonille ei ole tiedossa analyyttista kaavaa. Väitöskirjan ensimmäisessä julkaisussa esitellään muun muassa uusia eksakteja rengassolitonin kaltaisia ratkaisuja Grossin-Pitaevskiin yhtälölle. Väitöskirjassa kehitetään ja esitellään myös kaksi kokeellista menetelmää pimeiden rengassolitonien luomiseen laboratoriossa. Pimeiden rengassolitonien hajoamista ja sitä seuraavaa vorteksi-antivorteksiparien fysiikkaa tutkitaan väitöskirjan loppupuolella. Osoitetaan, että pimeän solitonin hajoaminen ei olekaan peruuttamatonta kuten aiemmin on luultu, vaan se on mahdollista, mikäli atomiloukun muoto valitaan sopivasti.
Unlike the well-known planar dark solitons, exact analytic expressions for RDSs are not known. We address this problem by presenting exact localized soliton-like solutions to the radial Gross-Pitaevskii equation. To date, RDSs have not been experimentally observed in cold atomic gases, either. To this end, we propose two protocols for their creation in experiments.
It is also currently well known that in dimensions higher than one, (ring) dark solitons are susceptible, in general, to an irreversible decay into vortex-antivortex pairs through the snake instability. We show that the snake instability is caused by an unbalanced quantum pressure across the soliton's notch, linking the instability to the Bogoliubov-de Gennes spectrum. In particular, if the angular symmetry is maintained (or the toroidal trapping is restrictive enough), we show that the RDS is stable (long-lived with a lifetime of order seconds) in two dimensions. Furthermore, when the decay does take place, we show that the snake instability can in fact be reversible, and predict a previously unknown revival phenomenon for the original (many-)RDS system: the soliton structure is recovered and all the point-phase singularities (i.e. vortices) disappear. Eventually, however, the decay leads to an example of quantum turbulence; a quantum example of the laminar-to-turbulent type of transition.
Kokoelmat
- Väitöskirjat [2771]