Relaxation and decoherence in quantum spin system Yuan, Shengjun

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1 Relaxation and decoherence in quantum spin system Yuan, Shengjun IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2008 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Yuan, S. (2008). Relaxation and decoherence in quantum spin system s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 109 Samenvatting Aan de hand van een grote verzameling simulatieresultaten voor een ferroen antiferromagnetisch Heisenberg systeem, gekoppeld aan verschillende spinbad omgevingen geprepareerd in de grondtoestand, hebben we de voorwaarden bepaald waaronder het centrale Heisenberg systeem evolueert van de initiële spin-up - spin-down toestand naar zijn grondtoestand of naar andere pointer toestanden. We hebben vastgesteld dat de evolutie naar de grondtoestand of een pointer toestand een aanzienlijk gecompliceerder proces is dan wat men zou verwachten. De evolutie hangt op een essentiële, niet-intuïtieve manier af van de verhouding van de sterkte van de interaktie en van het type spin-bad Hamiltonianen. Veranderen we de interne dynamica van de omgeving (= spinbad) dan verloopt de decoherentie van het centrale systeem meestal, maar niet altijd, anders. Het centrale systeem relaxeert gemakelijker naar zijn grondtoestand indien deze laatste minder verstrengeld (entangled) is, zoals bij de spin-up - spindown toestand en de singlet toestand. Heeft het systeem bijvoorbeeld extra behouden grootheden dan kan de evolutie naar de grondtoestand sneller verlopen. Op het eerste zich lijkt dit laatste een beetje vreemd omdat het zou suggereren dat een meer regulier systeem sneller zou kunnen relaxeren dan een meer chaotisch systeem. Een verklaring voor dit gedrag is te vinden in het feit dat in de afwezigheid van extra behouden grootheden, het decoherentieproces veel gecompliceerder is, met verschillende decoherentietijden voor de verschillende elementen van de dichtheidsmatrix, en dit omdat de toegankelijke Hilberruimte groter is. We hebben gevonden dat omgevingen die op één of andere manier gefrustreerd zijn, zoals bvb, een spin-glas of een antiferromagneet op een driehoekig rooster, aanleiding geven tot een zeer effectief decoherentieproces. We hebben laten zien dat de efficiëntie van het decoherentieproces drastisch afneemt indien we het type van spin-bad als volgt kiezen:

3 110 Samenvatting 1) Spin-glas en random waarde voor de koppelingsterkte van de spins met alle spins in het centrale systeem; 2) Gefrustreerde antiferromagneet (driehoekig rooster met naaste-nabuur interacties); 3) Bipartiete antiferromagneet (vierkant rooster met naaste-nabuur interacties); 4) En-dimensionale ring met naaste-nabuur interacties. Verder hebben we aangetoond dat voor een spin bad omgeving met een vast aantal spins en in die gevallen waarin het decoherentieproces efficiënt is, verschillende realisaties van de random parameters geen significant effect geeft. Gebruiken we het spin-glas of de gefrustreerde magneet als omgeving dan blijkt dat dit een zeer effectieve manier is om het decoherentieprocessen to simuleren. Omgevingen met 14 tot 16 spins zijn dan voldoende groot om de Rabi oscillaties volledig te onderdrukken, dit in tegenstelling met spin bad omgevingen die een eenvoudigere struktuur hebben, zoals een ketting of vierkant rooster van spins. Onze resultaten zijn een stimulans om het zogenaamde decoherence program verder te ontwikkelen en verhelderen. Indien we aannemen dat de interacties met de omgeving zwak genoeg zijn dan is de stelling dat de pointer toestand een eigentoestand van de Hamiltoniaan van het centrale systeem moet zijn, met het ambitieuze doel om het fenomeen van de zogenaamde quantum jumps te verklaren. Onze resultaten bevestigen dat onder de genoemde condities de pointer toestanden inderdaad de eigentoestanden zijn van het centrale systeem. Anderzijds tonen onze resultaten ook aan dat de decoherentie verre van generiek is, wat dan de algemene toepasbaarheid van het decoherence program sterk in vraag stelt. In de aanwezigheid van Ising-achtige anisotrope interacties blijken domeinmuren in ferromagnetische spin-1/2 systemen dynamisch stabiel te zijn over zeer lange tijden. Het magnetisatieprofiel van de domeinmuur verschilt van het profiel van de grondtoestand in de deelruimte met totale magnetisatie nul. Als het systeem meer isotroop wordt en het in de buurt van het quantum kritische punt wordt gebracht dan divergeert de breedte van de muur als een macht van de afstand tot het kritisch punt en met kritische exponent 1/2. Ten slotte hebben we de propagatie van spingolven door domeinmuren in quantum spin-1/2 kettingen bestudeerd. We hebben gevonden dat de longitudinale component van de spingolf versnelt bij het doorboren van een domeinmuur.

4 111 De transverse component wordt echter bijna volledig gereflecteerd. Dit gedrag, afgeleidt uit de oplossing van de tijdsafhankelijke Schrödinger vergelijking, is eigen aan het quantum spin model, dit in tegenstelling met het gedrag in mesoscopische magnetische systemen. Deze laatste worden veelal beschreven door de Landau-Lifschitz-Gilbert vergelijking die het mesoscopische magnetische systeem als een klassiek continue medium beschrijft en waarin de transverse component van de spingolf zonder reflectie maar met een faseverschuiving van 90 0 aan de andere kant van de domeinmuur verschijnt. Welke van de twee beschrijvingen het meest geëigend is hangt uiteraard af van het specifieke materiaal. Echter, het verschil in het gedrag tussen een mesoscopisch en een microscopisch systeem kan van belang worden nu het met hedendaagse bottom-up synthetische chemie mogelijk wordt om magnetische materialen steeds kleiner te maken.

5 112 Samenvatting

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