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Thesis University of Iceland > Verkfræði- og náttúruvísindasvið > Meistaraprófsritgerðir - Verkfræði- og náttúruvísindasvið >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1946/10771

  • Nonperturbative Approach to Circuit Quantum Electrodynamics
  • February 2012
  • We investigate the coupling between a quantized electromagnetic field in a cavity resonator and a Coulomb interacting electronic system in a nanostructure in an external magnetic field. We use a nonperturbative approach with a stepwise introduction of complexity to the description of the system and a corresponding stepwise truncation of the ensuing many-body spaces. We are able to explicitly take into account effects caused by the geometry of the electronic system and the polarization of the electromagnetic field, including both the full interaction between electrons and photons and Coulomb interaction between electrons. Our numerical results demonstrate that the two-level system approximation and the Jaynes-Cummings model remain valid in the weak electron-photon coupling regime, while the quadratic vector potential in the diamagnetic part of the charge current leads to significant correction to the energy spectrum in the strong coupling regime. Investigation of numerical convergence shows that convergence with respect to the number of electron eigenstates is slow, requiring a large basis of many-electron eigenstates to be included in the model.
    Keywords: Mesoscopic physics, light-matter interaction, circuit-QED, cavity QED.

  • Abstract is in Icelandic

    Við rannsökum tengsl milli skammtaðs rafsegulsviðs í hermuholrúmi og Coulomb víxlverkandi rafeindakerfis í ytra segulsviði á nanóskala. Við notum aðferð sem byggist ekki á truflunarreikningi þar sem Fock rými er stækkað skref fyrir skref við lýsingu á kerfinu og samsvarandi niðurskurður skref fyrir skref er gerður á margra-einda rúminu. Fullt tillit er tekið til lögunar rafeindakerfisins og skautunar rafsegulsviðsins. Líkanið inniheldur bæði fulla víxlverkun rafeinda og ljóseinda og Coulomb víxlverkunar milli rafeinda. Tölulegar niðurstöður sýna að nálgun með tvístiga kerfi og Jaynes-Cummings líkani gilda fyrir veik rafeinda-ljóseinda tengsl en annars stigs liðurinn fyrir vigurmætti rafsegulsviðsins hefur mikil áhrif fyrir sterk tengsli. Rannsóknir á tölulegri samleitni sýna að samleitni með tilliti til fjölda rafeinda eiginástanda er hæg og því þarf stóran grunn af margra rafeinda eiginástöndum í líkaninu.

  • Feb 1, 2012
  • http://hdl.handle.net/1946/10771

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