Vinsamlegast notið þetta auðkenni þegar þið vitnið til verksins eða tengið í það: http://hdl.handle.net/1946/21852
In this thesis, I model quantum mechanical systems and investigate their quantum properties based on mathematical formulations of quantum mechanics. Modeling of quantum systems such as qubits in quantum information processing is studied. Transport of correlated electrons through a quantized electronic system such as single or double quantum dots embedded in a quantum wire, and double quantum waveguide is investigated using a non-Markovian quantum master equation formalism. The quantized electronic system is weakly connected to external leads and strongly coupled to a single photon mode in a cavity. The total system, the central electronic system and the leads, is in an external homogeneous magnetic field perpendicular to the plane of the electron motion in the system. The photons in the cavity are linearly polarized either parallel ($x$-polarization) or perpendicular ($y$-polarization) to the direction of electron propagation in the central system. The full electron electron and electron-photon interactions are taken into account using an ``exact diagonalization'' technique in a truncated many-body space.
I observe that a cavity-photon can enhance the electron transport in the single or double quantum dot system. In the absence of the cavity, a peak (main peak) in the net charge current is found due to an electron tunneling almost elastically from the leads to the central system. In the presence of an $x$-polarized photon field, a side peak to the main peak is observed. The side peak indicates inelastic electron tunneling from the leads to the central system in which the electrons absorb photons in the cavity. The side peak current is very weak in the $y$-polarized photon field. This is caused by the anisotropy of the central system. Furthermore, I notice that the mechanism of electron transport from the leads to the central system in the main peak is different from what happens for the the side peak and depends on the photon number initially in the cavity.
In addition, I use cavity-photons to implement a quantum logic gate in a double waveguide system which consists of control- and target-waveguide. The two waveguides are coupled via a coupling element the so called coupling window. The coupling window (CW) relies on interference of quantum waves causing electron switching between the waveguides.
In the case of the waveguide system without the photon cavity, oscillation in the net charge current is found by tuning the length of the CW indicating inter-waveguide backward and forward scattering. A current peak for a crossover energy displaying 'resonant' energy levels between the waveguides and a current dip for split energy levels are observed. In the non-interacting waveguide system, electron charge from input control-waveguide splits 'equally' between the output of the control- and target waveguide at the current peak. The charge splitting feature indicates a quantum logic gate action called square-root-of-Not-operation ($\sqrt{\rm NOT}$-operation). Including electron-electron interaction in the waveguide system, the net charge current is suppressed because the Coulomb interaction raises the two-electron states in the energy spectrum leading to vanishing participation the two-electron states in the electron transport.
In the presence of an $x$-polarized photon field, I observe suppression in the net charge current in both current peak and the current dip. This is due to contribution of the photon replica states to the electron transport leading to inter-waveguide backward scattering. We find that I can influence the logic-gate action of the system by selecting the initial status of the photon field (number of photons and polarization) and the size of the coupling
window.
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Thesis.pdf | 6.71 MB | Opinn | Heildartexti | Skoða/Opna |