Landau-Zener Transitions in Open Quantum Systems

Patnaik, Pratik (2022) Landau-Zener Transitions in Open Quantum Systems. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Pratik Patnaik (17MS033)) 17MS033_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

In the first part of the project, we numerically solve the Von-Neumann Liouville Equation, equivalent to the Schrodinger equation, for the case of a two level system with a resonant frequency ω0. The two levels are coupled by a dipolar coupling which is affected in the presence of a drive whose frequency sweeps through resonance at a particular sweep rate. The excitation of an ensemble of such TLSs, initially in the ground state, to the excited state is studied and the results predicted by the theoretical calculations of Landau [0], Zener [0] and Wittig[0] are verified numerically. The similarity of this to the case considered historically studied. How a Gaussian pulse profile affects these transitions as mentioned in [0] is considered in the numerical solution. We shift our attention to a more realistic scenario involving an ensemble of TLSs coupled to their local environments via JC coupling. TLSs do not interact with one another, and their local environments experience thermal fluctuations in the bath. These TLSs are coherently driven by a frequency sweep drive. In various situations, the excited state population of such a situation is studied. Finally, the effect of a Gaussian Pulse on such a situation is investigated, as well as how this affects population transfer.

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