Measurement-induced geometric phases

Abstract: In this thesis, we combine the idea of geometric phases in quantum mechanics with the notion of weak measurements, in the sense of measurements with small back action. For this purpose, we examine two different measurement methods: Firstly, dynamics induced by the interaction with a binary detector system which could describe, for instance, measurements with qubit-like detectors such as two-level atoms. Secondly, dynamics due to continuous measurements which describe average measurement schemes like, for instance, electric currents flowing through quantum systems. The back action of the detector on the system modifies the state of the system. It follows that a number of measurements along different directions in the space of quantum states may drag the system along a certain quantum trajectory. If this trajectory is closed, a geometric phase may be assigned to the evolution, where the former is proportional to the solid angle enclosed by the trajectory on the Bloch sphere. First, we show how this measurement-induced geometric phase can be observed in an appropriate interference experiment. In the case of the binary measurement model, we find an analytic dependence of the geometric phase on the measurement strength for one chosen realization of the measurements. For the continuous measurement model, we use Monte Carlo simulations and find a highly fluctuating geometric phase in dependence of the measurement strength. Although, for weak measurements, the back action is small, there are large fluctuations in the induced trajectories and consequently also in the geometric phases. We use different deterministic approaches to obtain analytical approximations for the average and most probable geometric phase for each measurement strength. Finally, we discuss the phenomenon of geometric dephasing and show that it vanishes in the adiabatic limit

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Universität Freiburg, Masterarbeit, 2017

Classification and Topics

• Keyword: Quantenmechanik ; Theoretische Physik ; Mathematische Physik

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2019
• Creator: Gebhart, Valentin
• Contributor: Buchleitner, Andreas ; Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik

Further information

• DOI: 10.6094/UNIFR/17276
• URN: urn:nbn:de:bsz:25-freidok-172765
• Rights: Kein Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 25.03.2025, 1:46 PM CET