|title||Measurement of currents in optical lattices via the quantum Zeno eﬀect|
The investigation of quantum systems in highly controllable environments via cold atoms in optical lattices has accounted for major advances in many-body physics of strongly correlated systems. Thereby, the demand for ﬂexible experimental techniques in order to measure currents, as a striking feature in many-body systems, has increasingly gained importance for example in the context of topological insulators or in the investigation of quantum transport in general. In this thesis, a novel measurement protocol is introduced which allows for current measurements that, in contrast to most established measurement procedures, can be performed in a non-destructive and minimally invasive manner by exploiting the quantum Zeno eﬀect. The main experimental requirement is the ability to count single atoms. The proposed measurement protocol is benchmarked at the example of ultracold bosons in a two-legged ladder shaped potential subject to an artiﬁcial magnetic ﬁeld. By the help of exact diagonalisation techniques, the protocol is investigated with special emphasis on experimental feasibility with the aim of paving the way towards direct experimental implementation. As a demonstration of its versatile applicability, the current measurement protocol is expanded to direct measurements of current-current correlations at equal time in a similar non-destructive manner. Thereby, on the one hand, existing experimental techniques for measuring currents in cold atom systems are supplemented by a more ﬂexible and less destructive protocol, while on the other hand, one of the ﬁrst techniques for measuring current-current correlations in many-body systems is introduced. Potential applications include the characterisation of material properties such as conductivity as well as the investigation of topological phases of matter.