| Summary: | Recent advances in the manipulation of cold atoms within a tailored optical tweezer array allow for the production of Rydberg quantum simulators. In this thesis we analyze disordered and constrained many-body dynamics by utilizing such a system. Using a one-dimensional quantum simulator platform, we employ single-site addressing to analyze three distinct protocols based on the Rydberg blockade mechanism. These protocols allow for the preparation of an antiferromagnetic GHZ state and a matrix product state, as well as the transport of a quantum state.
Furthermore, Rydberg simulators allow for the study of many body dynamics under the so-called facilitation condition. Under this condition, the system can be represented by a single-particle hopping model on a synthetic lattice that features flat bands supporting localized states. We discuss the dynamics of this system in a ladder geometry focusing on the localization properties under the influence of disorder originating from an uncertainty of the atomic position in the optical tweezer.
Additionally, we explore an interacting spin chain with kinetic facilitation constraints and disorder in the many particle sector. This system can be mapped onto an XX-chain with an unconventional non-local disordered interaction resulting in interesting non-ergodic behavior. We analyze the localization properties using theoretical tools from the domain of many-body localization and find signatures indicating a crossover between a localized and delocalized phase.
In the final part of the thesis, we study the constrained dynamics of an effectively open, two-dimensional system of hard-core bosons. The constraint enters the system through the Zeno effect due to strong, non-local pair loss instead of energy barriers, as in the previous considerations. This system, which can be studied in a Rydberg atom setup, exhibits intriguing localization phenomena, even in the absence of disorder.
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