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Title: Optimally driven quantum systems
Author: Verdeny Vilalta, Albert
ISNI:       0000 0004 5371 9502
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2015
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Periodically driven quantum systems offer an exceptional platform for quantum simulations due to the possibility to approximate their dynamics in terms of time-independent effective Hamiltonians. This, together with the recent experimental advances, has situated driven systems at center stage of engineered quantum-mechanical devices. The aim of this thesis is to develop theoretical methods in order to design optimal quantum simulations with driven systems. By applying the derived tools to experimentally relevant models, the applicability and significance of the methods are furthermore demonstrated. First, we introduce a method to derive accurate effective Hamiltonians by merging two seemingly unrelated tools: Floquet theory and flow equations. With this, the required analytical identification of the effective Hamiltonian in terms of the system's parameters is achieved. Second, we identify structural properties that determine the accessible effective dynamics of a system of particles on shaken optical lattices, which is arguably one of the most remarkable systems for many-body quantum simulations. In particular, we identify fundamental symmetries of the underlying lattice geometry that determine the emergence of new tunneling processes. Third, we develop an optimal control scheme to design polychromatic driving protocols that optimally simulate specifically targeted dynamics. We apply this scheme to demonstrate an optimal realization of Raman transitions with a Lambda system, a building block in many quantum simulations. Then, we employ it to implement a topological Chern insulator through suitably engineering the geometry-dependent tunneling of particles on a shaken hexagonal lattice. Hereby, a realistic route to experimentally test strongly-correlated topological phases of matter is provided. By determining structural properties of driven systems and suitable driving protocols, the methods described in this thesis open substantial possibilities for the development of optimal quantum simulations and, ultimately, reliable quantum technologies.
Supervisor: Mintert, Florian Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available