EUROCORES_EuroQUAM 1. Call_Quantum Simulation using cold atoms in optical lattices (DQS)

This proposal is an individual project (IP) within the EUROCORES Collaborative Research Project (CRP) DQS, which is being proposed under the EuroQUAM call and comprises groups in Oxford, Mainz, Innsbruck, and Florence. This CRP is set against the backdrop of the significant recent developments with atoms in optical lattices, which have shifted attention from weakly interacting ultra-cold atomic gases to strongly-correlated multi-particle systems. The properties of atoms in an optical lattice are closely related to many systems of interest in Condensed Matter Physics (CMP), and there is an intense interest in this powerful new and interdisciplinary approach to fundamental quantum many body problems. With strong relationship between theory and experiment, the field has advanced towards a stage where it is possible to obtain: 1. detailed microscopic understanding of the Hamiltonians describing laboratory experiments, 2. extremely precise control and tunability of system parameters in the experiments over a wide range, 3. clean experimental realizations of Hamiltonians that can be tailored to mimic certain CMP systems, and 4. methods to study the dynamics of strongly correlated quantum systems. It will thus be increasingly possible in the near future to take models that are difficult to solve in CMP, and investigate them experimentally, and also to ask new questions about these systems in the new context, especially related to coherent dynamics (without dissipation that is prevalent in most CMP experiments), and time dependence. The Individual Project The Individual project in Innsbruck contributes theoretical investigations to all three workpackages of the CRP. These contributions build on the PI`s experience studying systems of atoms in optical lattice, and especially working with numerical methods for time-dependent simulation of many-body systems. 1. Generation of quantum states in a lattice: We will investigate the addition of noise through lattice modulation to a many-body system of atoms in an optical lattice, both through analytical and numerical calculations. Controlled modulation of the lattice depth could be used to manipulate specific many-body correlations, driving a system from a weakly interacting superfluid phase to a state more characteristic of a strongly interacting gas. 2. Direct quantum simulation (DQS): We will investigate the engineering of lattice Hamiltonians that correspond to situations that appear in mesoscopic transport systems. In traditional experiments in such systems, two reservoirs are coupled by a wire, and effects occurring in the wire and at boundaries are measured by probing steady state current and current correlation properties. In the context of optical lattices, the new system offers new possibilities and generates new questions, especially with respect to the time dependence of these setups. For example, phenomena such as Andreev reflections could potentially be observed time-dependently in an optical lattice experiments. We will also investigate disordered systems specifically in the context of current experiments, such as those being performed in the Florence group, which also belongs to the CRP. We will use numerical tools to perform simulations directly modelling the corresponding states prepared in laboratories, and measurement techniques such as spectroscopy by lattice modulation. 3. DQS experiments with dipolar molecules: We will develop numerical simulations for atoms in optical lattices that can account for finite range interactions. These will be applied to example systems of interest in the experiments in the Mainz group belonging to the CRP, and systems to be studied by the theory group in Oxford.