Final Report Summary - ODYCQUENT (Optimal dynamcal control of quantum entanglement) The aim of the project is to identify time-dependent control fields that help to exploit interactions in composite quantum systems in an optimal fashion.We have developed novel methodology that permit to construct such control fields for a large variety of systems.Numerically exact techniques offer the basis for finding highly accurate controls. We have devised exact pulse shaping techniques based on Floquet theory that offer the construction of control sequences with well-defined spectral properties.Analytical methods are subject to approximations, but apply to large systems where a numerical treatment is prohibited. We have employed the concept of flow equations that permit to describe the dynamics of controlled systems with high accuracy what permits to improve control in many-body systems substantially.With the developed methodology we have devised controls for nitrogen vacancy centres, trapped ions and ultra-cold atomic gases.In the work on nitrogen vacancy centres we have demonstrated highly sensitive magnetic field sensing and we have demonstrated that even spectrally narrow control pulses can compensate for experimental imperfections such as inhomogeneous broadening very well.In our work on trapped ions we have devised temporally shaped control fields that make entangling gates largely insensitive to motional heating, which is the effect that currently limits that achievable gate fidelities.In our work on ultra-cold atomic gases, we have formulated a general framework characterising the impact of geometric symmetries on the controllability of quantum manybody systems and we have devised driving patterns that permit to exploit tunnelling processes in an ideal fashion for the realisation of topologically non-trivial quantum manybody states.In this work, we have extended many tools for the description or control of closed quantum systems towards optimal control of open quantum systems.
