Together with our international partners, we develop numerical tools based on optimal control theory to design experimental techniques with improved performance for magnetic resonance. We focus on applications to solid-state nuclear magnetic resonance (NMR) of biomolecules such as proteins and amyloids. The aim is to improve the quality of multidimensional spectra necessary to assign resonances to individual atoms and to extract structural information. We developed a sophisticated model that accounts for the hardware response to a pulse sequence  and presented experiments with improved efficiency for magnetization transfer . We showed that optimal control can be used to develop new type of experiments for transverse mixing  – the problem that does not have a solution in terms of the classical design approach based on average Hamiltonian or Floquet theories. The transverse mixing method systematically improves signal-to-noise ratio of multidimensional experiments by a factor of 1.41 for each indirectly sampled dimension (it translates to reducing measurement time by a factor of two for each dimension).
Our recent approach is based on spin dynamics evaluated on the level of full density matrix. It requires a detailed knowledge of interaction constants and other parameters of the spin system. On the other hand, analytical approaches based on average Hamiltonian or Floquet theories work on the level of effective Hamiltonians. It allows abstraction from interaction constants to the actual form of spin couplings. The form of spin interactions can be effectively shaped (averaged) by rf irradiation to produce desired spin dynamics.
This PhD project will concentrate on merging the Hamiltonian approach with numerical optimization by means of optimal control. In addition to applications in biomolecular solid-state NMR, another branch of the project will be oriented towards dynamic nuclear polarization, that is, developing methods for transferring electron polarization to nuclear spins, providing a theoretical signal gain of 660.
The project will be conducted in close collaboration with the Technical University of Munich (bio-solid-state NMR) and Aarhus University (DNP), which are both equipped with the latest instrumentation necessary for experimental verification.
The ideal candidate should have basic knowledge of solid-state NMR. A theoretical background and programming skills would be an advantage.