Alexander Karabanov

On the accuracy of the state space restriction approximation for spin dynamics simulations

We present an algebraic foundation for the state space restriction approximation in spin dynamics simulations and derive applicability criteria as well as minimal basis set requirements for practically encountered simulation tasks. The results are illustrated with nuclear magnetic resonance (NMR), electron spin resonance (ESR), dynamic nuclear polarization (DNP), and spin chemistry simulations. It is demonstrated that state space restriction yields accurate results in systems where the time scale of spin relaxation processes approximately matches the time scale of the experiment. Rigorous error bounds and basis set requirements are derived.

Dynamic Nuclear Polarization as Kinetically Constrained Diffusion.

Dynamic nuclear polarization (DNP) is a promising strategy for generating a significantly increased nonthermal spin polarization in nuclear magnetic resonance (NMR) and its applications that range from medicine diagnostics to material science. Being a genuine nonequilibrium effect, DNP circumvents the need for strong magnetic fields. However, despite intense research, a detailed theoretical understanding of the precise mechanism behind DNP is currently lacking. We address this issue by focusing on a simple instance of DNP-so-called solid effect DNP-which is formulated in terms of a quantum central spin model where a single electron is coupled to an ensemble of interacting nuclei. We show analytically that the nonequilibrium buildup of polarization heavily relies on a mechanism which can be interpreted as kinetically constrained diffusion. Beyond revealing this insight, our approach furthermore permits numerical studies of ensembles containing thousands of spins that are typically intractable when formulated in terms of a quantum master equation. We believe that this represents an important step forward in the quest of harnessing nonequilibrium many-body quantum physics for technological applications.

Symmetries of the master equation and long-lived states of nuclear spins

In terms of the master equation of relaxation, long-lived states in systems of n interacting spin-1/2 nuclei are described as those with eigenvalues much less than the characteristic T(1) rate. It is demonstrated that degeneracies of correlations between interacting dipole-dipole pairs are responsible for their presence. The case n=3 is considered in full detail.

Conversion of parahydrogen induced longitudinal two-spin order to evenly distributed single spin polarisation by optimal control pulse sequences

Strongly enhanced spin polarization in the form of longitudinal spin order can be generated on target molecules by using parahydrogen in a catalyzed hydrogenation reaction. An optimal control algorithm was used to generate radiofrequency pulse sequences which convert the arising longitudinal two-spin order into single-spin Zeeman order with high efficiency and distribute it evenly between three coupled spins within the same molecule. The pulses are designed to be very robust towards variations in the B(0) and B(1) fields. Furthermore, this strategy is applied to enhance the NMR signal in an ultrafast gradient assisted single excitation two-dimensional spectroscopy experiment.

Solid effect DNP polarization dynamics in a system of many spins

We discuss the polarization dynamics during solid effect dynamic nuclear polarization (DNP) in a central spin model that consists of an electron surrounded by many nuclei. To this end we use a recently developed formalism and validate first its performance by comparing its predictions to results obtained by solving the Liouville von Neumann master equation. The use of a Monte Carlo method in our formalism makes it possible to significantly increase the number of spins considered in the model system. We then analyse the dependence of the nuclear bulk polarization on the presence of nuclei in the vicinity of the electron and demonstrate that increasing the minimal distance between nuclei and electrons leads to a rise of the nuclear bulk polarization. These observations have implications for the design of radicals that can lead to improved values of nuclear spin polarization. Furthermore, we discuss the potential to extend our formalism to more complex spin systems such as cross effect DNP.

Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator

Relaxation plays a crucial role in the spin dynamics of dynamic nuclear polarisation. We review here two different strategies that have recently been used to incorporate relaxation in models to predict the spin dynamics of solid effect dynamic nuclear polarisation. A detailed explanation is provided on how the Lindblad–Kossakowski form of the master equation can be used to describe relaxation in a spin system. Fluctuations of the spin interactions with the environment as a cause of relaxation are discussed and it is demonstrated how the relaxation superoperator acting in Liouville space on the density operator can be derived in the Lindblad–Kossakowski form by averaging out non-secular terms in an appropriate interaction frame. Furthermore we provide a formalism for the derivation of the relaxation superoperator starting with a choice of a basis set in Hilbert space. We show that the differences in the prediction of the nuclear polarisation dynamics that are found for certain parameter choices arise from the use of different interaction frames in the two different strategies. In addition, we provide a summary of different relaxation mechanisms that need to be considered to obtain more realistic spin dynamic simulations of solid effect dynamic nuclear polarisation.

Dynamic nuclear polarisation by thermal mixing: quantum theory and macroscopic simulations

A theory of dynamic nuclear polarisation (DNP) by thermal mixing is suggested based on purely quantum considerations. A minimal 6-level microscopic model is developed to test the theory and link it to the well-known thermodynamic model. Optimal conditions for the nuclear polarization enhancement and effects of inhomogeneous broadening of the electron resonance are discussed. Macroscopic simulations of nuclear polarization spectra displaying good agreement with experiments, involving BDPA and trityl free radicals, are presented.

Phase transitions in electron spin resonance under continuous microwave driving

We study an ensemble of strongly coupled electrons under continuous microwave irradiation interacting with a dissipative environment, a problem of relevance to the creation of highly polarized nonequilibrium states in nuclear magnetic resonance. We analyze the stationary states of the dynamics, described within a Lindblad master equation framework, at the mean-field approximation level. This approach allows us to identify steady-state phase transitions between phases of high and low polarization controlled by the distribution of disordered electronic interactions. We compare the mean-field predictions to numerically exact simulations of small systems and find good agreement. Our study highlights the possibility of observing collective phenomena, such as metastable states, phase transitions, and critical behavior, in appropriately designed paramagnetic systems. These phenomena occur in a low-temperature regime which is not theoretically tractable by conventional methods, e.g., the spin-temperature approach.