Generation and transfer of coherence in electron-nuclear spin systems by non-ideal microwave pulses

Abstract

A quantum mechanical treatment based on a suitably truncated Hamiltonian is developed for the evolution during microwave (MW) irradiation of an S = 1/2, I = 1/2 electron–nuclear spin system with anisotropic hyperfine coupling. It is shown that there is a close analogy between this problem and the well understood phenomena in heteronuclear spin systems with resolved J couplings during double irradiation (L. Müller and R. R. Ernst, 1979, Molec. Phys., 38, 963). A general expression is derived for the MW field strength necessary to establish the modified Hartmann–Hahn condition where electron and nuclear spin states mix completely and maximum nuclear coherence can be generated. The theory is then applied to the discussion of hyperfine decoupling and coherence generation from Boltzmann equilibrium by a MW pulse of arbitrary field strength and duration. It is demonstrated that the build-up of nuclear coherence during such a pulse is slow and oscillatory, and that maximum nuclear coherence is achieved at nominal flip angles considerably larger than 2 π. The creation of both nuclear coherence and coherence on forbidden electron transitions is found to be optimum at the modified Hartmann–Hahn condition, and not to be limited by the modulation depth parameter known from electron spin echo envelope modulation (ESEEM) theory. The theoretical results are used to interpret a number of recent experimental observations that could not be understood by existing theories, and to propose an alternative explanation for nuclear modulations observed in experiments on bacterial photosystems. Effects in systems with a nuclear spin I = 1 are discussed taking into account nuclear quadrupole interactions. It is demonstrated both by numerical simulations and experiments that the well established two-pulse ESEEM experiment can be optimized by using pulses with matched microwave field strength and nominal flip angles larger than 2 π.