NMR effective Hamiltonian engineering and decoupling

Abstract

We introduce a method of designing NMR pulse sequences, with a specific focus toward complete decoupling of carbon-13 spin qubits coupled to a nitrogen-vacancy (NV) center in diamond. Using Average Hamiltonian Theory, we calculate different intermediate Hamiltonians corresponding to different rotations implemented by NMR pulses. Two novel pulse sequences are obtained containing 24 and 12 evolution periods respectively. Assuming ideal and instantaneous pulses, performance for both sequences is better than the WAHUHA + echo sequence for total evolution times of less than 5 ms and comparable for greater evolution times. Analysis of sensitivity points toward non-robustness for angle errors in the applied pulses when the direction of pulses is not taken into account, however this can be corrected for using chirality sums. Suggestions for further research include the study of non-globally applied pulses and application of the design method to non-zero effective Hamiltonians.