Lang, Jacob; (2018) Dynamical decoupling based quantum sensing: Floquet analysis and finite-duration-pulse effects. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

A spin qubit can be protected from a dephasing spin bath using dynamical decoupling (DD). Microwave pi-pulses are repeatedly applied to the spin qubit to invert its state and average out any dephasing. Importantly, this protection fails when the DD pulse spacing is resonant with nuclear spins in the bath and characteristic dips appear in coherence traces forming the basis for nanoscale NMR and MRI. This emerging quantum technology has been demonstrated with the nitrogen vacancy center in diamond. Most DD protocols apply periodic repetitions of a basic pulse unit. This repetition motivates us to model the experiments using Floquet analysis. The characteristic coherence dips are found to be associated with avoided crossings in an underlying Floquet spectrum. The width and shape of these crossings determines the contrast and sharpness of the coherence dips. We derive analytic expressions for the coherence dips in terms of the Floquet quasienergies and Floquet modes. Typically, the DD microwave pulses are modelled as being instantaneous; however, real pulses have some finite duration and it was recently demonstrated that this pulse duration can cause extra dips to appear in coherence traces. We apply Floquet analysis to accurately model the complete system dynamics in the presence of these finite duration pulses and derive analytic expressions for the complete coherence response. We interpret the arrival of extra coherence dips as the opening of previously closed avoided crossings. We use this new understanding to propose protocols to exploit (for increased resolution) or suppress these extra coherence dips. Finally, we model the interplay between finite-duration-pulse effects and microwave detuning errors - an important problem as the detuning error is completely removed by instantaneous pulses so is not captured by most analytic models. We observe drastic effects including the splitting and suppression of the expected DD signal.

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