Control and Characterization of the Central Spin System

Abstract

Precise, coherent, robust quantum control and characterization of quantum systems play important roles in the development of applications of quantum technologies. In particular, advancing the quality of control requires precise characterization, which, in turn, depends on the quality of control.

In the first part of the thesis, we introduce a general framework for designing efficient, precise, and robust quantum control strategies using effective Hamiltonian engineering. The methods enable designs that are robust to systematic control errors and variations in the Hamiltonian. The efficiency benefit of achieving control at zeroth order in the Magnus expansion is highlighted. Design tools, such as methods that identify the space of achievable effective Hamiltonians at each order from the Magnus expansion, are introduced. Objective functions for engineering arbitrary effective Hamiltonians are provided and can be used by numerical optimizers for control sequence design.

The second part of the thesis explores the characterization of general noise models based on experiments on a central spin system. The noise is probed through stimulated echo experiments, multi-dimensional correlation spectroscopy, and multi-quantum experiments to characterize system/environment correlation and environmental memory effects. Combined with Bayesian inference, these experiments provide quantitative measures of correlation growth, environmental mixing, and deviations from stochastic noise models. Measures that influence the choice of control schemes include non-Gaussianity, non-stationarity, and non-Markovianity. The multi-quantum experiments can also reveal an extended environment and show how the environmental mixing propagates quantum information throughout the environment.