Abstract
Estimating the parameters of an unknown Hamiltonian is crucial for understanding the dynamics of quantum systems and has significant implications in quantum information processing, optimal control, metrology, and sensing. The Nitrogen-vacancy (NV) center in diamond as a solid state defect is known to preserve remarkable spin properties in ambient condition, making it a promising candidate for a wide variety of quantum applications. Hence, it can serve as the perfect platform for demonstration of this topic.
In this article, we begin with chapter 1 dedicated to introduce some basic properties of the NV center, including the standard procedure to realize spin state initialization, control and readout, followed by a discussion about hyperfine interaction between NV and its surrounding nuclear spin. In chapter 2, different strategies for parameter estimation are introduced, namely Rabi, ODMR, spin-echo, DD and correlation sequences. Then, we use the hyperfine interaction as an example to demonstrate that frequency filter can be a sensitive band-pass filter.
In chapter 3, we present a straightforward approach for both static and arbitrary timedependent Hamiltonian estimation. The current cutting-edge techniques for parameters estimation often require a complicated entanglement initial state or using a large number of pulses for the aforementioned frequency filter which is challenging to prepare in systems with insufficient prior knowledge and limited accessibility. Our scheme utilizes a set of randomly shaped pulses to continuously drive the qubit states, which leads to an efficient exploration of the Hamiltonian dynamics on the Hilbert space. Then, the best estimator to the system Hamiltonian is found by minimizing a cost function which characterizes how well the estimator matches the unknown Hamiltonian. Our approach is demonstrated experimentally in the system of NV center in diamond. We show that satisfactory estimations of the Hamiltonian can be obtained for systems with both strong and weak hyperfine coupling parameters, which fills the gap between the effective detection ranges of ODMR and frequency filter approaches. Furthermore, the same approach could be used to turn the NV electron spin into a quantum oscilloscope which enables detection of a randomly shaped magnetic signal with 10 MHz time resolution. At the end in chapter 4, a brief discussion as well as some preliminary result related to stabilization
of parallel and transverse magnetic field are shown.