THESIS
2023
1 online resource (xii, 71 pages) : illustrations (chiefly color)
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 nucl...[
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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 time-dependent
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.
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