Quantum Optimal Control Theory Based On Nitrogen-vacancy Center

Quantum control plays a major role in the study and utilization of quantum systems.It has a wide range of applications in the fields of nuclear magnetic resonance imaging,spectroscopy,precise control of chemical reactions,as well as quantum information technologies including quantum computation,quantum communication,and quantum sensing.As an interdisciplinary theory based on quantum physics,mathematical control theory,and numerical simulation,quantum optimal control theory(QOCT)aims to give answers to two fundamental questions:the controllability of quantum systems and the specific control designs.Among many quantum systems with promising application perspectives,nitrogen-vacancy(NV)centers in diamond have been shown to be appealing candidates owing to their excellent properties of long coherence times at room temperature and superb operability,e.g.,simple initialization and readout by lasers,as well as the biological nontoxicity which is important for in vivo imaging.The studies in this thesis focus on the quantum optimal control of these NV centers in diamond.We present an optimal optical control strategy for single NV center systems,as well as a phase-modulated optical method for NV center ensembles showing inhomogeneous broadening.As compared with microwave control,optical control allows addressing individual NV center spins,leading to a high spatial resolution and a faster speed of coherent spin manipulation.Optical quantum control of NV center spins is essentially based on coherent population transfer and stimulated Raman adiabatic passage(STIRAP)techniques,which exploits a system of two ground-state spin sublevels with an excited state.Therefore,the complicated energy levels of the excited state of the NV center spins would affect the achievable fidelity of optical manipulation in cases that the evolution time is not long enough to satisfy the adiabatic condition.We adopt four different optimization methods and obtain control laser fields that can achieve a significantly improved fidelity of coherent state transfer.These optimal laser fields give the same fidelity above 0.9 with an evolution time two orders of magnitude shorter than that of STIRAP.Under a 10 GHz constraint for the maximal laser amplitude,the optimal laser fields achieve a fidelity of 0.984 within an evolution time of T=1 ns,while the performance of the fields is robust against deviations in the amplitude and frequency of the laser field.Moreover,the optimal results maintain a 0.972 fidelity with a decreased time resolution of the laser shape modulation.Such results show that our optimization scheme has high experimental feasibility and will facilitate the development of high-fidelity and fast-speed all-optical quantum control for NV center spins in diamond.Ensembles of NV centers are a promising implementation platform for wide-field sensing and vector magnetometry.However,due to the fact that each NV center may experience a slightly different local environment,an inhomogeneous broadening in the ensembles is inevitable,which will degrade the fidelity of the control of the ensembles.We introduce a direct-optimization method based on a phase modulated(PM)function basis that is feasible for applications in robust quantum control problems.As an example,we apply this method to find robust control fields for the control of an ensemble of two-level systems exhibiting an inhomogeneous broadening.Constrained by the same maximal field strength and the same maximal search resources,the PM method reaches highly improved results compared with the widely used standard Fourier basis(SFB)and comparable results with the phase-introduced standard Fourier basis(SFB-P2),using one order of magnitude less optimization time.A detailed analysis of the overall optimization results further reveals that the PM method shows a stable capability to find the global optimum in the parameter landscape with comparable or lower search resources,while SFB-P2 with more parameters is unable to plausibly obtain the same results in every trial run with the same search resources.As a further example,we also demonstrate the utilization of the PM function basis in the optimization of robust gate control fields for dynamical decoupling,leading to a prolonged coherence time of the system and a higher signal sensitivity in AC field measurements,compared to traditional rectangular pulses.With shorter optimization times and a strong robustness,the PM method provides a potentially superior gradient-free optimization method and shows a high potential value in the field of spin-ensemble manipulations and optimal control in many-body physics.