Electron Spin Dynamics In An Inhomogeneously Polarized Quantum Dot

In this thesis,we focused on the semiconductor quantum dot utilized as the physical realization of quantum computation,as well as the decoherence phenomena of the electron spin qubit due to the hyperfine interaction with the nuclear spins.We paid much more attention on the inhomogeneously polarization method employed to polarize the nuclear spins inside the quantum dot,and investigated its influence on the electron spin decoherence behavior.Firstly,we introduced some basic knowledge of quantum computation,focused on illustrating the basic working principle of quantum computing,the various physical realizations of quantum computers,the potential applications of quantum algorithms,and the problems confronted with the development of quantum computation.Then we used semiconductor quantum dot as the illustrated physical system for the implemen-tation of quantum computing,in order to introduce the main components of quantum computation,including preparation and measurement of the quantum state,manipu-lation of the qubit,etc.However,due to the deteriorative hyperfine interaction,the fidelity of the quantum state storage and the accuracy of the quantum gate operation are reduced severely.We demonstrated the relaxation of spin singlet state(entangled state)in a double dot system,along with the phase refocusing using spin echo tech-nique.As a comparison,we also briefly introduced the diamond color center system as the realization of quantum computation.The maintenance of quantum coherence is the key factor to realize quantum com-puting,since the coherence time of a quantum system determines the fidelity of quantum state storage and the accuracy of quantum logic gate operation.In the following part,we analyzed the general decoherence process occurred in a quantum dot due to the electron-spin nuclear-spin contact hyperfine interaction.First of all,we applied the semiclassical method,which treats the hyperfine interaction as the electron spin in-teracts with an effective magnetic field generated by the nuclear spins(the Overhauser field).The magnitude and direction of this effective field is random,different from each dot to each dot or from each experimental run to each experimental run,and here we assumed this random field follows Gaussian distribution.This semiclassical treatment is actually equivalent to the quasistatic approximation,which assumes the hyperfine in-teraction strength the same for all nuclear spins.However,this semiclassical treatment or the quasistatic approximation can not completely describe the whole decoherence behavior of the electron spin,especially when the evolution time is long and the nu-clear spin dynamics can not be neglected.Besides,when the magnitude of the applied external magnetic field is modest,or the nuclear polarization is small,the perturbation theory can not be applied either.At the end,we had to use numerical simulations to investigate these situations which may be relevant to the practical experimental ar-rangement.We introduced two numerical methods in this thesis,the exact Chebyshev expansion of time evolution operator and the approximate spin coherent state P repre-sentation of density matrix.We compared these numerical methods with each other,and with the previous semiclassical treatment.We analyzed the applicability range of these quasistatic approximation and discussed the general characteristics of the deco-herence process in a central spin system.Besides,we studied the influence of applying an external static magnetic field and employing thermal nuclear polarization.Spin exchange between electron spin and nuclear spins can be induced by the flip-flop term of the hyperfine interaction.The dynamic nuclear polarization is realized through successive injection of polarized electrons.We applied independent spin ap-proximation to analyze the process of dynamic nuclear polarization and discovered that the polarization of each nuclear spin is proportional to the square of its hyperfine cou-pling strength,as long as the duration of the polarization pulse is short enough.Besides,we employed numerical calculations to simulate this process and the result also proved that the dynamic nuclear polarization will lead to the polarization inhomogeneity.Next,we employed the nuclear spin state after dynamic nuclear polarization as the initial state,in order to investigate the electron spin decoherence behavior in an inho-mogeneously polarized quantum dot.We found that,under the same average nuclear polarization,the longitudinal relaxation time in the inhomogeneous nuclear polarization case is extended much more significantly than in the homogeneous case.Using the core-skirt model,we found that the orders of the coherence time extension is approximately equal to the number of highly polarized(nearly perfect)nuclear spins.At the same time,we also simulated the decoherence of the transverse component of the electron spin.We discovered that decoherence anisotropy appears in the inhomo-geneous polarization case,i.e.,the ratio of the longitudinal decoherence time with the transverse relaxation time is significantly dependent on the average nuclear polarization for the inhomogeneous case,while for the homogeneous case,this effect is not apparent.Next,we quantitively investigated the relation of decoherence anisotropy with polar-ization inhomogeneity.This decoherence anisotropy effect can be used to detect the polarization inhomogeneity inside a nanometer scale quantum dot,which can be useful in researching the spin dynamics and finding ways to suppress spin decoherence in solid state quantum bit systems.In the end,we studied the inhomogeneously polarized quantum dot utilized as the quantum memory implementation.We briefly illustrated the quantum memory protocol using electron spin and nuclear spins in a quantum dot,and defined the minimal fidelity to measure the performance of the quantum state storage.We compared the inhomoge-neous case with the homogeneous case,focused on the minimal fidelity as a function of the average nuclear polarization.The result shows that,for the given minimal fidelity,the required average nuclear polarization is significantly smaller in the inhomogeneous case.Besides,when the distribution of the coupling strength becomes narrower,this effect becomes even more significant.With the help of investigating the von Neumann entropy change during the encoding stage,we found that the strongly coupled nuclear spins play a much more important role in the quantum memory protocol.Based on our numerical calculations,using the inhomogeneously polarized quantum dot to implement quantum memory under current experimental techniques becomes practical.