The time evolution of the quantum mechanical state of an electron is calculated in the framework of the effective-mass envelope function theory for an InAs/GaAs quantum dot. The results indicate that the superposition state electron density oscillates in the quantum dot, with a period on the order of femtoseconds. The interaction energy Eij between two electrons located in different quantum dots is calculated for one electron in the ith pure quantum state and another in the jth pure quantum state. We find that E11〉E12〉E22, and Eij decreases as the distance between the two quantum dots increases. We present a parameter-phase diagram which defines the parameter region for the use of an InAs/GaAs quantum dot as a two-level quantum system in quantum computation. A static electric field is found to efficiently prolong the decoherence time. Our results should be useful for designing the solid-state implementation of quantum computing.
The time evolution of the quantum mechanical state of an electron is calculated in the framework of the effective-mass envelope function theory for an InAs/GaAs quantum dot. The results indicate that the superposition state electron density oscillates in the quantum dot, with a period on the order of femtoseconds. The interaction energy Eij between two electrons located in different quantum dots is calculated for one electron in the ith pure quantum state and another in the jth pure quantum state. We find that E11〉E12〉E22, and Eij decreases as the distance between the two quantum dots increases. We present a parameter-phase diagram which defines the parameter region for the use of an InAs/GaAs quantum dot as a two-level quantum system in quantum computation. A static electric field is found to efficiently prolong the decoherence time. Our results should be useful for designing the solid-state implementation of quantum computing.
In an unsymmetrical parabolic potential quantum dot(QD),the eigenenergies of the grornd state and the first-excited state,the eigenfounctions of the ground state and the first-excited state are obtained.This system in QD may be employed as a two-level quantum system—qubit,we obtain the relationship of the decoherence time based on the Fermi Golden Rule,the period of oscillation and longitudinal confined length.The time evolution of the electron density are discussed.It can be seen that the decoherence time and the period of oscillation increases with increasing the longitudinal confined length,the density of electron oscillates with a period in the space.
Since the development of microsized devices is moving forward at enormous speed, there is huge amount of new industrial opportunities. However such devices also require high precision and understanding of the operating of their constituent parts up to the quantum level. The device of the purely quantum nature being developed so far is quantum computer. However the physical realization of it is still not performed, as the requirements for it are very rigorous. \n \nIn the pioneering work by Loss and DiVincenzo it was suggested to use a spin of electron placed in a quantum dot as an information qubit. Following this work the study of electron or hole spin qubits developed. Both experimental and theoretical tools for studying them greatly advanced. \n \nIn the first part of the thesis we study the phonon-induced decoherence and relaxation of singlet-triplet qubits in the double quantum dots. First of all we consider AlGaAs/GaAs double quantum dots. The important result we present here is the strong dephasing that occurs at large detuning. This dephasing is due to two-phonon process that affects mainly singlet state of the qubit and consequently changes the splitting between singlet and triplet leading to dephasing. Remarkably at small detuning this dephasing process is suppressed and the decoherence time is by orders of magnitude longer than in case of large detuning and is mainly defined by one-phonon process. We also present the dependence of relaxation time and decoherence time on the strength of spin-orbit interaction and different directions of the system. Our results provide a deeper insight into the recently obtained experimental data. \n \nWe also studied Si/SiGe quantum dots as a potential candidate for a qubit. Apart from the absence of hyperfine interaction and bulk spin-orbit interaction in the isotopically purified 28Si, its electron-phonon interaction is different from GaAs that also leads to longer qubit lifetimes. We study S-T− qubit near the anticrossing of the basis states. This particular region is interesting due to possibilities in operating the qubit. We show that the type of singlet plays a crucial role, i.e. whether it is a singlet with each dot singly occupied or a singlet with only one dot doubly occupied. Depending on the type of singlet the qubit lifetimes change by several orders of magnitude. We also study the influence of a micromagnet, usually used in experiments to operate the qubit, on the relaxation time and decoherence time and present the regime where its effect is negligible. We suggest how to test experimentally our theory of one-phonon and two-phonon processes separately. We also show how the relaxation and decoherence time depend on different system parameters for S-T0 qubits. \n \nThe second part of the thesis is devoted to the other important constituent part of microsized devices, namely nanowires. We are interested in the dynamic of polarization of localized spins in the nanowires, as it can affect such important device characteristics as e.g. conductance. \n \nWe studied Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction-induced polarization in the nanowire in case when the voltage is applied to it. It was already proposed theoretically that in the ground state the localized spins in 1D systems align in a helix due to RKKY interaction. This polarization is still present until some critical temperature. The presence of such polarization acts as a spin filter for electrons, that most likely affects the conductance of the nanowire. Therefore we studied how this helical polarization changes when the voltage is applied. The key result is the appearance of the uniform polarization perpendicular to the helix plane, that occurs due to backscattering of electrons that is accompanied by flip-flop process with localized spins. When this uniform polarization is formed, the helix starts to rotate as a whole around the direction of the uniform polarization. We present the dependence of polarization of the localized spins on temperature and voltage. Remarkably the uniform polarization grows both with voltage and temperature in the given range of parameters. \n \nWe also considered the electron-induced relaxation of the nuclear spins. As the electron spins and nuclear spins interact via hyperfine interaction, the nuclear relaxation time reflects some properties of electron bath. Namely, we see a strong dependence of nuclear relaxation time on spin-orbit interaction strength. We present here the dependence of the nuclear relaxation time on the external magnetic field and chemical potential of the wire, that can be experimentally varied via gate. The dependences for the strong spin-orbit interaction and for the weak one are substantially different. Moreover, they have distinct peaks, that allow to get the value of spin-orbit interaction amplitude with the high precision.
In this paper, we investigate the time evolution of the quantum mechanical state of a polaron using the Pekar type variational method on the electric-LO-phonon and the magnetic-LO-phonon strong coupling in a quantum dot. We obtain the Eigen energies and the Eigen functions of the ground state and the first excited state, respectively. In a quantum dot, this system can be viewed as a two level quantum system qubit. The superposition state polaron density oscillates in the quantum dot with a period τ_0when the polaron is in the superposition of the ground and the first-excited states. The spontaneous emission of phonons causes the decoherence of the qubit. We show that the density matrix of the qubit decays with the time while the coherence term of the density matrix element 〖 p〗_01 (〖 or p〗_10) decays with the time as well for different coupling strengths, confinement lengths, and dispersion coefficients. The Shannon entropy is evaluated in order to investigate the decoherence of the system.
Solid state based quantum information processing is focused on physical implementation of all necessary elements of quantum computation and quantum information in solid state systems, mainly due to their scalability compared to e.g. optical systems. Among many proposals to realize these types of devices, such as quantum dots as charge qubits or Josephson junction circuits, we study here one of the most promising candidates, i.e., the spin of an electron confined to a quantum dot as a qubit. Experimentally, it has been shown that the relaxation rate of this two level system can be pushed above few seconds in low magnetic fields. Moreover, using spin echo techniques, \nthe spin dephasing time can be maximized up to milliseconds with the current technology. This long spin decay time is one of the main reasons that make this system desirable for quantum computation and quantum information purposes. \nWe reexamined the recent measurement based proposal called one-way quantum computation which exploits entanglement and local measurements as tools to perform quantum computation on N qubits. Although it was suggested in the original work to entangle the qubits via the nearest neighbor Ising interaction, we investigated how one can generate the so-called cluster states with the Heisenberg interaction. We extended our method to include more general forms of Heisenberg interaction such as asymmetric coupling of adjacent qubits. These forms of couplings, rather than Ising interaction, are more encountered in solid state devices, and therefore make it possible to perform one-way quantum computation with electron spins in quantum dots coupled via exchange interaction to their adjacent spins. \n \nChapters II, III, and IV of my thesis are devoted to the study of the spin-orbit interaction in heterostructure quantum dots and its effect on the spin dynamics. We observed that one can actually use spin-orbit interaction to manipulate the spin state of an electron on time scales much smaller than the spin dephasing time. Specifically, in chapter II, we studied the effect of a nearby functioning quantum point contact (QPC) on the relaxation of the electron spin and show that the charge fluctuations in QPC lead to spin relaxation of the confined electron in the presence of spin-orbit interactiom and an applied magnetic field. We also addressed the relation of this rate to the microscopic parameters of the system and found some geometrical dependence of the spin relaxation time on the orientation of the QPC on the substrate. Moreover, we showed in chapters III and IV that the spin-orbit interaction can play a positive role, in order to rotate the spin around the Bloch sphere. We considered different mechanisms, particularly, Electron Dipole Spin Resonance (EDSR) and holonomic unitary gates in quantum dots. We verified that these mechanisms of spin manipulation can be realized in solid state systems with the state of the art semiconductor technologies. \n \nChapter V of the thesis covers a slightly different topic and focuses on the role of the Coulomb interaction in electronic transport. There, we reviewed the non-analytic corrections to the Fermi liquid behavior and their consequences on the momentum occupation number of the electrons in a two dimensional electron gas (2DEG). As an example, we calculated the tunneling rate from an interacting electron reservoir onto a quantum dot and compared our result to the corresponding case for electron tunneling between bilayer 2DEGs. Moreover, within RPA approximation, we found that the electron-plasmon coupling leads to a quadratic frequency dependence of the electron self-energy at low frequencies at the Fermi surface. This correction suppresses the same order corrections due to the particle-hole bubble. \n \n \n
We theoretically study a double-quantum-dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer, with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states, and the relative energy scales of these states. We point out that at zero magnetic field it is difficult to have both a vanishing double occupation probability for a small error rate and a sizable exchange coupling for fast gating. On the other hand, finite magnetic fields may provide finite exchange coupling for quantum computer operations with small errors. We critically discuss the applicability of the envelope-function approach in the current scheme, and also the merits of various quantum-chemical approaches in dealing with few-electron problems in quantum dots, such as the Hartree-Fock self-consistent-field method, the molecular-orbital method, the Heisenberg model, and the Hubbard model. We also discuss a number of relevant issues in quantum dot quantum computing in the context of our calculations, such as the required design tolerance, spin decoherence, adiabatic transitions, magnetic-field control, and error correction.
We investigate the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to LO-phonon in an asymmetric quantum dot (QD) by using variational method of Pekar type. The present system may be used as a two-level qubit. When the electron is in the superposition state of the ground and the first excited states, the probability density of the electron oscillates in the QD with a certain period. It is found that the oscillation period is an increasing function of the transverse and the longitudinal effective confinement lengths of the QD, whereas it is a decreasing one of the electron–phonon coupling strength.