We study theoretically the phonon-induced relaxation and decoherence of spin states of two electrons in a lateral double quantum dot in a SiGe/Si/SiGe heterostructure. We consider two types of singlet-triplet spin qubits and calculate their relaxation and decoherence times, in particular as a function of level hybridization, temperature, magnetic field, spin orbit interaction, and detuning between the quantum dots, using Bloch-Redfield theory. We show that the magnetic field gradient, which is usually applied to operate the spin qubit, may reduce the relaxation time by more than an order of magnitude. Using this insight, we identify an optimal regime where the magnetic field gradient does not affect the relaxation time significantly, and we propose regimes of longest decay times. We take into account the effects of one-phonon and two-phonon processes and suggest how our theory can be tested experimentally. The spin lifetimes we find here for Si-based quantum dots are significantly longer than the ones reported for their GaAs counterparts.
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
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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
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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.
The spin of an electron confined into a lateral semiconductor quantum dot has been proposed as a possible physical realization of a qubit. While the spin has the advantage of large decoherence times, operations with more than one qubit will necessarily involve orbital degrees of freedom, namely, charge, which is much more prone to decoherence. There are also alternative quantum dot qubit proposals that are entirely based on charge. We have used a realistic model to quantify the limitations imposed by acoustic phonons on the operation of quantum dot-based qubits. Our treatment includes essential aspects of the setup geometry, wave function profile and materials characteristics. The time dependence of the qubit density matrix is the presence of a phonon bath solved within the Born-Markov approximation. We find that the inclusion of geometric form factors makes the phonon-induced decoherence rates in double dot charge qubits nearly one order of magnitude lower than estimates previously in the literature. Moreover, our theoretical prediction for the quality factor of coherent charge oscillations based on phonon decoherence are higher than the values recently observed experimentally. This allows us to conclude that phonons are not the primary source of decoherence in double quantum dot qubits.
Abstract The unavoidable effect of the environmental noise due to nuclear spins and charge traps is included in the study of the hybrid qubit dynamics. Hybrid qubit owes its name to the advantageous combination of manipulation speed of a charge qubit with the longevity of a spin qubit. It consists of three electrons confined through external gate voltages in a double quantum dot and deserves special interest in quantum computation applications due to its advantages in terms of fabrication, control, and only electrical manipulation. The fluctuations of the global magnetic field do not affect the dynamics of the hybrid qubit that is defined in a decoherence‐free subspace. The main sources of decoherence come from local magnetic fluctuations and charge fluctuations. This work is based on the hypothesis that gate voltages are fixed and kept constant while qubit evolves in time. Coherence time of the hybrid qubit is extracted when model parameters take values achievable experimentally in the nuclear‐free isotope 28 Si, natural Si, and GaAs hosts.
We consider charge qubits based on shallow donor electron states in silicon and coupled quantum dots in GaAs. Specifically, we study the feasibility of
P2+ charge qubits in Si, focusing on single qubit properties in terms of tunnel coupling between the two phosphorus donors and qubit decoherence caused by electron-phonon interaction. By taking into consideration the multivalley structure of the Si conduction band, we show that intervalley quantum interference has important consequences for single-qubit operations of
P2+ charge qubits. In particular, the valley interference leads to a tunnel-coupling strength distribution centered around zero. On the other hand, we find that the Si band structure does not dramatically affect the electron-phonon coupling and consequently, qubit coherence. We also critically compare charge qubit properties for
Si:P2+ and GaAs double quantum dot quantum computer architectures.
Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate
1/T1 as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons and quantum dots. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.