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Journal of Inner Mongolia University for the Nationalities

Influence of the Confined Length of Quantum Dot on the Quality Factors of Free Rotation of Qubit

Xiao Jing-lin

Published Jan 1, 2008• 0 citations
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Abstract

Using a two-level electron as a qubit in parabolic quantum dot,we have studied the correlation between the quality factors of free rotation of qubit and the confined length for a single quantum dot.In the mode of this paper,we obtain the quality factors of free rotation decrease with the longitudinal confined length increase and doesn't change with the transverasal confined length.We found that the energy level with the confined length changes at the same time.

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Journal of Inner Mongolia University for the Nationalities•Jan 1, 2009•0 citations
Using a two-level electron as a qubit in parabolic quantum dot,we have studied the correlation between the quality factors of free rotation of qubit and the confined length for a single quantum dot.In the mode of this paper,we obtain the quality factors of free rotation decrease with the longitudinal confined length increase and doesn't change with the transverasal confined length.We found that the energy level with the confined length changes at the same time.
In the condition of electron-LO phonon strong coupling in a three-dimention parabolic quantum dot,we obtain the eigenenergy of the ground state and the first excited state,the eigenfunction of the ground state and the first excited state by using variational method of pekar type.This system in quantum dot may be employed as a two-level quantum system-qubit,we obtain the quality factors of free rotation of qubit.It is shown that the quality factors of free rotation decrease with increasing confined length and the quality factors of free rotation increase with increasing strength coupling.
To study the influence of an anisotropic parabolic potential (APP) on the properties of a quantum dot (QD) qubit, we obtain the eigenenergies and eigenfunctions of the ground and first excited state of an electron, which is strongly coupled to the bulk longitudinal optical (LO) phonons, in a QD under the influence of an APP by the celebrated Lee—Low—Pines (LLP) unitary transformation and the Pekar type variational (PTV) methods. Then, this kind of two-level quantum system can be excogitated to constitute a single qubit. When the electron locates at the superposition state of its related eigenfunctions, we get the time evolution of the electron's probability density. Finally, the influence of an APP on the QD qubit is investigated. The numerical calculations indicate that the probability density will oscillate periodically and it is a decreasing function of the effective confinement lengths of the APP in different directions. Whereas its oscillatory period is an increasing one and will diminish with enhancing the electron—phonon (EP) coupling strength.
The effects of the temperature on the coherence time of a parabolic quantum dot (PQD) qubit are investigated by using the variational method of Pekar type. We obtain the ground and the first excited states’ eigenenergies and the corresponding eigenfunctions of an electron strongly coupled to bulk longitudinal optical phonons in the PQD. This two-level PQD system may be employed as a single qubit. The phonon spontaneous emission causes the decoherence of the qubit. We find that the coherence time will decrease with increasing temperature. It is an increasing function of the effective confinement length, whereas it is decreasing one of the polaron radius. We find that by changing the temperature, the effective confinement length and the polaron radius one can adjust the coherence time. Our research results would be useful for the design and implementation of the solid-state quantum computation.
Selecting the double-parameter asymmetric Gaussian (AG) potential to describe the confinement effect of electrons in a quantum dot, the ground state and the first excited state energy eigenvalues and eigenfunctions of the three-body interaction system that are composed of the electrons, the impurity and the longitudinal optical phonon are derived by using the Lee-Low-Pines unitary transformation and the Pekar-type variational method, and the two-level structure required for a qubit is constructed. The influences of material parameters such as the dispersion coefficient, dielectric constant (DC) ratio, and electron-phonon coupling (EPC) constant on the probability density and the oscillation period of electron in the AG potential qubit are investigated. Based on the Fermi gold rule and the even-order approximation, the effects of the DC ratio, the dispersion coefficient and the EPC constant on the qubit decoherence are studied. And then the influences of the dispersion coefficient, the DC ratio and the EPC constant on the phase rotation manipulation of the qubit sphere are discussed. Numerical results show that the dispersion coefficient, the DC ratio and EPC constant of the medium have both advantages and disadvantages for the formation and information storage of qubits. The probability density of electrons in quantum dot qubits decreases with DC ratio increasing and exhibits significant oscillations as the well width of the AG potential decreases; the oscillation period of the qubit decreases with the well depth of the AG potential or the DC ratio increasing; the decoherence time increases with DC ratio or dispersion coefficient increasing; the phase rotation quality factor increases with DC ratio or dispersion coefficient increasing. Using the double-parameter AG potential to describe the confinement of electrons in quantum dot will better reflect the quantization properties of qubit. Increasing the dispersion coefficient or the DC ratio of the material is beneficial to not only the phase rotation manipulation of the qubit sphere, but also improving the coherence of the quantum dot qubit. The results of this paper can be used for reference in the experimental work on the constructing and manipulating of the quantum dot qubits.
The quality factors of quantum bit (qubit) rotations in single self-assembled quantum dots were investigated using photoluminescence spectroscopy. Rotations with azimuthal angle ϕ along the equator of the qubit sphere were implemented by varying the time delay between two π∕2 pulses, resulting in a “free rotation” quality factor Q0=9.8×104. Qubit rotations with polar angle θ as large as 10π along the meridian of the qubit sphere (Rabi oscillations with zero detuning) were realized with a quality factor QR∼18, in experiments probing an excited excitonic state.
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.