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Low Temperature Physics

Effect of temperature on the coherence time of a parabolic quantum dot qubit

Wei Xiao, Hongwei Wang

Published Mar 1, 2015• 10 citations
Publisher

Abstract

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.

DOI
10.1063/1.4913756

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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.
On the condition of electric-LO phonon strong coupling in parabolic quantum dot, we obtained the eigenenergy of the ground state and the first excited state, the eigenfuctions of the ground state and the first excited state by using variational method of Pekar type. This system of quantum dot may be employed as a two-level quantum system-qubit. The phonon spontaneous emission causes the decoherence of the qubit. We discussed the relatoion between the decoherence time and the Coulomb binding parameter，the couping strength, the confinement length, and the conefficient dispersion.
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 electric field and temperature on a RbCl asymmetry quantum dot (AQD) qubit are investigated by using a variational method of the Pekar type. We first study the eigenenergies and eigenfunctions of the ground and first excited states of an electron strongly coupled to bulk longitudinal optical (LO) phonons with a three-dimensional (3D) harmonic potential under the influence of an electric field. This AQD two-level system may serve as a single qubit. We then obtain the time evolution of the electron's probability density when the electron is in the superposition state of the ground and first excited states. Finally, we investigate the effects of the electric field and temperature on the oscillating period, the time evolution of the electron's probability density and the coherence time. The numerical results show that the electron's probability density and its oscillatory period will increase (decrease) with increasing temperature in the low (high) temperature regime. The electron's probability density oscillates with a certain period in the AQD. The oscillating period is an increasing function of the temperature and the electric field. The coherence time is an increasing function of the temperature and the electric field, but it is a decreasing one of the transverse and longitudinal confinement strengths.
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.
In this work, the energies and eigenfunctions of ground state and first-excited states (GFES) of a strongly coupled polaron in a quantum pseudo-dot (QPD) were studied by using variational method of Pekar type (VMPT). A single qubit can be realized in this two-level quantum system. Then, we calculated the coherence time of a QPD qubit by employing the Fermi Golden Rule. The temperature effects on the coherence time are taken into account by using the quantum statistics theory (QST) and self-consistent calculation method. According to the obtained results, it is found that the coherence time increases with decreasing temperature. Also, this time is a decaying function of the chemical potential of the two-dimensional electron gas and the zero point of the PHP.
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.