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Chinese Journal of Luminescence

Properties of Strong-coupling Bipolaron Qubit in Parabolic Potential Quantum Dot

Han Cha

Published Jan 1, 2016• 0 citations
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Abstract

On the basis of Lee-Low-Pines( LLP) unitary transformation,the eigenenergy and eigenfunction of the ground-state and the first excited state of the strong-coupling bipolaron in two-dimensional quantum dot( QD) were obtained by using the variational method of Pekar type. A qubit was formed by overlaying both the ground state and the first excited state of the bipolaron system. Numerical calculations indicate that the oscillating period T0 of qubits decreases with the increasing the electron-phonon coupling strength α,the confinement strength ω0of the quantum dot,and the dielectric constant ratio η; the distribution of the probability density Q of the electrons in quantum dot oscillates periodically with time t,angle coordinate φ2,and the dielectric constant ratio η,and there is a maximum at near the center and zero away from the center of quantum dot.

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On the basis of Lee-Low-Pines( LLP) unitary transformation,the eigenenergy and eigenfunction of the ground-state and the first excited state of the strong-coupling bipolaron in two-dimensional quantum dot( QD) were obtained by using the variational method of Pekar type. A qubit was formed by overlaying both the ground state and the first excited state of the bipolaron system. Numerical calculations indicate that the oscillating period T0 of qubits decreases with the increasing the electron-phonon coupling strength α,the confinement strength ω0of the quantum dot,and the dielectric constant ratio η; the distribution of the probability density Q of the electrons in quantum dot oscillates periodically with time t,angle coordinate φ2,and the dielectric constant ratio η,and there is a maximum at near the center and zero away from the center of quantum dot.
Based on the variational method of Pekar type, we study the energies and the wave-functions of the ground and the first-excited states of magneto-bipolaron, which is strongly coupled to the LO phonon in a parabolic potential quantum dot under an applied magnetic field, thus built up a quantum dot magneto-bipolaron qubit. The results show that the oscillation period of the probability density of the two electrons in the qubit decreases with increasing electron–phonon coupling strength α , resonant frequency of the magnetic field ω c , confinement strength of the quantum dot ω 0 , and dielectric constant ratio of the medium η ; the probability density of the two electrons in the qubit oscillates periodically with increasing time t , angular coordinate φ 2 , and dielectric constant ratio of the medium η ; the probability of electron appearing near the center of the quantum dot is larger, and the probability of electron appearing away from the center of the quantum dot is much smaller.
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.
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.
We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to the LO-phonon in a quantum dot with triangular bound potential by using the Pekar variational method. This system may be used as a two-level qubit. Our numerical results indicate that the decoherence rate will decrease with increasing the confinement length of the quantum dot (QD) and decrease with increasing electron-LO-phonon coupling constant. The influences of the polar angle on the decoherence rate are dominant when the coupling constant increases, while the effects of the polar angle on that are strong when the confinement length increases. Meanwhile, the decoherence rate varies periodically with respect to the polar angle.
The electromagnetic-field dependence of the ground and the first excited-state (GFES) energy eigenvalues and eigenfunctions of the strong-coupling polaron in a quantum dot (QD) was studied for various QD thicknesses by using the variational method of the Pekar type (VMPT). On this basis, we construct a qubit in the quantum dot (QQD) by taking a two-level structure of the polaron as the carrier. The results of numerical calculations indicate that the oscillation period of the qubit, {itT}{in0}, increases with increasing the thickness of the quantum dot (TQD) {itL}, but decreases with increasing the cyclotron frequency of the magnetic field (CFMF) ω{in{itc}}, electric-field strength {itF}, and electron-phonon coupling strength (EPCS) α. The probability density of the qubit |Ψ({itρ}, {itz}, {itt})|{su2} presents a normal distribution of the electronic transverse coordinate ρ, significantly influenced by the TQD and effective radius of the quantum dot (ERQD) {itR}{in0}, and shows a periodic oscillation with variations in the electronic longitudinal coordinate {itz}, polar angle φ and time {itt}. The decoherence time τ and the quality factor {itQ} of the free rotation increase with increasing the CFMF ω{in{itc}}, dispersion coefficient η, and EPCS α, but decrease with increasing the electric-field strength {itF}, TQD {itL}, and ERQD {itR}{in0}. The TQD is an important parameter of the qubit. Theoretically, the target, which is to regulate the oscillation period, decoherence time and quality factor of the free rotation of the qubit, can be achieved by designing different TQDs and regulating the strength of the electromagnetic field.
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.