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Research & Progress of SSE Solid State Electronics

Polar Slab Qubit and Its Optical Phonon Effect

Xiuqing Wang, Xiao Jing-lin

Published Jan 1, 2012• 0 citations
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Abstract

By using variational method of Peakar type,the qubit and its optical phonon effect in a polar slab is studied in this paper.The system in a polar slab may be employed as a system-qubit.When the electron is in the superposition state of the ground state and the first excited state,the time evolution of the electron density can be obtained.It shows that the period of oscillation decreases with the strength of coupling increasing,but increases with the slab thickness.

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Acta Physica Sinica•Jan 1, 2012•3 citations
By using variational method of Peakar type,the qubit and its optical phonon effect in a polar slab is studied in this paper.The system in a polar slab may be employed as a system-qubit.When the electron is in the superposition state of the ground state and the first excited state,the time evolution of the electron density can be obtained.It shows that the period of oscillation decreases with the strength of coupling increasing,but increases with the slab thickness.
The Hamiltonian of a quantum rod with an ellipsoidal boundary is given by using a coordinate transformation in which the ellipsoidal boundary is changed into a spherical one. Under the condition of strong electron—longitudinal optical phonon coupling in the rod, we obtain both the electron eigenfunctions and the eigenenergies of the ground and first-excited state by using the Pekar-type variational method. This quantum rod system may be used as a two-level qubit. When the electron is in the superposition state of the ground and first-excited states, the probability density of the electron oscillates in the rod with a certain period. It is found that the oscillation period is an increasing function of the ellipsoid aspect ratio and the transverse and longitudinal effective confinement lengths of the quantum rod, whereas it is a decreasing function of the electron—phonon 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.
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.
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.
The influence of phonon on the properties of polaron and qubit in spherical shell quantum dot is studied by solving accurately the time-independent Schrödinger equation, Lee-Low-Pines unitary transformation and variation methods. The numerical results indicate that phonon effect leads to a lower energy of ground (or excited) state of polaron than electronic energy of ground (or excited) state and the increased oscillating period of a qubit, and the phonon effect becomes more obvious with outer radius increasing when inner radius is const. The numerical results also show that the phonon effect cannot influence the amplitude of probability density distribution of electrons in quantum bit, and that the probability density distribution of electrons is dependent on co-ordinate and time and its amplitude is maximal in centre spherical surface and but zero in boundary surface. The probability density of electrons at each position oscillates periodically with time.