Polaron in CsI quantum pseudo dot under an electromagnetic field was considered, and the ground and first excited state energies were derived by employing the combining Pekar variational and unitary transformation methods. With the two-level system obtained, single qubit was envisioned and the decoherence was studied using non-extensive entropy (Tsallis entropy). Numerical results showed: (i) the increase (decrease) of the energy levels (period of oscillation) with the increase of chemical potential, the zero point of pseudo dot, cyclotron frequency, and transverse and longitudinal confinements; (ii) the Tsallis entropy evolved as a wave envelop that increase with the increase of non-extenxive parameter and with the increase of electric field strength, zero point of pseudo dot and cyclotron frequency the wave envelop evolve periodically with reduction of period; (iii) The transition probability increases from the boundary to the centre of the dot where it has its maximum value. It was also noted that the probability density oscillate with period T0=ℏ/ΔΕ with the tunnelling of the chemical potential and zero point of the pseudo dot. These results are helpful in the control of decoherence in quantum systems and may also be useful for the design of quantum computers.
Polaron in CsI quantum pseudo dot under an electromagnetic field was considered, and the ground and first excited state energies were derived by employing the combining Pekar variational and unitary transformation methods. With the two-level system obtained, single qubit was envisioned and the decoherence was studied using non-extensive entropy (Tsallis entropy). Numerical results showed: (i) the increase (decrease) of the energy levels (period of oscillation) with the increase of chemical potential, the zero point of pseudo dot, cyclotron frequency, and transverse and longitudinal confinements; (ii) the Tsallis entropy evolved as a wave envelop that increase with the increase of non-extenxive parameter and with the increase of electric field strength, zero point of pseudo dot and cyclotron frequency the wave envelop evolve periodically with reduction of period; (iii) The transition probability increases from the boundary to the centre of the dot where it has its maximum value. It was also noted that the probability density oscillate with period T0=ℏ/ΔΕ with the tunnelling of the chemical potential and zero point of the pseudo dot. These results are helpful in the control of decoherence in quantum systems and may also be useful for the design of quantum computers.
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.
Many methods have been experimented to study decoherence in nanostructures. Tsallis, Shannon and Gaussian entropy have been used to study decoherence separately; in this paper, we compared the results of the sus-mentioned entropies in nanostructures. The linear combination operator and the unitary transformation was used to derive the magnetopolaron spectrum that strongly interact with the LO phonons in the presence of electric field in the pseudo harmonic and delta quantum dot. Numerical results revealed for the quantum pseudo dot that: (i) The amplitude of Gauss entropy is greater than the amplitude of Tsallis entropy which inturn is greater than the amplitude of Shannon entropy. The Tsallis entropy is not more significant in nanostructure compared to Shannon and Gauss entropies, (ii) With an increase of the zero point, the dominance of the Gauss entropy on the Shannon entropy was observed on one hand and the dominance of the Shannon entropy on the Tsallis entropy on the other hand ; this suggested that in nanostructures, Gauss entropy is more suitable in the evaluation of the average of information in the system, for the delta quantum dot it was observed that (iii) when the Gauss entropy is considered, a lot of information about the system is missed. The collapse revival phenomenon in Shannon entropy was observed in RbCl and GaAs delta quantum dot with the enhancement of delta parameter; with an increase in this parameter, the system in the case of CsI evolved coherently; with Shannon and Tsallis entropies , information in the system is faster and coherently exchanged; (iv) The Shannon entropy is more significant because its amplitude outweighs on the others when the delta dimension length enhances. The Tsallis entropy involves as wave bundle; which oscillate periodically with an increase of the oscillation period when delta dimension length is improved.
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.
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.
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.