Influence of the LO Phonon Effect on the Transition Rate and the Spontaneous Emission Rate in Donor-Center Quantum Dot with Spherical Gaussian Confinement Potential

Based on Lee-Low-Pines transformation, the longitudinal optical (LO) phonon effect in a donor-center quantum dot with a spherical Gaussian confinement potential is studied. The energy expressions of the ground state and the first excited state are derived by using a Pekar-type variational method, and then, a superposition state of the two-level system is constructed. On the basis of Fermi Golden Rule, two kinds of the decoherence of superposition states caused by LO phonon effects are discussed, which are the spontaneous emission of LO phonon and the quantum transition from the ground state to the excited state by absorbing a LO phonon, respectively. The numerical results show that for the former, the superposition state can be suppressed by increasing the electron–phonon coupling constant, the dielectric constant ratio, or the dispersion coefficient. For the latter, it can be used to suppress the decoherence of the superposition state by increasing the dielectric constant ratio or decreasing the electron–phonon coupling constant, or using the low-temperature environment. This work enriches and improves the theoretical scheme to suppress the decoherence of a semiconductor quantum dot qubit caused by LO phonon-related effects.