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_0 when 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.
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