Properties of a polaron in a quantum dot: a squeezed-state variational approach
The ground-state energy and the average number of virtual phonons around the electron in a parabolic quantum dot for the entire range of the electron-phonon coupling constant are obtained using the single-mode squeezed-state variational approach. The variational approach we applied is based on two successive canonical transformations and using a displaced-oscillator type unitary transformation to deal with the bilinear terms which are usually neglected. In order to study the relationship between the ground-state energy and the average number of virtual phonons around the electron of a polaron in a parabolic quantum dot with the electron-LO-phonon coupling constant and the confinement length, numerical calculations are carried out in the electron-LO-phonon strong- and weak-coupling regions. In this paper, we study the properties of a polaron confined in a three-dimensional parabolic QD in the overall range of the coupling constant .The electron is trapped in a parabolic poten- tial and we only take into account the coupling with the bulk LO phonon. The ground-state energy and the average number of virtual phonons around the electron are calculated by the squeezed-state variational approach. Our variational approach is based on two successive canonical transformations. One is a displaced-oscillator type unitary transformation to diagonalize the relevant Frohlich Hamiltonian. The other is a single-mode squeezed-state transformation which is used to deal with the bilinear terms of phonon creation and annihilation operators arising from the first transformation. In numerical results, we discuss the relationship of the ground-state energy and the av- erage number of virtual phonons around the electron on the electron-LO-phonon coupling constant and the confinement length compared to the results using the FH and LLPH ap- proaches.