Non-classical eigen state and the persistent current in one-dimensional mesoscopic ring with the electron-two-phonon interaction

For the one-dimensional mesoscopic ring with the ferromagnetic texture, to restrain the quantum fluctuations caused by the electron-one-phonon interaction, the non-classical correlation effects are used in our research to solve this puzzling problem, i.e. 1) the hopping electron-displaced phonon state correlation; 2) the process correlation between the phonon squeezed state, and the one-phonon coherent state, originating from the squeezed coherent state of phonon; 3) the renormalization of the phonon displacement. It is found that due to the electron-two phonon interaction, the squeezing effect of phonon is enhanced significantly. Because of the effect of the electron-displaced phonon correlation the non-classical eigen state energy declines significantly and the amplitude of the persistent current increases substantially. Particularly the process correlation between the squeezed phonon state and the one-phonon coherent state is by far the most important contribution to these non-classical effects. First of all, this effect more greatly increases the squeezing effect of phonon field in contrast to the ideal squeezed state. As a result, it will restrain effectively the Debye-Waller effect (factor wph) with wph wph(0). Furthermore, when we combine the effective renormalization of the phonon displacement with the effect of process correlation between the phonon squeezed state and the one-phonon coherent state, the phonon squeezing effect will increases substantially, at the same time, the D-W effect decreased more substantially (wph wph(0), thereby weakening the quantum fluctuation to a bigger degree. With these results, the non-classical eigen energy (En) is much lowered (En En(0)), while the amplitude of eigen persistent current is increased most significantly (In In(0)).