Polaron-soliton squeezed states, ground state and quantum fluctuation in one-dimensional molecular crystals

On the basis of the Hamiltonian of the Holstein one-dimensional molecular crystals, using the squeezed-coherent state expansion method, the influence of the electron-two phonon interaction on the properties of the ground state and quantum fluctuation for the polaron-soliton system were investigated by including the quantum correlation between the polarons and the squeezed phonons, and the renormalized displacement correction. The nonlinear Schroinger equation for one-dimensional polaron-soliton state has been found in a closed form. By the use of the nonlinear expansion, we have given the analytical solution of the corresponding nonlinear equation so as to obtain the ground state energy,the quantum fluctuation and the polaron energy of the polaron-soliton system in analytical form. We have found that, when the electron-two phonon coupling strength g(1) < 0, the nonlinear Schroinger equation has the solitary wave solution. As a result, the ground state energy and the polaron energy are more negative than the electron-single phonon coupling. At the same time, the stability of the polaron-soliton state is enhanced and the soliton localization is decreased. Particularly, when g(1) < 0, the quantum fluctuation <Delta(2)n > and <Delta(2)p > <Delta(2)q > for the two-phonon effect are larger than the one-phonon one and the polaron energy for the two-phonons effect is more negative compared with the one-phonon one.