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We discuss the density-density response functions and the collective excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state. For the short-range intersite interaction we find the sound wave-like modes with the velocity interpolating smoothly between the weak (v is-proportional-to 2Zt, Absolute value of U much less than 2Zt) and strong coupling (v is-proportional-to Zt2/Absolute value of U, Absolute value of U much greater than 2Zt) limits. The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong coupling limit. In the weak coupling regime, we obtain that apart from a commensurate charge density wave instability, an increase in the intersite Coulomb repulsion can give rise to a charge density wave incommensurate with the lattice period, away from half-filling. The ground state phase diagram for 2D square lattice, including singlet superconducting ground state, electronic droplet formation, and charge density waves is determined. It is also shown that the energy of collective excitations evolves smoothly from weak to strong coupling limit for a 2D lattice, in the case of a long-range Coulomb interaction. Finally, the mode coupling effects in the frequency behavior of the density-density response functions are analyzed.

From Weak to Strong Coupling Superconductivity: Collective Modes in a Model with Local Attraction