SQUEEZING PHENOMENA IN INTERACTING ELECTRON-PHONON SYSTEMS

The molecular crystal model of electrons coupled to Einstein phonons is studied as function of the two parameters: the coupling constant lambda and the ratio of the electron-phonon coupling energy to the phonon energy, denoted by alpha. Both the one-electron and the many-electron models are studied, starting (for the former) from the adiabatic limit and (for the latter) from the anti-adiabatic one. In the "multiphonon" regime alpha > 1, the sharp crossover between quasi-free electrons (lambda << 1) and small polarons (lambda >> 1) is investigated, emphasizing the anomalous lattice fluctuations which occur in the intermediate regime (lambda approximate to 1). These fluctuations are due to the band motion of the electrons strongly coupled to the lattice and are shown in turn to weaken the electron mass renormalization inherent to self-trapping. In a relevant part of the intermediate region the effective electron mass slowly increases with lambda, due to a competition between the phonon dressing effect and the reduction of lattice momentum fluctuations. This reduction is reminiscent of squeeezing phenomena occurring in quantum optics. In a gaussian approximation squeezed states imply a dynamical phonon softening.