SQUEEZING PHENOMENA IN INTERACTING ELECTRON-PHONON SYSTEMS

Abstract

The molecular crystal model of electrons coupled to Einstein phonons is studied as a function of the two parameters: the coupling constant A and the ratio of the electron-phonon coupling energy to the phonon energy, denoted by α. 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 α>1, the sharp crossover between quasi-free electrons (λ≪1) and small polarons (λ≫1) is investigated, emphasizing the anomalous lattice fluctuations which occur in the intermediate regime (λ≈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 λ, due to a competition between the phonon dressing effect and the reduction of lattice momentum fluctuations. This reduction is reminiscent of squeezing phenomena occurring in quantum optics. In a gaussian approximation squeezed phonon states imply a dynamical phonon softening.