Chapter Seven - Vibrational Quantum Squeezing Induced by Inelastic Collisions☆

The energy transfer between vibrational and translational degrees of freedom during an inelastic collision between two molecules induces quantum squeezing in the vibrational molecular coordinate under very diverse circumstances. In this chapter, we present the relevant calculation for the very simple case of an atom-diatomic collinear transition, the Landau-Teller model. Both the uncertainty of the vibrational coordinate and the Husimi function show clear evidence of quantum squeezing. Our model treats the relative translation of the colliding species as a classical variable. The vibrational motion of the diatomic molecule is treated quantum mechanically in terms of the evolution operator and coherent states. The corresponding classical and quantum equations of motion are coupled. We first consider the squeezing of a coherent vibrational state where we include the dynamic evolution of the Husimi function. The second case corresponds to an initial thermal distribution of vibrational states where we plot the position uncertainty for the squeezed vibrational state.