WKB calculations have revealed that tunneling dynamics of localized wave packets in simple potential wells depend sensitively on the degree of squeezing of the wave function. Squeezed states are shown to tunnel more slowly in general than eigenstates of the well and states which are initially localized near the bottom of a well have much lower tunneling rates than states localized at the sides of the well. The dependence of tunneling time on energy also exhibits steps related to quasi-bound-state energies in a complex way. Additionally, modulations in the tunneling probability correlate with the motion of the squeezed wave packet in the well. These results have implications both for the dynamics of squeezed radiation fields and squeezed matter states, and examples of applications to controlled vibrational-state chemistry, ultralow-noise measurements of weak signals with Josephson junctions, and optical crystals are discussed.
An introduction to quantum rotational tunneling and libration is presented with an emphasis on obtaining a qualitative understanding of this phenomenon through visualization of the dynamics, simple approximations, and measurements. The tunneling and librational dynamics of small molecular rotors are discussed using a very simple model of the rotational potential. Numerical calculations of the evolution of probability packets are carried out for the low-lying states and the connection is made between the quantum and classical librational dynamics. Finally, we present measurements of these quantum rotations using inelastic neutron scattering and show in particular how neutron scattering measurements of the ground state tunnel splitting and first librational transition can be used to characterize the magnitude and shape of the potential hindering the motion of the rotor. Some conceptual and computational problems are included that are suitable for undergraduate students.