Dynamical squeezing in quantum mechanics
Gebhard Grübl · Journal of Physics A Mathematical and General · 1989
The time evolution orbits of Gaussian vectors under a harmonic oscillator dynamics are computed and discussed. The generic case is shown to be this: a minimum uncertainty vector which is coherent with respect to a harmonic oscillator Hamiltonian with smaller frequency than the one of the driving Hamiltonian, evolves into a minimum uncertainty vector with reduced position variance for exactly two discrete instants of time per period. The results are applied to the case of a perturbing frequency jump in the driving harmonic oscillator Hamiltonian. The total transition probability to the excited (unperturbed) oscillator levels from the ground-state vector is computed.