Dynamical squeezing in quantum mechanics

Gebhard Grübl

Institut für Theoretische Physik der Universität Innsbruck,
A-6020 Innsbruck, Technikerstr. 25, Austria

Received 13 February 1989


Abstract. 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 verctor with reduced position variance for exactly two discrete instants of time per period. The results are applied to the case of a perturbing jump in the driving harmonic oscillator Hamiltonian. The total transition probability to the excited (unperturbed) oscillator levels from the ground-state vector is computed.

J. Phys. A: Math. Gen. 22, 3243 - 3252 (1989).