Squeezing in harmonic oscillators with time-dependent frequencies

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Abstract
It is shown that squeezing will inevitably be generated in a harmonic oscillator with time-dependent frequency for any nonvanishing rate of frequency change, sudden or smooth. The general form of the time-dependent transition probabilities among the eigenstates of the initial Hamiltonian is obtained with an exact operator approach. Results for the case of a sudden frequency jump are explicitly given as an illustration. It is also pointed out that to generate squeezing in a harmonic oscillator, the Hamiltonian does not have to be a unitary squeeze transformation of the free Hamiltonian.