Squeezing induced in a harmonic oscillator by a sudden change in mass or frequency

The Kanai-Caldirola (Bateman) Hamiltonian is used to derive the dynamics of a simple harmonic oscillator, initially in a minimum uncertainty state, under the influence of an external agency which causes the mass parameter to change from ${\mathit{M}}_0$ to ${\mathit{M}}_1$ in a short time ε. Then the frequency changes from ${\mathrm{\omega }}_0$ to ${\mathrm{\omega }}_1$=(${\mathit{M}}_0$/${\mathit{M}}_1$)${\mathrm{\omega }}_0$+O(${\mathrm{\epsilon }}^2$). In the limit ε→0, no squeezing or loss of coherence occurs. If ${\mathit{M}}_1$/${\mathit{M}}_0$=1±η (0<η≪1), then a squeezing of order ${\mathrm{\epsilon }}^2$η occurs. If ${\mathit{M}}_1$/${\mathit{M}}_0$ is appreciably different from unity, then the quadrature variances are unequal but the state no longer has minimum uncertainty. An application could be made in quantum optics.