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

Abstract

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 \ensuremath{\epsilon}. Then the frequency changes from ${\mathrm{\ensuremath{\omega}}}_{0}$ to ${\mathrm{\ensuremath{\omega}}}_{1}$=(${\mathit{M}}_{0}$/${\mathit{M}}_{1}$)${\mathrm{\ensuremath{\omega}}}_{0}$+O(${\mathrm{\ensuremath{\epsilon}}}^{2}$). In the limit \ensuremath{\epsilon}\ensuremath{\rightarrow}0, no squeezing or loss of coherence occurs. If ${\mathit{M}}_{1}$/${\mathit{M}}_{0}$=1\ifmmode\pm\else\textpm\fi{}\ensuremath{\eta} (0\ensuremath{\ll}1), then a squeezing of order ${\mathrm{\ensuremath{\epsilon}}}^{2}$\ensuremath{\eta} 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.