The Kanai-Caldirola (Bateman) Hamiltonian is used to derive the dynamics of a simple harmonic oscillator, initially in a minimum uncertainty state, under the inhuence of an external agency which causes the mass parameter to change from Mp to M, in a short time e. Then the frequency changes from cop to ct)i = (Mp/Mi )cop+ Q(e ). In the limit e -+0, no squeezing or loss of coherence occurs. If M& /Mp = 1+7) (0 & q « 1), then a squeezing of order e g occurs. If M& /Mp 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.PACS number(s): 42.50.Dv, 03.20. +i

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The Holstein-Primakoff transformation is used to transform the model of N (~1) two-level atoms collectively interacting with multiphotons of a single quantized mode of the field (the TavisCummings model) into a boson-boson model. Formal solutions are obtained in the strong-coupling limit and/or the large-number-of-atoms limit, The analogy is drawn with a simple model of frequency conversion. The characteristic function in the p representation for the transformed model is calculated.

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