Generic Contractive States and Quantum Monitoring of Free Masses and Oscillators

Abstract

Monitoring photon quadratures and free masses are useful tools to detect small disturbances such as gravitational waves.Here we report a large class of states for photon quadratures and free masses potentially useful for this purpose: (1)'generic coherent states' (GCS) of photons, whose width is independent of time and uncertainty product $\sigma (x) \sigma (p) $ is arbitrarily large (a generalization of the minimum uncertainty Schr\"odinger coherent states and (2) `squeezed generic contractive states' (SGCS) for photons and free masses (a generalization of the Yuen states \cite{Yuen}) whose width decreases with time ,uncertainty product is arbitrarily large, and the covariance squared $ <\{\Delta \hat{x}, \Delta \hat{p} \}>^2 $ has an arbitrary value within the allowed range $(0,4 \sigma ^2 (x) \sigma ^2 (p) -1\>)$. Dedicated to the 125th birth anniversary of S. N. Bose.