# Generic Contractive States and Quantum Monitoring of Free Masses and Oscillators

## TL;DR

This paper introduces a broad class of quantum states, including generic coherent and squeezed contractive states, that maintain or reduce uncertainty widths over time, enhancing the detection of small disturbances like gravitational waves.

## Contribution

The paper generalizes existing quantum states to include states with arbitrary uncertainty products and time-dependent widths, useful for quantum monitoring applications.

## Key findings

- Generic coherent states with time-independent width
- Squeezed contractive states with decreasing width over time
- States with arbitrarily large uncertainty products

## 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.