Coherence and squeezing along quantum trajectories

TL;DR

This paper analyzes how coherence and squeezing evolve over time in quantum systems, providing explicit formulas for expectation values and uncertainties in both linear and nonlinear cases.

Contribution

It offers a detailed analytical study of the dynamics of coherent and squeezed states in linear and nonlinear quantum systems, including explicit formulas for their evolution.

Findings

Coherence and squeezing are quantitatively characterized during time evolution.

Explicit formulas for expectation values and uncertainties are derived.

Differences between linear and nonlinear system dynamics are analyzed.

Abstract

We perform a detailed analysis of the behavior of coherent and squeezed states undergoing time evolution. We calculate time dependence of expectation values of position and momentum in coherent and squeezed states (which can be interpreted as quantum trajectories in coherent and squeezed states) and examine how coherence and squeezing is affected during time development, calculating time dependence of position and momentum uncertainty. We focus our investigations on two quantum systems. First we consider quantum linear system with Hamiltonian quadratic in $q$ and $p$ variables. As the second system we consider the simplest quantum nonlinear system with Hamiltonian quartic in $q$ and $p$ variables. We calculate the explicit formulas for the time development of expectation values and uncertainties of position and momentum in an initial coherent state.