Time-dependent coherent squeezed states in a nonunitary approach

TL;DR

This paper develops a nonunitary approach using integrals of motion to analyze time-dependent coherent squeezed states in quantum systems, providing explicit constructions and properties for systems with time-dependent quadratic Hamiltonians.

Contribution

It introduces a novel nonunitary method to derive time-dependent coherent squeezed states and applies it to systems with time-dependent quadratic Hamiltonians, including oscillators with variable frequency.

Findings

Derived explicit expressions for time-dependent displacement and squeezing parameters.

Analyzed properties such as uncertainty minimization and transition probabilities.

Applied the method to an oscillator with time-dependent frequency, solving Mathieu's equation.

Abstract

In this work, we have applied the integrals of motion method in a nonunitary approach and so obtained the time-dependent displacement and squeezed parameters of the coherent squeezed states (CSS). On its turn, CSS for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. We discuss the properties of these states, in particular, minimization of uncertainty relation and transition probabilities. As an application, we calculate the CSS of an oscillator with a time-dependent frequency and shown that the solution can be obtained from these well-known Mathieu's equation.