Photon and Photon-Added Intelligent States of Coupled Parametric Oscillators

TL;DR

This paper investigates the quantum states of coupled parametric oscillators under periodic excitation, deriving explicit expressions for intelligent and photon-added states using Floquet-Lyapunov theory.

Contribution

It introduces a method to construct intelligent and photon-added states of coupled oscillators with explicit wavefunction and Wigner function expressions.

Findings

Derived linear integrals of motion for the system

Constructed explicit wavefunctions and Wigner functions for the states

Linked covariance matrices to canonical observables

Abstract

We study a quantum system of coupled oscillators subject to a periodic excitation of its parameters. Using Floquet-Lyapunov theory we derive the linear integrals of motion of the system and relate their covariance matrix to that for the canonical observables. The operator integrals allows us to construct the intelligent (minimum uncertainty) states of the system and the corresponding photon-added states. We found explicit expressions for the wavefunction, Wigner function and covariance matrix of these states.