Nonlinear Quantum Optical Spring

TL;DR

This paper generalizes the concept of quantum optical springs to include nonlinear dependencies of frequency on radiation intensity, analyzing the resulting nonclassical states and their quantum properties such as collapse, revival, and squeezing.

Contribution

It introduces a nonlinear quantum optical spring model that accounts for intensity-dependent frequency modulation in nonlinear coherent states.

Findings

Demonstrates collapse and revival phenomena in the nonlinear quantum optical spring

Shows nonclassical properties like squeezing in the generated states

Provides analytical solutions for the generalized Hamiltonian

Abstract

The original idea of quantum optical spring arises from the requirement of quantization of the frequency of oscillations in Hamiltonian of harmonic oscillator. This purpose is achieved by considering a spring whose constant (and so its frequency) depends on the quantum states of another system. Recently, it is realized that by the assumption of frequency modulation of $\omega$ to $\omega\sqrt{1+\mu a^\dagger a}$ the mentioned idea can be established. In the present paper we generalize the approach of quantum optical spring (has been called by us as nonlinear quantum optical spring) with attention to the {\it dependence of frequency to the intensity of radiation field} that {\it naturally} observed in nonlinear coherent states. Then, after the introduction of the generalized Hamiltonian of nonlinear quantum optical spring and it's solution, we will investigate the nonclassical properties of the obtained states. Specially, typical collapse and revival in the distribution functions and squeezing parameters as particular quantum features will be revealed.