Time evolution of two harmonic oscillators with cross-Kerr interactions

Time evolution of two harmonic oscillators with cross-Kerr interactions

WoS Article

We study the time evolution of two coupled quantum harmonic oscillators interacting through nonlinear optomechanical-like Hamiltonians that include cross-Kerr interactions. We employ techniques developed to decouple the time-evolution operator and obtain the analytical solution for the time evolution of the system. We apply these results to obtain explicit expressions of a few quantities of interest. Our results do not require approximations and therefore allow us to study the nature and implications of the full nonlinearity of the system. As a potential application, we show that it is possible to greatly increase the population of phonons using a suitable combination of cubic and cross-Kerr interactions.

We study the time evolution of two coupled quantum harmonic oscillators interacting through nonlinear optomechanical-like Hamiltonians that include cross-Kerr interactions. We employ techniques developed to decouple the time-evolution operator and obtain the analytical solution for the time evolution of the system. We apply these results to obtain explicit expressions of a few quantities of interest. Our results do not require approximations and therefore allow us to study the nature and implications of the full nonlinearity of the system. As a potential application, we show that it is possible to greatly increase the population of phonons using a suitable combination of cubic and cross-Kerr interactions.

harmonic oscillators

harmonic oscillators

BRUSCHI, D.

2021

01.03.2020

AMER INST PHYSICS

MELVILLE

0022-2488

JOURNAL OF MATHEMATICAL PHYSICS

61

3

United States of America

032102-1

032102-13

13

https://aip.scitation.org/doi/10.1063/1.5121397