Higher-order interactions in quantum optomechanics: Revisiting theoretical foundations

TL;DR

This paper reconstructs the fundamental theory of quantum optomechanics from first principles, rigorously demonstrating the existence of quadratic and higher-order interactions and their significance in various regimes.

Contribution

It provides a first-principles derivation of nonlinear interactions in quantum optomechanics, including quadratic and higher-order terms, which were previously assumed phenomenologically.

Findings

Quadratic mechanical parametric interaction is rigorously demonstrated.

Higher-order interactions do not vanish under any canonical parameter choice.

Corrections to quadratic terms are significant when mechanical frequency is comparable or larger than electromagnetic frequency.

Abstract

The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order interactions, do not vanish under any possible choice of canonical parameters, and lead to coupling of momentum and field. The existence of quadratic mechanical parametric interaction is then demonstrated rigorously, which has been so far assumed phenomenologically in previous studies. Corrections to the quadratic terms are particularly significant when the mechanical frequency is of the same order or larger than the electromagnetic frequency. Further discussions on the squeezing as well as relativistic corrections are presented.