Higher-order interactions in quantum optomechanics: Revisiting theoretical foundations

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.

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Cited by in corpus (6)

• Solution of Cross-Kerr Interaction Combined with Parametric Amplification
• Coherent coupling completes an unambiguous optomechanical classification framework
• Method of Higher-Order Operators for Quantum Optomechanics
• Higher-order interactions in quantum optomechanics: Analytical solution of nonlinearity
• Higher-Order Interactions in Quantum Optomechanics: Analysis of Quadratic Terms
• Temporal evolution of a forced optomechanical system with linear and quadratic field -- mechanical oscillator couplings