Functional integral for optical parametric amplification

TL;DR

This paper demonstrates that optical parametric amplification is fundamentally a quantum phenomenon, deriving its equations of motion and quantum state evolution using path integrals and Lagrangian formalism without relying on traditional Hamiltonian methods.

Contribution

It introduces a novel approach to analyze optical parametric amplification through path integrals of coherent states, highlighting its quantum nature and deriving key equations from classical Newtonian principles.

Findings

Optical parametric amplification is shown to be a quantum phenomenon.

The system's Lagrangian and equations of motion are derived via path integrals.

Quantum state evolution can be obtained without quantum Hamiltonian or Lagrangian.

Abstract

It is demonstrated that the nature of optical parametric amplification is a quantum phenomenon. The system Lagrangian can be constructed by the path integral of coherent state. The equations of motion for photon operators are indeed the Euler-Lagrange equations of a Lagrangian. The quantum state evolution equation can also be obtained without resorting to quantum Hamiltonian or Lagrangian. Starting with classical Newton equation, quantum transition amplitude of the system can be educed by surface integral.