2019/07/31 by Nicolás Quesada, Gil Triginer, Mihai D. Vidrighin +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Beam (structure) #Classical mechanics #Laser-Matter Interactions and Applications #Mathematics #Nonlinear system #Optics #Parametric statistics #Photonic and Optical Devices #Physics #Quantum mechanics #physics.optics #quant-ph
paper · pdf · doi:10.1103/physreva.102.033519
published as Phys. Rev. A 102, 033519 (2020)
openalex created_date 2019/07/12 · openalex publication_date 2020/09/21 · arxiv created 2020/11/15 · arxiv updated 2020/11/17 · openalex updated_date 2026/08/05
We provide an efficient method for the calculation of high-gain, twin-beam generation in waveguides derived from a canonical treatment of Maxwell's equations. Equations of motion are derived that naturally accommodate photon generation via spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing and, also, include the effects both of self-phase modulation of the pump and of cross-phase modulation of the twin beams by the pump. The equations we solve involve fields that evolve in space and are labeled by a frequency. We provide a proof that these fields satisfy bona fide commutation relations and that in the distant past and future they reduce to standard time-evolving Heisenberg operators. Having solved for the input-output relations of these Heisenberg operators we also show how to construct the ket describing the quantum state of the twin beams. Finally, we consider the example of high-gain SPDC in a waveguide with a flat nonlinearity profile, for which our approach provides an explicit solution that requires only a single matrix exponentiation.