Theory of high-gain twin-beam generation in waveguides: From Maxwell's equations to efficient simulation

Nicolás Quesada, Gil Triginer, Mihai D. Vidrighin, and J. E. Sipe
Phys. Rev. A 102, 033519 – Published 21 September 2020

Abstract

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.

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  • Received 17 February 2020
  • Accepted 1 July 2020

DOI:https://doi.org/10.1103/PhysRevA.102.033519

©2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Nicolás Quesada1,*, Gil Triginer2,*, Mihai D. Vidrighin2,*,†, and J. E. Sipe3

  • 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
  • 2Clarendon Labs, Department of Physics, Oxford University, Parks Road, OX1 3PU Oxford, United Kingdom
  • 3Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada

  • *These authors contributed equally to this article.
  • mihai.vidrighin@gmail.com

See Also

Understanding High-Gain Twin-Beam Sources Using Cascaded Stimulated Emission

Gil Triginer, Mihai D. Vidrighin, Nicolás Quesada, Andreas Eckstein, Merritt Moore, W. Steven Kolthammer, J. E. Sipe, and Ian A. Walmsley
Phys. Rev. X 10, 031063 (2020)

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Vol. 102, Iss. 3 — September 2020

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