Effects of time ordering in quantum nonlinear optics

Abstract

We study time ordering corrections to the description of spontaneous parametric down-conversion (SPDC), four wave mixing (SFWM) and frequency conversion (FC) using the Magnus expansion. Analytic approximations to the evolution operator that are unitary are obtained. They are Gaussian preserving, and allow us to understand order-by-order the effects of time ordering. We show that the corrections due to time ordering vanish exactly if the phase matching function is sufficiently broad. The calculation of the effects of time ordering on the joint spectral amplitude of the photons generated in spontaneous SPDC and SFWM are reduced to quadrature.

References in corpus (2)

• The Magnus expansion and some of its applications
• Efficient computation of the Zassenhaus formula

Cited by in corpus (7)

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• Time ordering effects in the generation of entangled photons using nonlinear optical processes
• Engineering the Frequency Spectrum of Bright Squeezed Vacuum via Group Velocity Dispersion in an SU(1,1) Interferometer
• Theory of high-efficiency sum-frequency generation for single-photon waveform conversion
• Frequency-domain engineering of bright squeezed vacuum for continuous-variable quantum information
• On multi-variable Zassenhaus formula
• General ordering theorem