Abstract
Waves in the spatio-spectral and -temporal coherence of evolving ultra-intense twin beams are predicted: Twin beams with low intensities attain maximal coherence in the beam center until certain threshold intensity is reached. Then the area of maximal coherence moves with increasing intensity from the beam center towards its edges leaving the beam center with low coherence (the first coherence wave). For even larger intensities, a new coherence maximum is gradually built in the beam center with the increasing intensity and, later, it again moves towards the beam edges forming the second coherence wave. Rotationally-symmetric twin beams are analyzed within a three-dimensional model that couples spectral and spatial degrees of freedom. Relation between the twin-beam coherence and its local density of modes during the nonlinear evolution is discussed.
Highlights
Parametric down-conversion, in parallel with its applications in classical nonlinear optics[1], nowadays serves as a common source of three types of highly nonclassical states[2]: states of individual entangled photon pairs, intense twin beams composed of macroscopic numbers of photon pairs and states with squeezed phase and photon-number fluctuations
The model presented in ref.[39] has shown that the maximal coherence quantified by spatially and spectrally averaged intensity correlation functions attains its maximum for certain twin beams (TWB) intensity
Our prediction is based upon the analysis of a three-dimensional model of an intense rotationally-symmetric twin beam that was developed in the transverse wave-vector and frequency domains and extended to the time domain
Summary
We assume that the overall number of pump photons present in the incident pump beam is distributed into these modes linearly proportionally to the squared overall Schmidt coefficients λm2lq, i.e. the incident pump-beam amplitude Ap ,mlq of mode mlq related to normal ordering of field’s operators is given as. Ginavt(z) for parametric down-conversion with the incident vacuum signal and idler beams was found in ref.[39] in the generalized parametric approximation In this approximation, independent evolution of the interacting modes’ triplets is first treated classically (using symmetric ordering of fields’ operators) which provides the pump-mode amplitude Ap,mlq of an (mlq)th triplet along the crystal in the form: Ap,mlq (z ′).
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