Quantum cascaded up-conversion (CUpC) of parametric down conversion (PDC) in a finite nonlinear χ(2)-crystal is studied theoretically within parametric approximation. The exact solution for creation and annihilation operators presented in the form of Bogoliubov transformation is valid for the high-gain regime and explicitly includes the non-zero wavevector-mismatch both for the PDC and CUpC. With the use of characteristic equation parametric amplification and oscillating regimes are analysed for degenerate, three- and four-mode cases. We show that the parametric amplification exists under the fulfilment of the cascaded phase-matching conditions while both the PDC and CUpC processes are separately non-phase-matched. The influence of CUpC on quadrature squeezing of degenerate PDC is estimated.
Cite
@article{arxiv.2011.11505,
title = {Quantum spatial dynamics of high-gain parametric down-conversion accompanied by cascaded up-conversion},
author = {A. V. Rasputnyi and D. A. Kopylov},
journal= {arXiv preprint arXiv:2011.11505},
year = {2021}
}