Quantum spatial dynamics of high-gain parametric down-conversion accompanied by cascaded up-conversion

Quantum cascaded up-conversion (CUpC) of parametric down conversion (PDC) in a finite nonlinear chi((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 nonzero wave-vector mismatch both for PDC and CUpC. Characteristic equation is used to analyze parametric amplification and oscillating regimes for degenerate, three- and four-mode cases. We show that the parametric amplification exists under the fulfillment 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.

Automated summary

Theoretical study of quantum cascaded up-conversion (CUpC) of parametric down conversion (PDC) in a finite nonlinear crystal is conducted within parametric approximation, highlighting the exact solutions in high-gain regime and the analysis of parametric amplification and oscillating regions for different mode cases. The influence of CUpC on quadrature squeezing of degenerate PDC is also estimated.