Single-mode approximation of parametric down-conversion (5 pages)

Silvia Carrasco, Juan P. Torres

Filippus S. Roux

Yongmin Li, Hideharu Mikami, Haibo Wang +1 more

In this paper, we study the theory of spontaneous parametric down-conversion pumped by a short coherent pulse. It is shown that when single spatial mode filters and narrow band optical filters are used to filter the output state of parametric down-conversion, the postselected state of parametric down-conversion can be approximately described by a simple single-mode theory.

Andrei Rasputnyi, Д. А. Копылов

Quantum cascaded up-conversion (CUpC) of parametric down conversion (PDC) in a finite nonlinear ${\ensuremath{\chi}}^{(2)}$ 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.

Dmitri S. Mogilevtsev

Filippus S. Roux