Quantitative estimation of simultaneous parametric down-conversion

Dmitri S. Mogilevtsev

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.

Filippus S. Roux

E. Brambilla, Lucia Caspani, Luigi A. Lugiato +1 more

We investigate the spatiotemporal structure of the biphoton correlation in type-II parametric down-conversion (PDC). As in type-I PDC [Phys. Rev. Lett. 102, 223601 (2009)], we find that the correlation is nonfactorizable in space and time. Differently from type I, the type-II correlation in the spontaneous regime displays an asymmetric V-shaped structure in any cross section including time and one transverse dimension. This asymmetry along the temporal coordinate originates from the signal-idler group velocity mismatch and tends to disappear as the parametric gain is raised. We observe a progressive transition toward a symmetric X-shaped geometry similar to that found in type I when stimulated PDC becomes dominant. We also give quantitative evaluations of the localization in space and in time of the correlation, analyze its behavior for different crystal tuning angles, and underline qualitative differences with respect to type-I PDC.

E. Brambilla, A. Gatti, Morten Bache +1 more

We study the spatial correlations of quantum fluctuations that can be observed in multimode parametric down-conversion in the regime of high gain. We investigate both a type-I and a type-II phase-matching configuration: in the latter case spatial correlations at the quantum level are shown to exist both in the near-field and in the far-field zones of the down-converted light. In the stationary and plane-wave approximation we treat the problem analytically. A stochastic model is solved numerically to obtain quantitative results beyond this approximation. The finite transverse size and pulse duration of the pump beam and other features of the system, such as spatial walk-off and diffraction are taken into account, and we show that correlations beyond the standard quantum limit exist for values of parameters consistent with realistic experiments.

Stephen Patrick Walborn, Carlos Henrique Monken, Sebastião Pádua +1 more