  Orbital Angular Momentum (OAM) modes are an important resource used in
various branches of quantum science and technology due to their unique helical
structure and countably infinite basis. Generating light that simultaneously
carries high-order orbital angular momenta and exhibits quantum correlations is
a challenging task. In this work, we present a theoretical approach to the
generation of correlated Schmidt modes carrying OAM via parametric
down-conversion (PDC) in cascaded nonlinear systems (nonlinear interferometers)
pumped by Laguerre-Gaussian beams. We demonstrate how the number of generated
modes and their population can be controlled by varying the pump parameters,
the gain of the PDC process and the distance between the crystals. We
investigate the angular displacement sensitivity of these interferometers and
demonstrate that it can overcome the classical shot noise limit.
