Characterization of Schmidt modes in high-gain SU(1,1) interferometers

Abstract: Multimode quantum light has promising applications in many areas of physics, such as quantum communications and quantum computing. However, its multimode nature also makes it challenging to measure its properties. Recently [Optica Quantum 3, 36 (2025)], a method for the simultaneous measurement of the level of squeezing in multiple broadband Schmidt modes has been developed using a phase-sensitive amplification technique. Effectively, this setup corresponds to an SU(1,1) interferometer. Here, we aim to provide a thorough theoretical analysis of this technique and the broadband SU(1,1) interferometer in general in terms of its Schmidt modes. Utilizing the joint Schmidt decomposition of the transfer functions, we investigate the shape and the phase profile of the modes of a single parametric down-conversion (PDC) section and a full (in general, unbalanced) SU(1,1) interferometer for different parametric gain regimes. We consider the complicated interplay between the modes, which is reflected in their overlap coefficients, present a rigorous theoretical approach for the aforementioned multimode phase-sensitive amplification technique, and discuss approximations to make this method experimentally feasible.