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Abstract

A bright squeezed vacuum (BSV) is a nonclassical macroscopic state of light, which is generated through high-gain parametric down-conversion or four-wave mixing. Although the BSV is an important tool in quantum optics and has a lot of applications, its theoretical description is still not complete. In particular, the existing description in terms of Schmidt modes with gain-independent shapes fails to explain the spectral broadening observed in the experiment as the mean number of photons increases. Meanwhile, the semiclassical description accounting for the broadening does not allow us to decouple the intermodal photon-number correlations. In this work, we present a new generalized theoretical approach to describe the spatial properties of a multimode BSV. In the multimode case, one has to take into account the complicated interplay between all involved modes: each plane-wave mode interacts with all other modes, which complicates the problem significantly. The developed approach is based on exchanging the (k, t ) and (ω, z) representations and solving a system of integrodifferential equations. Our approach predicts correctly the dynamics of the Schmidt modes and the broadening of the angular distribution with the increase in the BSV mean photon number due to a stronger pumping. Moreover, the model correctly describes various properties of a widely used experimental configuration with two crystals and an air gap between them, namely, an SU(1,1) interferometer. In particular, it predicts the narrowing of the intensity distribution, the reduction and shift of the side lobes, and the decline in the interference visibility as the mean photon number increases due to stronger pumping. The presented experimental results confirm the validity of the new approach. The model can be easily extended to the case of the frequency spectrum, frequency Schmidt modes, and other experimental configurations.