Enhancing entanglement detection of quantum optical frequency combs via stimulated emission

We investigate the performance of a certain nonclassicality identifier, expressed via integrated second-order intensity moments of optical fields, in revealing bipartite entanglement of quantum-optical frequency combs (QOFCs), which are generated in both spontaneous and stimulated parametric down-conversion processes. We show that, by utilizing that nonclassicality identifier, one can well identify the entanglement of the QOFC directly from the experimentally measured intensity moments without invoking any state reconstruction techniques or homodyne detection. Moreover, we demonstrate that the stimulated generation of the QOFC improves the entanglement detection of these fields with the nonclassicality identifier. Additionally, we show that the nonclassicality identifier can be expressed in a factorized form of detectors quantum efficiencies and the number of modes, if the QOFC consists of many copies of the same two-mode twin beam. As an example, we apply the nonclassicality identifier to two specific types of QOFC, where: (i) the QOFC consists of many independent two-mode twin beams with non-overlapped spatial frequency modes, and (ii) the QOFC contains entangled spatial frequency modes which are completely overlapped, i.e., each mode is entangled with all the remaining modes in the system. We show that, in both cases, the nonclassicality identifier can reveal bipartite entanglement of the QOFC including noise, and that it becomes even more sensitive for the stimulated processes.Comment: 11 p., 8 fig

Geometry of the Field-Moment Spaces for Quadratic Bosonic Systems: Diabolically Degenerated Exceptional Points on Complex kk-Polytopes

$k$-Polytopes are a generalization of polyhedra in $k$ dimensions. Here, we show that complex $k$-polytopes naturally emerge in the higher-order field moments spaces of quadratic bosonic systems, thus revealing their geometric character. In particular, a complex-valued evolution matrix, governing the dynamics of $k$th-order field moments of a bosonic dimer, can describe a complex $k$-dimensional hypercube. The existence of such $k$-polytopes is accompanied by the presence of high-order diabolic points (DPs). Interestingly, when the field-moment space additionally exhibits exceptional points (EPs), the formation of $k$-polytopes may lead to the emergence of diabolically degenerated EPs, due to the interplay between DPs and EPs. Such intriguing spectral properties of complex polytopes may enable constructing photonic lattice systems with similar spectral features in real space. Our results can be exploited in various quantum protocols based on EPs, paving a new direction of research in this field.Comment: 9 page