Engineering multipartite coupling in doubly pumped parametric down-conversion processes

We investigate the quantum state generated by optical parametric down-conversion in a $\chi^{(2) } $ medium driven two noncollinear light modes. The analysis shows emergence of multipartite, namely 3- or 4-partite, entangled states subset spatio-temporal modes process. These appear as bright spots against background fluorescence, providing an interesting analogy with phenomenology recently observed two-dimensional nonlinear photonic crystals. study realistic setups: i) Non-critical phase-matching periodically poled Lithium Tantalate slab, characterized 3-mode among hot spots. ii) A type I setup Beta-Barium Borate crystal, where spatial walk-off between pumps can be exploited to make transition quadripartite state. In both cases we show that properties controlled modulating relative intensity pump waves, making device versatile tool for engineering.