Production of genuine multimode entanglement in circular waveguides with long-range interactions

Starting with a product initial state, squeezed (coherent squeezed) state in one of the modes, and vacuum in the rest, we report that a circular waveguide comprising modes coupled with varying interaction strength is capable of producing genuine multimode entanglement (GME), quantified via the generalized geometric measure (GGM). We demonstrate that for a fixed interaction and squeezing strength, the GME content of the resulting state increases as the range of interactions between the waveguides increases, although the GGM collapses and revives with the variation of interaction strength and time. To illustrate the advantage of long-range interactions, we propose a quantity, called accumulated GGM, measuring the area under the GGM curve, which clearly illustrates the growing trends with the increasing range of interactions. We analytically determine the exact expression of GGM for systems involving an arbitrary number of modes, when all the modes interact with each other equally. The entire analysis is performed in phase-space formalism. We manifest the constructive effect of disorder in the coupling parameter, which promises a steady production of GME, independent of the interaction strength.