摘要
Beam splitters allow us to superpose two continuous single-mode quantum systems. To study the behavior of their strong mode mixing dynamics, we consider variable beam splitters and their dynamics using Wigner's phase space distribution, W, the evolution of which is governed by the continuity equation partial derivative partial derivative tau W= -del <middle dot> J. We derive the form of the corresponding Wigner current, J, of each outgoing mode after tracing out the other. The influence of the modes on each other is analyzed and visualized using their respective Wigner distributions and Wigner currents. This allows us to perform geometrical analyses of the mode interactions, casting new light on beam splitter behavior. Several of the presented results should be immediately testable in experiments. (c) 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.