Strong coupling, energy splitting, and level crossings: A classical perspective

Strongly interacting quantum systems are at the heart of many physical processes, ranging from photosynthesis to quantum information. We demonstrate that many characteristic features of strongly coupled systems can be derived classically for a simple coupled harmonic oscillator. This model system is used to derive frequency splittings and to analyze adiabatic and diabatic transitions between the coupled states. A classical analog of the Landau–Zener formula is derived. The classical analysis is intuitive and well suited for introducing students to the basic concepts of strongly interacting systems.