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Abstract: Often, topological properties of quantum matter manifests themselves into a pumping phenomenon. We reinterpret topological pumps as a topological coupling between slow and fast quantum systems. The topological nature of the coupling induces a transfer of energy between the slow degrees of freedom.
We introduce the simplest example of topological coupling between a two-level system and two slow bosonic modes.
We show that any initial state decomposes into a pair of adiabatic components. Each of these adiabatic components effectively pumps energy between the two modes, but in two opposite directions. This separation of energy content of the modes thereby realizes a new kind of cat state.
At intermediate timescales, the adiabatic components are subjected to Landau-Zener transitions, which reverse the sign of the topological energy flow between the two modes. These non-adiabatic effects lead to a chaotic dynamics at longer timescales.
