Topological dynamics of adiabatic cat states

We consider a quantum topological frequency converter, realized by coupling a qubit to two slow harmonic modes. The dynamics of such a system is the quantum analog of topological pumping. Our quantum mechanical description shows that an initial state generically evolves into a superposition of two adiabatic states. The topological nature of the coupling between the qubit and the modes splits these two components apart in energy: for each component, an energy transfer at a quantized rate occurs between the two quantum modes, in opposite directions for the two components, reminiscent of the topological pumping. We denote such a superposition of two quantum adiabatic states distinguishable through measures of the modes’ energy an adiabatic cat state. We show that the topological coupling enhances the entanglement between the qubit and the modes, and we unveil the role of the quantum or Fubini-Study metric in the characterization of this entanglement.