Photonic Mode Description of the Jaynes–Cummings Hamiltonian States

ABSTRACT

Jaynes–Cummings Hamiltonian provides the elemental description of a two‐level system interacting with a photonic mode. In this work, we review the Jaynes–Cummings formalism for an electronic two‐level system. The purpose is to summarize and connect together the key theory concepts relevant for the transmission response probed typically in the experiments. The review provides a photonic mode description of the response with analytical results for several limiting cases. These expressions are useful for gaining understanding and intuition on what influences the measured response. We also connect the photonic response to several key concepts in the field: the dispersive shift in qubit readout, the quantum capacitance of semiconductor nanostructures and the effective dissipation rate of the two‐level system.