Probing non-classical light fields with energetic witnesses in Waveguide Quantum Electro-Dynamics

We analyze energy exchanges between a qubit and a resonant field propagating a waveguide. The joint dynamics is analytically solved within a repeated model. The work received by the qubit is defined as the unitary of the field-induced energy change. Using the same definition for the, we show that both work flows compensate each other. Focusing on the of a qubit battery by a pulse of light, we evidence that the work by a coherent field is an upper bound for the qubit ergotropy, while bound can be violated by non-classical fields, e. g. a coherent of zero- and single-photon states. Our results provide, energy-based witnesses to probe the non-classical nature of a field.