Comparison between continuous- and discrete-mode coherent feedback for the Jaynes-Cummings model

Using the example of the Jaynes-Cummings model, we present a comparison between time-delayed coherent feedback mediated by reservoirs with continuous and discrete mode structures and work out their qualitative differences. In contrast to the discrete-mode case, the continuous-mode case results in the well-known single-delay dynamics which can, e.g., stabilize Rabi oscillations. The discrete-mode case, however, shows population trapping, not present in the continuous-mode model. Given these differences, we discuss the cavity output spectra and show how these characteristic properties are spectrally identifiable. This work demonstrates the fundamental difference between the continuous-mode case, which represents a truly dissipative mechanism, and the discrete-mode case that is in principle based on a coherent excitation exchange process.