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

## TL;DR

This paper compares continuous- and discrete-mode coherent feedback in the Jaynes-Cummings model, highlighting their qualitative differences in dynamics, population trapping, and spectral features, with implications for understanding dissipative versus coherent processes.

## Contribution

It provides a detailed analysis of the fundamental differences between continuous- and discrete-mode feedback in quantum systems, emphasizing their distinct dynamical behaviors and spectral signatures.

## Key findings

- Continuous-mode feedback leads to single-delay dynamics and stabilizes Rabi oscillations.
- Discrete-mode feedback results in population trapping not seen in continuous modes.
- Spectral analysis reveals characteristic differences between the two feedback types.

## Abstract

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.