Spectral response of a nonlinear Jaynes-Cummings model

TL;DR

This paper derives analytical expressions for the spectral response of a nonlinear Jaynes-Cummings model, revealing asymmetric spectra and similarities to experimental results in circuit QED, advancing understanding of light-matter interactions.

Contribution

It provides the first analytical time-dependent spectral response for a nonlinear Jaynes-Cummings model using deformed field operators, highlighting spectral asymmetry due to nonlinearity.

Findings

Spectral response is asymmetric with nonlinear coupling.

Long-time response resembles experimental circuit QED results.

Resonant conditions are impossible for finite excitations.

Abstract

The Jaynes-Cummings quantum optics model allows us to understand the dialogue between light and matter at its most fundamental level, which is crucial for advancements in quantum science and technology. Several generalizations of the model have long been proposed, emphasizing their dynamic behavior but paying less attention to their spectroscopy. Here, we obtain analytical expressions of the time-dependent spectral response of a nonlinear Jaynes-Cummings model based on deformed field operators. We show that the long-time response of the resulting nonlinear cavity field resembles the one experimentally obtained in the strong-dispersive regime of circuit quantum electrodynamics. The spectrum is intrinsically asymmetric with the nonlinear coupling, a signature of the impossibility of getting resonant conditions for finite field excitations.