# The Physical Spectrum of a Driven Jaynes–Cummings Model

## TL;DR

This paper studies how external driving affects the spectral properties of a quantum system involving an atom and a cavity, revealing how coherent field displacement influences the observed spectra.

## Contribution

The paper introduces a framework to analyze the physical spectrum of a driven Jaynes–Cummings model using time-dependent Hamiltonian transformations and derives closed-form correlation functions.

## Key findings

- External driving modifies the atomic spectral response with controllable frequency shifts and asymmetric line shapes.
- A specific driving regime cancels the cavity field's initial amplitude, recovering the standard vacuum Rabi splitting.
- Spectral features are shown to arise from coherent field displacement rather than changes in atom–cavity coupling.

## Abstract

We analyze the time-dependent physical spectrum of a driven Jaynes–Cummings model in which both the two-level system and the quantized cavity mode are subject to coherent classical driving. The time-dependent Hamiltonian is mapped, via well-defined unitary transformations, onto an effective stationary Jaynes–Cummings form. Within this framework, we derive closed-form expressions for the two-time correlation functions of both the atomic and field operators. These correlation functions are subsequently used to evaluate the time-dependent physical spectrum according to the Eberly–Wódkiewicz definition, which properly accounts for finite spectral resolution and transient emission dynamics. We show that the external driving leads to substantial modifications of the atomic spectral response, including controllable frequency shifts and asymmetric line shapes. Importantly, we identify a regime in which the driving parameters are chosen such that the coherent displacement induced in the cavity field exactly cancels out the initial coherent amplitude. In this limit, the system dynamics reduce to that of an effectively vacuum-initialized Jaynes–Cummings model, and the standard vacuum Rabi splitting is recovered. This behavior provides a clear and physically transparent interpretation of the spectral features as arising from coherent field displacement rather than from modifications of the underlying atom–cavity coupling.