# Spectrum of the Dicke model in a superconducting qubit-oscillator system

## TL;DR

This paper analyzes the transmission spectrum of a superconducting circuit implementing the Dicke model, identifying spectral signatures that distinguish normal and superradiant phases, especially through bias variation at fixed coupling.

## Contribution

It introduces a method to detect superradiant phase signatures in superconducting circuits by analyzing spectral lines as a function of bias, without needing to vary coupling strength.

## Key findings

- Normal phase shows two spectral lines.
- Superradiant phase exhibits four spectral lines.
- Spectral signatures are observable with low decoherence and parameter fluctuations.

## Abstract

We calculate the transmission spectrum of a superconducting circuit realization of the Dicke model and identify spectroscopic features that can serve as signatures of the superradiant phase. In particular, we calculate the resonance frequencies of the system as functions of the bias term, which is usually absent in studies on the Dicke model but is commonly present in superconducting qubit circuits. To avoid over-complicating the proposed circuit, we assume a fixed coupling strength. This situation precludes the possibility of observing signatures of the phase transition by varying the coupling strength across the critical point. We show that the spectrum obtained by varying the bias point under fixed coupling strength can contain signatures of the normal and superradiant phases: in the normal phase one expects to observe two spectral lines, while in the superradiant phase four spectral lines are expected to exist close to the qubits' symmetry point. Provided that parameter fluctuations and decoherence rates are sufficiently small, the four spectral lines should be observable and can serve as a signature of the superradiant phase.