# Two-photon exchange interaction from Dicke Hamiltonian under parametric modulation

## TL;DR

This paper demonstrates how to engineer two-photon exchange interactions in a circuit QED system with multiple qubits by using parametric modulation, providing both analytical and numerical insights for experimental realization.

## Contribution

It introduces a method to generate two-photon exchange interactions in multi-qubit circuit QED systems through parametric modulation, with analytical and numerical validation.

## Key findings

- Two-photon exchange interaction can be engineered via frequency modulation.
- Analytic expressions are derived for weak atom-field coupling.
- Numerical simulations confirm experimental feasibility.

## Abstract

We consider the nonstationary circuit QED architecture in which a single-mode cavity interacts with N>1 identical qubits, and some system parameters undergo a weak external perturbation. It is shown that in the dispersive regime one can engineer the two-photon exchange interaction by adjusting the frequency of harmonic modulation to (approximately) $2|\Delta _{-}|$, where $\Delta _{-}$ is the average atom--field detuning. Closed analytic description is derived for the weak atom-field coupling regime, and numeric simulations indicate that the phenomenon can be observed in the present setups.