# Circuit QED with qutrit: coupling three or more atoms via virtual photon exchange

## TL;DR

This paper proposes a model for circuit QED systems with qutrits that enables coherent, virtual-photon-mediated interactions among multiple atoms, including those in different cavities, with potential applications in quantum information processing.

## Contribution

It introduces a novel scheme for coupling multiple atoms via virtual photons in circuit QED, including multi-cavity interactions, expanding capabilities for quantum information tasks.

## Key findings

- Coherent exchange of excitation among three or more atoms is achievable.
- The model operates with negligible population in the third atomic level and low photon numbers.
- The scheme is feasible with current experimental parameters.

## Abstract

We present a model to describe a generic circuit QED system which consists of multiple artificial three-level atoms, namely qutrits, strongly coupled to a cavity mode. When the state transition of the atoms disobey the selection rules the process that does not conserve the number of excitations can happen determinatively. Therefore, we can realize coherent exchange interaction among three or more atoms mediated by the exchange of virtual photons. In addition, we generalize the one cavity mode mediated interactions to the multi-cavity situation, providing a method to entangle atoms located in different cavities. Using experimental feasible parameters, we investigate the dynamics of the model including three cyclic-transition three-level atoms, for which the two lowest-energy levels can be treated as qubits. Hence, we have found that two qubits can jointly exchange excitation with one qubit in a coherent and reversible way. In the whole process, the population in the third level of atoms is negligible and the cavity photon number is far smaller than 1. Our model provides a feasible scheme to couple multiple distant atoms together, which may find applications in quantum information processing.