# Ultrastrong Jaynes-Cummings Model

## TL;DR

This paper introduces a scheme to realize an ultrastrong Jaynes-Cummings model by modulating system frequencies, enabling ultrafast quantum operations and exploring quantum phase transitions without reducing coupling strength.

## Contribution

It presents a novel method to achieve the ultrastrong JC Hamiltonian through frequency modulation, suppressing counter-rotating terms while maintaining strong coupling.

## Key findings

- Counter-rotating terms can be fully suppressed in both modulation regimes.
- Ultrastrong JC interaction enables ultrafast quantum operations.
- Potential for demonstrating quantum phase transitions across the deep-strong coupling point.

## Abstract

We propose a reliable scheme to realize the ultrastrong Jaynes-Cummings (JC) model by simultaneously modulating the resonance frequencies of the two-level system and the bosonic mode in the ultrastrong quantum Rabi model. We find that in both the high- and low-frequency modulation regimes, the counter-rotating terms can be completely suppressed without reducing the coupling strength of the rotating-wave terms, and hence the ultrastrong JC Hamiltonian is achieved. The ultrastrong JC interaction can not only be used to implement ultrafast quantum operations, but also will open up a new route to the demonstration of quantum phase transition associated with the JC Hamiltonian across the deep-strong coupling point. Some discussions on the experimental implementation of this scheme with circuit-QED systems are presented.