# Simulating Anisotropic quantum Rabi model via frequency modulation

## TL;DR

This paper proposes a feasible method to simulate the anisotropic quantum Rabi model in circuit QED using frequency modulation, enabling exploration of ultra-strong and deep-strong coupling regimes with tunable parameters.

## Contribution

It introduces a novel scheme for implementing the anisotropic quantum Rabi model via periodic frequency modulation in circuit QED systems, allowing tunable coupling strengths.

## Key findings

- Effective Hamiltonian accurately describes the system in ultrastrong coupling regimes
- Periodic driving can induce ultra-strong and deep-strong coupling regimes
- The scheme is extendable to multi-qubit systems and applications in quantum states and gates

## Abstract

Anisotropic quantum Rabi model is a generalization of quantum Rabi model, which allows its rotating and counter-rotating terms to have two different coupling constants. It provides us with a fundamental model to understand various physical features concerning quantum optics, solid-state physics, and mesoscopic physics. In this paper, we propose an experimental feasible scheme to implement anisotropic quantum Rabi model in a circuit quantum electrodynamics system via periodic frequency modulation. An effective Hamiltonian describing the tunable anisotropic quantum Rabi model can be derived from a qubit-resonator coupling system modulated by two periodic driving fields. All effective parameters of the simulated system can be adjusted by tuning the initial phases, the frequencies and the amplitudes of the driving fields. We show that the periodic driving is able to drive a coupled system in dispersive regime to ultrastrong coupling regime, and even deep-strong coupling regime. The derived effective Hamiltonian allows us to obtain pure rotating term and counter-rotating term. Numerical simulation shows that such effective Hamiltonian is valid in ultrastrong coupling regime, and stronger coupling regime. Moreover, our scheme can be generalized to the multi-qubit case. We also give some applications of the simulated system to the Schr\"{o}dinger cat states and quantum gate generalization. The presented proposal will pave a way to further study the stronger anisotropic Rabi model whose coupling strength is far away from ultrastrong coupling and deep-strong coupling regimes in quantum optics.