Critical Quantum Metrology in the Non-Linear Quantum Rabi Model

The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.

Automated summary

The quantum Rabi model with linear coupling exhibits a second-order phase transition at zero mode frequency, enhancing quantum metrology in few-body systems. However, the inclusion of a nonlinear coupling term in the model leads to a first-order-like phase transition at finite frequency, resulting in higher measurement precision and avoiding the detrimental slowing-down effect near the critical point. When a bias term is added, the system can be used as a fluxmeter or magnetometer in circuit QED platforms.