Bath-engineering technique for criticality-based quantum metrology with amplitude noise

Quantum critical systems are extremely sensitive to parameter variation near the critical point. Moreover, the derivatives with respect to the order parameter may exhibit divergence. This quantum criticality is widely utilized to enhance the performance of quantum metrology. In this study, we take the dissipative quantum Rabi model (QRM) as an example and use the bath-engineering technique to simulate the dissipative QRM to explore the impact of the quantum criticality on the quantum metrology under dissipation. We numerically calculate the dynamics of the inverse variance of the dissipative QRM around the critical point by using the quantum-simulation method and compare our results with those obtained by the numerically exact hierarchical equations of motion (HEOM). Our simulations show that in the case of the strong dissipation or the high temperature, the precision does not exhibit divergence when approaching the point of the quantum phase transition, and the enhancement of quantum metrology by quantum criticality is relatively limited. More importantly, the quantum-simulation method based on the bath-engineering technique can accurately simulate the dynamical evolution of the critical system and consumes significantly fewer resources as compared with the HEOM. Thus, it can be an alternative solution for investigating the dynamical evolution of larger critical systems for quantum metrology.