Quantum simulation of bound-state-enhanced quantum metrology

Quantum metrology explores quantum effects to improve the measurement accuracy of some physical quantities beyond the classical limit. However, due to the interaction between the system and the environment, the decoherence can significantly reduce the accuracy of the measurement. Many methods have been proposed to restore the accuracy of the measurement in the long-time limit. Recently, it has been found that the bound state can assist the error-free measurement and recover the $t^{-1}$ scaling [K. Bai, Z. Peng, H. G. Luo, and J. H. An, Phys. Rev. Lett. 123, 040402 (2019)]. Here, by using $N$-qubits, we propose a method to simulate the open quantum dynamics of the hybrid system including one atom and coupled resonators. We find that the error of the measurement can vanish as the time increases due to the existence of the bound state. By both analytical and numerical simulations, we prove the $t^{-1}$ scaling of the measurement error can be recovered when there is a bound state in the hybrid system. Interestingly, we observe that there are perfect oscillations which can be used for the evaluation of the atomic transition frequency. For a finite-$N$, the duration of the perfect oscillations doubles as one more qubit is involved.