Enhancement of the Quantum Coherence in a Hierarchical Environment System by Weak Measurement and Weak Measurement Reversal

The quantum coherence of a two-qubit system in which each qubit is coupled to its own hierarchical environment is studied. The effect of the hierarchical environment is explored in order to improve the coherence effectively. It is discovered that the dynamics of coherence can be manipulated by the number N of the second-layer cavities (mn$m_{n}$), the coupling strengths omega(0), omega, kappa, respectively for the qubit-cavity (m(0)), nearest-neighbor, and m(0)-mn$m_{n}$ cavities. It depends also on the decay rate Gamma of second-layer cavities. Furthermore, an effective scheme for enhancing coherence is proposed by using weak measurement and weak measurement reversal. The explicit conditions of the optimal measurement strengths to improve the coherence comparatively are derived. It is seen that the final stable value of the coherence is independent of the number N of second-layer cavities but is related to the weak measurement strength m when the coupling strength between two nearest-neighbor cavities is taken into account.