Quantum thermometry based on a cavity-QED setup

We present a quantum thermometry scheme based on a cavity-QED setup, which attains a sensitivity with Heisenberg scaling. A stream of identical two-level systems passes through a thermal bath to be tested. Each system partially thermalizes, carrying information on the temperature of the thermal bath, and it then interacts with a dissipative single-mode cavity. The Heisenberg scaling is attained from the initial coherence of each system. The systems cannot be fully thermalized by the thermal bath. The optimal interaction time between the system and the thermal bath is derived. Direct photon detection is proved to be an optimal measurement when there is no extra thermal bath in the cavity. In the case where there is an extra thermal bath in the cavity independent of the thermal bath to be tested, homodyne detection is the optimal measurement. Moreover, we show that direct photon detection obtains less information in the case where the extra thermal bath in the cavity is in thermal equilibrium with the thermal bath. However, the optimal measurement can utilize the information from the extra thermal bath to improve the estimation precision of the temperature.