Mixing thermal coherent states for precision and range enhancement in quantum thermometry

The unavoidable interaction between thermal environments and quantum systems typically leads to the degradation of quantum coherence, which can be fought against by reservoir engineering. We propose the realization of a special mixture of thermal coherent states by coupling a thermal bath with a two-level system that is longitudinally coupled to a resonator. We find that the state of the resonator is a special mixture of two oppositely displaced thermal coherent states, whereas the two-level system remains thermal. This observation is verified by evaluating the second-order correlation coefficient for the resonator state. Moreover, we reveal the potential benefits of employing the mixture of thermal coherent states of the resonator in quantum thermometry. In this context, the resonator functions as a probe to measure the unknown temperature of a bath mediated by a two-level system, strategically bridging the connection between the two. Our results show that the use of an ancillary-assisted probe may enhance the precision and broaden the applicable temperature range.