Thermometry with a Dissipative Heavy Impurity

Improving the measurement precision of low temperature is significant in fundamental science and advanced quantum technology application. However, the measurement precision of temperature $T$ usually diverges as $T$ tends to 0. Here, by utilizing a heavy impurity to measure the temperature of a Bose gas, we obtain the Landau bound to precision $\delta^2 T\propto T^2$ to avoid the divergence. Moreover, when the initial momentum of the heavy impurity is fixed and non-zero, the measurement precision can be $\delta^2 T\propto T^3$ to break the Landau bound. We derive the momentum distribution of the heavy impurity at any moment and obtain the optimal measurement precision of the temperature by calculating the Fisher information. As a result, we find that enhancing the expectation value of the initial momentum can help to improve the measurement precision. In addition, the momentum measurement is the optimal measurement of the temperature in the case of that the initial momentum is fixed and not equal to 0. The kinetic energy measurement is the optimal measurement in the case of that the expectation value of the initial momentum is 0. Finally, we obtain that the temperatures of two Bose gases can be measured simultaneously. The simultaneous measurement precision is proportional to $T^2$ when two temperatures are close to $T$.