Thermometry with a dissipative heavy impurity

Abstract

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 zero. Here, by utilizing a heavy impurity to measure the temperature of a Bose gas, we obtain the Landau bound to precision δ2T∝T2 to avoid the divergence. When the initial momentum of the heavy impurity is close to be fixed and nonzero, the measurement precision can be δ2T∝T3 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 increasing the expectation value P0 and reducing the variance Δ/2 of the initial momentum can help to improve the measurement precision. Moreover, under certain conditions, Δ/P0 is a relevant parameter, the smallness of which helps improve the thermometric precision of the probe. In addition, the momentum measurement is the optimal measurement of the temperature in the case that the initial momentum is close to be fixed and not equal to zero. The kinetic energy measurement is the optimal measurement in the case that the expectation value of the initial momentum is close to zero. Finally, we obtain that the temperatures of two Bose gases can be measured simultaneously. The simultaneous measurement precision is proportional to T2 when two temperatures are close to T. Published by the American Physical Society 2024