Achieving Heisenberg scaling in low-temperature quantum thermometry

Abstract: We investigate correlation-enhanced low temperature quantum thermometry. Recent studies have revealed that bath-induced correlations can enhance the low-temperature estimation precision even starting from an uncorrelated state. However, a comprehensive understanding of this enhancement remains elusive. Using the Ramsey interferometry protocol, we illustrate that the estimation precision of $N$ thermometers sparsely coupled to a common low-temperature bath can achieve the Heisenberg scaling in the low-temperature regime with only a $\pi/2$ rotation of the measurement axis, in contrast to the standard Ramsey scheme. This result is based on the assumption that interthermometer correlations are induced exclusively by low-frequency noise in the common bath, a condition achievable in practical experimental scenarios. The underlying physical mechanism is clarified, revealing that the Heisenberg scaling arises from the intrinsic nature of the temperature, which is associated solely with the fluctuation of thermal noise. In contrast to the paradigm of independent thermometers, our proposed scheme demonstrates a significant enhancement in precision for low-temperature measurement, making it suitable for precisely measuring the temperature of ultracold systems.