Enhancing low-temperature quantum thermometry via sequential measurements

We propose a sequential measurement protocol for accurate low-temperature estimation based on Ramsey interferometry. The resulting correlated outputs significantly enhance the low-temperature precision compared to that of the independent measurement scheme. This enhancement manifests a Heisenberg scaling of the signal-to-noise ratio for small measurement numbers $N$. Detailed analysis reveals that the final precision is determined by the pair correlation of the sequential outputs induced by the low-frequency noise of the thermal sample, which produces a dependence ${N}^{2}$ on the signal-to-noise ratio. Remarkably, we find that quantum thermometry within the sequential protocol functions as a high-resolution quantum spectroscopy of the thermal noise, underscoring the pivotal role of the sequential measurements in enhancing the spectral resolution and the temperature-estimation precision. Our methodology signifies the role of the temporal correlation induced by the thermal sample in low-temperature quantum thermometry, which represents an advancement in low-temperature measurement.