Bending the rules of low-temperature thermometry with periodic driving

Abstract

There exist severe limitations on the accuracy of low-temperature thermometry, which poses a major challenge for future quantum-technological applications. Low-temperature sensitivity might be manipulated by tailoring the interactions between probe and sample. Unfortunately, the tunability of these interactions is usually very restricted. Here, we focus on a more practical solution to boost thermometric precision – driving the probe. Specifically, we solve for the limit cycle of a periodically modulated linear probe in an equilibrium sample. We treat the probe-sample interactions exactly and hence, our results are valid for arbitrarily low temperatures T and any spectral density. We find that weak near-resonant modulation strongly enhances the signal-to-noise ratio of low-temperature measurements, while causing minimal back action on the sample. Furthermore, we show that near-resonant driving changes the power law that governs thermal sensitivity over a broad range of temperatures, thus `bending' the fundamental precision limits and enabling more sensitive low-temperature thermometry. We then focus on a concrete example – impurity thermometry in an atomic condensate. We demonstrate that periodic driving allows for a sensitivity improvement of several orders of magnitude in sub-nanokelvin temperature estimates drawn from the density profile of the impurity atoms. We thus provide a feasible upgrade that can be easily integrated into low-T thermometry experiments.

Optimal thermometers with spin networks

“…However, as we show in appendix D.1, there exist solutions that are mathematically sub-optimal but numerically indistinguishable in terms of C, with much more favorable scaling of the Hamiltonian parameters. In fact, even when limiting b to be bounded by a constant, it is possible to achieve the desired quadratic scaling of C, arbitrarily close to the optimal value equation (19). These solutions feature a finite b, whose precise value becomes irrelevant, and a linear scaling of a ∝ N, which admits a relative precision ∝ N −1 (see appendices C, D.1 and 'constrained' dots in figure 7(a)).…”

“…Relevant examples include nanodiamonds acting as thermometers of living cells [7,8], nanoscale electron calorimeters based on the absorption of single quanta of energy [9][10][11], and single-atom thermometry probes [12][13][14]. At the theoretical level, progress has been made in the understanding of ultraprecise thermometry via quantum probes in equilibrium [15][16][17][18][19][20][21][22][23] and out-of-equilibrium states [24][25][26][27][28][29][30][31][32][33][34]. Crucially, the energy structure of optimal thermometers has been revealed [35][36][37][38], suggesting that the precision can grow quadratically with the number of constituents [39].…”

Probe thermometry with continuous measurements

“…The Cramér-Rao bound on the true relative square deviation (12) also bounds Bayesian figures of merit. In particular, if we insert an unbiased estimator into equation (27), we obtain the inequality…”

“…The right-most panel of figure 5 shows that the bias leads to the estimated error D R [ T] under estimating the true error D R,T * [ T]. This ratio will approach one for more trajectories in the average according to equation (27). This is important from an experimental point of view as it shows that in a temperature range where the bias is the main contribution to the error, the actual accuracy of the temperature estimate is lower than would be expected from the variance of the posterior when not enough iterations of the experiment are The blue points and shaded region represents the results for the adaptive strategy when the measurement strength is λ = 25, here new trajectories need to be generated because the gap of the two level system changes in each step.…”

“…Relevant experimental realization of probe thermometry include single-atom probes for ultracold gases [7][8][9], NV centers acting as thermometers of living cells [10,11], and nanoscale electron calorimeters [12][13][14]. Theoretically, much progress has been achieved on characterizing the fundamental precision limits of probe thermometry in frequentist and Bayesian approaches [15][16][17][18][19][20][21][22][23], the precision scaling at ultralow temperatures [24][25][26][27][28], the impact of strong coupling and correlations [29][30][31][32][33][34], measurement back action [35,36], as well as enhanced sensing via non-equilibrium probes [37][38][39][40][41][42][43][44][45][46]. While providing remarkable progress on our understanding of thermometry, previous works are based on the assumption that the probe is measured and subsequently reset or discarded.…”