Bending the rules of low-temperature thermometry with periodic driving

Jonas Glatthard and Luis A. Correa

Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom

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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.

Precisely measuring ultracold temperatures is a challenging task not only in practice, but also in principle. Yet it is a crucial challenge to be met in order to facilitate the progress of quantum technologies. While the fragility of quantum systems is often seen as a nuisance, it can also be used to construct more sensitive instruments — quantum sensors. In this article we study a way of boosting the sensitivity of a quantum Brownian thermometer by periodically modulating its energy. Importantly, we analyse the problem avoiding commonly used approximations which break down at low temperatures. We find that periodic modulation can substantially boost thermal sensitivity with respect to undriven probes, and also make it drop off much more slowly as the absolute zero is approached. We illustrate the method in an experimentally realisable situation — an impurity thermometer measuring the temperature of an ultracold atomic gas. We further show that the protocol is robust when it comes to lack of synchronisation between measurements and drive. Finally, we show that the negative side-effects of pumping energy into a temperature probe immersed in an ultracold sample, i.e., spurious heating, are controllably small, thus rending our proposal a practical solution for sub-nanokelvin impurity thermometry in cold atomic gases.

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