Optimal nonequilibrium thermometry in Markovian environments

Abstract

What is the minimum time required to take the temperature? In this paper, we solve this question for any process where temperature is inferred by measuring a probe (the thermometer) weakly coupled to the sample of interest, so that the probe's evolution is well described by a quantum Markovian master equation. Considering the most general control strategy on the probe (adaptive measurements, arbitrary control on the probe's state and Hamiltonian), we provide bounds on the achievable measurement precision in a finite amount of time, and show that in many scenarios these fundamental limits can be saturated with a relatively simple experiment. We find that for a general class of sample-probe interactions the scaling of the measurement uncertainty is inversely proportional to the time of the process, a shot-noise like behaviour that arises due to the dissipative nature of thermometry. As a side result, we show that the Lamb shift induced by the probe-sample interaction can play a relevant role in thermometry, allowing for finite measurement resolution in the low-temperature regime (more precisely, the measurement uncertainty decays polynomially with the temperature as T → 0, in contrast to the usual exponential decay with T −1 ). We illustrate these general results for (i) a qubit probe interacting with a bosonic sample, where the role of the Lamb shit is highlighted, and (ii) a collective superradiant coupling between a N -qubit probe and a sample, which enables a quadratic decay with N 2 of the measurement uncertainty.

Uninformed Bayesian Quantum Thermometry

“…In practice however, thermal equilibrium between the reservoir and the probes may not always be achievable [24][25][26], or even desirable [27][28][29]. In fact, the transient dynamics induced by repeated finite-time collisions with nonequilibrium quantum probes can result in enhanced precision compared to equilibrium thermometry [30][31][32], once again quantified by the Fisher information.…”

Operational significance of nonclassicality in nonequilibrium Gaussian quantum thermometry

“…In this procedure, known as equilibrium thermometry, the initial state of the probe does not play a role and therefore the potential of quantum resources in the state preparation is not used. Nonetheless, the impact of initial probe states in a nonequilibrium (dynamical) scenario can be important and has been the subject of previous studies [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Continuous variable systems in Gaussian states are the relevant model in many physical platforms for thermometry such as quantum optics, quantum gases, Josephson junctions and mechanical resonators [19]. In this context, a framework for using Gaussian measurements was recently proposed with some preliminary results at thermal equilibrium [20].…”

“…In this context, a framework for using Gaussian measurements was recently proposed with some preliminary results at thermal equilibrium [20]. On the other hand, in a recent paper [18], the limits of nonequilibrium thermometry in the Markovian environments was established. These results, due to the infinite dimension of the Hilbert space for continuous variable systems, can be unphysical unless one restricts to a limited energy scenario.…”

“…Nonetheless, Ref. [18] predicts optimality of highly nonGaussian probes, which are hard to prepare, for thermometry. Therefore, of particular interest is to understand the limits and advantages of probe states that are readily available in the laboratory, such as Gaussian states, in nonequilibrium thermometry.…”

Thermometric machine for ultraprecise thermometry of low temperatures

“…Temperature measurements via small probes [5,10,11,18,[29][30][31][32][33][34][35] constitute a more practical or convenient approach for thermometry in many physical setupts, and particularly in many-body systems, where direct measurements are destructive or impossible in practice [7,14,18,29,36]. For probe-based thermometry, the best low-temperature scaling reported to date corresponds to a Brownian probe of frequency ω 0 → 0, which gives rise to a constant (i.e.…”