Thermometry in the quantum regime: recent theoretical progress

Abstract

Controlling and measuring the temperature in different devices and platforms that operate in the quantum regime is, without any doubt, essential for any potential application. In this review, we report the most recent theoretical developments dealing with accurate estimation of very low temperatures in quantum systems. Together with the emerging experimental techniques and developments of measurement protocols, the theory of quantum thermometry will decisively impinge and shape the forthcoming quantum technologies. While current quantum thermometric methods differ greatly depending on the experimental platform, the achievable precision, and the temperature range of interest, the theory of quantum thermometry is built under a unifying framework at the crossroads of quantum metrology, open quantum systems, and quantum many-body physics. At a fundamental level, theoretical quantum thermometry is concerned with finding the ultimate bounds and scaling laws that limit the precision of temperature estimation for systems in and out of thermal equilibrium. At a more practical level, it provides tools to formulate precise, yet feasible, thermometric protocols for relevant experimental architectures. Last but not least, the theory of quantum thermometry examines genuine quantum features, like entanglement and coherence, for their exploitation in enhanced-resolution thermometry.

Tight bound on finite-resolution quantum thermometry at low temperatures

“…As a consequence of the third law of thermodynamics, or more explicitly the assumption that the heat capacity vanishes at zero temperature, the variance of the system energy must vanish at least quadratically in temperature as absolute zero is approached [31]. Hence it follows that T 2 F Q T must vanish in the low-temperature limit, and that the relative error δT 2 est /T 2 must diverge by virtue of the Cramer-Rao inequality. This relation constitutes the ultimate bound on the optimal low-temperature scaling behavior of the Fisher information, applicable for any system and for any measurement strategy.…”

“…Increasingly detailed studies of biological, chemical, and physical processes, the miniaturization of electronics, and emerging quantum technology drive a need for new thermometry techniques applicable at the nanoscale and in regimes where quantum effects become important. Many new approaches are being developed [1][2][3][4][5][6][7][8][9][10][11][12], however, the fundamental limits to precision thermometry are not yet fully understood. Here, we determine a tight bound on the best possible precision with which temperature can be estimated in cold quantum systems, which accounts for limitations due to imperfect measurements.…”

Non-orthogonal bases for quantum metrology

“…Under certain regularity assumptions, the QFI matrix encodes the ultimate precision bounds on the estimation of unknown parameters encoded in a density matrix (know as quantum Cramer-Rao bounds), while the SLDs and their commutators determine whether such bounds may be saturated with physically realizable measurements [5,6]. The associated applications are plenty, including phase and frequency estimation [4,[7][8][9][10][11][12][13][14][15][16][17], estimation of noise parameters [18][19][20][21][22][23], joint estimation of unitary and/or noisy parameters [24][25][26][27][28][29][30][31], sub-wavelength resolution of optical sources [32][33][34][35][36][37][38], nano-scale thermometry [39][40][41][42][43][44][45], and estimation of Hamiltonian parameters in the presence of phase-transitions [46][47][48]. The most common approach for ...…”

Heat current control in trapped Bose–Einstein Condensates

“…Finally, it is desirable to investigate scenarios where the system is nonlinear, which raises difficulties in solving the problem analytically, nonetheless, it offers the opportunity to rectify heat even without periodic derivation. Moreover, motivated by the results in [75,76] where the squeezing in position of a single impurity embedded in a BEC was used to measure the temperature of the BEC in the sub-nano-Kelvin regime, one may study if the present two-particle set-up can be used for applications in quantum thermometry.…”