Quantum Thermodynamics Close to the Absolute Zero

Abstract

Quantum effects often become most pronounced close to the absolute zero. The prospect of quantum technologies therefore calls for theoretical understanding and experimental control of quantum systems at ultracold temperatures. Also from a fundamental perspective, it is compelling to extend the study of thermodynamic processes to the quantum regime. This thesis examines the dynamics of quantum systems in contact with ultracold environments, associated thermodynamic quantities (like heat currents and entropy), and the measurement of temperatures using quantum sensors. Throughout the thesis, a unifying theme is moving beyond idealisations which cease to be applicable close to the absolute zero. By benchmarking against exact and numerically exact solutions, it is shown that renormalisation can improve the precision of perturbative master equations in terms of dynamics, equilibrium states, and non-equilibrium heat currents, particularly at low temperatures. It is then shown that the unitarity of the global system-bath evolution leads to a dynamics of the entanglement entropy reminiscent of that of Hawking radiation, when the bath is close to the absolute zero. Turning to practical uses of quantum technologies, the thesis makes a number of contributions to quantum metrology in the context of temperature measurements. First, it extends equilibrium probe-based thermometry to the finite coupling regime, showing that energy measurements remain optimal beyond weak coupling. Second, in the non-equilibrium case, resonant periodic modulation is shown to improve the scaling of temperature sensitivity near the absolute zero. Lastly, using Bayesian techniques, it is shown on an experiment on ultracold atoms that information-theoretic reasoning can significantly reduce the resource cost of temperature measurements.