Many-body quantum engines

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Thermodynamics, the science of energy transformation, of heat and work, has always played an important and special role in physics. Its formulation in the 19th century was triggered by practical questions of energy balance and efficiency during the industrial revolution. Since then, the laws of thermodynamics have survived every subsequent scientific revolution of the 20th century, including quantum theory and relativity. A surprising connection to information theory came with Maxwell's daemon, a being imagined to be capable of making hot particles move from a cold to a hot thermostat, thus contrary to the normal hot-to-cold heat flow. The information-physics connection was made stronger in the 20th century by the works of Szilard and Landauer, who designed engines powered by information, and Bennett who exorcised the Maxwell's daemon paradox.As the physical dimension of engines get smaller and smaller, strong thermal fluctuations affect the amount of work produced and a new stochastic thermodynamics has been developed in response. Heat, work and entropy are not just functionals of a thermodynamic process anymore, but, because of random fluctuations, they become stochastic variables. The fundamental laws of thermodynamics are recovered when looking at average values. Thanks to the tremendous advance in the experimental realisations of quantum technologies applications of thermodynamics with quantum devices are foreseeable in the near future. In the new emerging field of quantum thermodynamics a considerable effort is being devoted to the design and analysis of thermal machines and refrigerators operating at the quantum level and the theoretical foundation of thermodynamics from quantum principles, including the definition of thermodynamic quantities like heat and work, with inputs from quantum information theory. There are currently several attempts at realising quantum machines, capable of producing work, with a few degrees of freedom, e.g. a single particle. Although quantum thermodynamics is developing very fast, it is not yet clear how to scale up such machines to systems composed of many quantum particles. This achievement would enable practical applications of quantum machines as autonomous devices capable of correcting errors and imperfections in quantum simulators and quantum computers as well as serving as assemblers of quantum materials at the nanoscale.The overarching challenge of this project is to theoretically design thermal machines, that use as working substance an ensemble of many interacting quantum particles. More specifically, we will consider a network of interacting quantum particles, quantum harmonic oscillators and localised spins, externally driven and coupled to thermal and non-equilibrium reservoirs. The network will be arranged in order to transform heat into mechanical work, thus operating as a thermal engine, or to employ external work to extract heat from a cold reservoir for the realisation of a refrigerator. As a further step, we will optimise the geometry and architecture of the network itself to deliver work and refrigeration with the largest power and efficiency. Since it would be a formidable task to optimise all the tens of parameters of the Hamiltonian, we will employ machine learning techniques to this end. Finally, an important fraction of the project will be done in collaboration with two experimental groups working on ultracold atoms with the aim of designing thermal machines that can be realised with their current experimental setups. In collaboration with the J. Sherson (Aarhus) we will design an engine whose working substance and reservoirs are realised with ultracold atoms in optical lattice potentials. In collaboration with T. Donner (Zürich) we will design a refrigerator made of two atomic Bose-Einstein condensates that interact with the common mode of an optical cavity.