Novel non-equilibrium states of matter in periodically driven spin systems: from time crystals to integrated thermal machines

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Timing is key to the operation of cyclic machines. A typical car engine, for example, uses a periodic four-step process to convert chemical energy into motive power: a fuel-air mixture is first injected into a cylinder and then compressed by a moving piston; igniting the fluid leads to an explosion that pushes the piston to the bottom of the cylinder, thus driving the axle of the car; the cycle is completed as the piston returns to its initial position and the burned fluid is exhausted from the cylinder. To run this process smoothly and reliably, the engine requires a precise external clock to determine the instants of fuel injection, ignition, and exhaustion.Recently, there has been a lot of interest in many-body systems called time crystals that exhibit order far from thermal equilibrium. Time crystals are characterised by emergent, persistent, robust oscillations that break time-translation symmetry and form a "crystal in time", just like standard crystalline materials break translation invariance in space. If these systems are provided with a continuous flow of energy, e.g. in the form of photons, an oscillating current or electromagnetic field can be generated and can act as an autonomous clock. That clock can be used to sustain the periodic motion of a microscopic piston and replace the classical working fluid of an engine. These new time-crystal engines are self-controlled devices, whose efficiency and constancy of operation are not limited by the precision of external clocks or feedback loops. As a result, they are promising candidates to become the motors of future nano-machines that require ultra-precise energy input, e.g. quantum sensors.With this proposal, we seek support for a new theory-experiment initiative, based at the University of Nottingham in close collaboration with the University of Tübingen. The aim will be to develop the fundamental understanding of the central aspects of time crystals, e.g. their robustness in the presence of long-range interactions and dissipation, and to explore new avenues towards their experimental realisation and their potential application in future technologies. One of the central goals is to establish viable strategies for the design and optimization of thermal machines that utilize the exceptional properties of time-crystalline phases for mechanical power generation and thermodynamic purposes in general, including cooling and the high-accuracy pumping of charge and matter on small length and energy scales. We will focus on the fundamental theory and on two complementary experimental platforms of periodically driven spin systems: solid-state nanomagnetism (with both theory and experiments carried out in Nottingham), and arrays of interacting Rydberg atoms (with theory carried out in Nottingham and experiments via our partnership with Tübingen, supported by an awarded BW Foundation grant). Our work will allow a new perspective on solid-state and atomic physics for uncovering and exploiting complex collective behaviour.Our team comprises researchers with ample experience in experimental and theoretical atomic physics, statistical physics, quantum thermodynamics, and condensed matter, who have made central contributions to open quantum systems, cold atomic systems, quantum magnets, optomechanical systems, and other topics related to this proposal. This joint project will allow us to work hand-in-hand so that new theoretical ideas can quickly be tested in experiments which directly feed back into theoretical developments.Quantum technologies are expected to shape our century in a similar way as the industrial revolution changed 19th and 20th century. Quantum time-crystal machines have the potential to become the motors of this exciting development. They will not move our future cars, but they might well determine the working rhythm of our future quantum computers, sensors, and communication devices.