Nonequilibrium quantum working fluids: dynamics and usage

A quantum simulator is a technological concept that has been ideated with the scope of overcoming the hard computational problems that arise for simulating a quantum physical system with a classical computer. The problem is that the resources needed grow exponentially with the number of elementary constituents of quantum systems (qubits) which makes even relatively small quantum systems practically impossible to analyze in full detail. However, also ideal quantum simulators have their drawback: it seems extremely hard, if not impossible to obtain a reliable computation, which is arguably the main present challenge for the practical implementation of quantum computers. In fact, recently the acronym Noisy Intermediate-Scale Quantum (NISQ) devices has been coniated, which refers in particular also to simulators of quantum dynamics that, even if not fully solving the original problem, still give some advantage, perhaps used in hybrid schemes which involve quantum and classical resources. It is in this framework that the final goal of the present project situates: the idea is to construct a new set of tools that, once combined together, would form a quantum machine capable of simulating interesting non-equilibrium quantum physics, otherwise impossible to study with just classical computational methods. At the same time, the idea is not to construct something like a universal gate set or building a universal quantum computer, but rather to consider a thermodynamical-like setup, or in other words develop a machine based on a working (quantum) fluid. The idea is to use such a piston for improving immediately state-of-art experiments, for example through improved refrigeration limits and control over phase transitions in cold atoms. On top of that, we avoid the problem of certification of universal computation and only aim at verifying some important properties of the dynamics, e.g., field correlation functions, via improved data-analysis methods and ansatz reconstruction algorithms.

The project developed new ways to understand and control quantum systems that are far from equilibrium, with the long-term goal of making quantum cooling and energy-control processes more efficient and experimentally realistic. Quantum systems are the building blocks of emerging technologies such as quantum computers, quantum sensors and ultra-precise measurement devices. However, they are extremely difficult to control, especially when they contain many interacting particles. This project addressed this challenge by studying how energy, information and quantum correlations behave in such complex systems. One of the main outcomes was the development of new theoretical tools to identify and characterize quantum correlations in many-body systems. These correlations are a key feature that distinguishes quantum systems from ordinary physical systems. Understanding them is essential for future quantum technologies, but also for fundamental physics, because they reveal how complex quantum matter behaves. The project produced several scientific publications on this topic, including work on how entanglement and other forms of quantum correlation can be detected in systems made of many interacting particles, and in close collaboration with experiments. A second major result concerned quantum thermodynamics: the study of heat, energy and work at the quantum scale. In everyday life, cooling and engines are described by thermodynamics. At the quantum level, however, these processes can behave in unfamiliar ways. The project investigated how cooling cycles and compression processes can be designed in one-dimensional Bose-Einstein condensates, a special form of ultra-cold matter in which many atoms behave collectively as a single quantum object. This work led to publications, including some developed in close collaboration with the experimental groups, thus connecting the theoretical results of the project to viable experimental implementations, in particular of a dynamical cooling cycle in a cold-atom setup. The project also studied situations in which quantum systems are driven strongly out of equilibrium. In such cases, the system is not simply relaxing toward a stable final state, but can display rich and unexpected behavior. The research explored how memory effects, known in physics as non-Markovianity, influence this behavior, and how quantum correlations may help us recognize unusual regimes or exotic steady states. Overall, the project advanced our understanding of how complex quantum systems can be characterized and manipulated, for example cooled, compressed or more generally driven, in ways that go beyond the usual rules of classical thermodynamics. Its results are mainly fundamental, but they are relevant for the future development of quantum technologies, where precise control of energy and correlations will be essential. The project also strengthened the bridge between theory and experiment, especially through the collaboration with cold-atom experiments in Vienna.