Non-equilibrium dynamics of long-range interacting quantum systems and their applications to quantum metrology

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Quantum metrology uses quantum effects such as interference, entanglement, or very generally non-classical quantum states to increase the sensitivity of the measurement of physical quantities. Interactions play a central role, as on the one hand they are needed to create the non-classical states, and on the other hand they can be measured themselves with a precision that scales favorably with the number of particles. The project aims at this second, so far little explored possibility and will investigate different non-equilibrium states in dynamically driven open quantum systems with long-range interactions and explore their usefulness for quantum metrology.Theoretically, we will study adiabatic and non-adiabatic (quenched) dynamics of the interacting many-body systems and examine their utility for increasing the sensitivity of measurements of external parameters, such as electromagnetic fields. We will elucidate the role of underlying phase-space structures for the sensitivity and develop and implement efficient quantum algorithms for simulating open complex quantum systems. Experimentally, we will employ two-dimensional clouds of cold trapped atoms coupled by resonant lasers to the highly excited Rydberg states in the presence of controlled electric fields. Small and fast changes of the electrical field permit dynamical tuning of the corresponding long-range dipole-dipole interaction strength. This will allow us to realise different kinds of dynamical driving schemes and to tune the relaxation and ionisation rates. Using an ion microscope with high spatiotemporal resolution, we will perform precise measurements of the spatial and temporal dynamics and correlations in this driven interacting quantum system. A proof-of-principle experiment for measuring the electric field with long-range interacting Rydberg atoms will be performed.