Nonequilibrium Quantum Matter beyond Unitary Dynamics

The field of quantum simulation holds immense promise for exploring new physical phenomena, however unlocking its full potential requires a paradigm shift. Modern quantum simulators naturally allow to measure a broad class of multi-body correlation functions for which we are lacking adequate theory, and operate in an uncharted regime where the system is subject to intrinsic unitary dynamics and driving, as well as nonunitary dynamics such as dissipation, projective or weak measurements, and feedback. In contrast, traditional theory often considers approximately unitary dynamics and simple observables. The goal of the QMbeyondU grant is to establish the paradigm of nonequilibrium quantum matter beyond unitary dynamics, uncovering quantum phenomena where nonunitary dynamics is essential. The proposed theoretical framework relies on a synergy between quantum condensed matter physics, quantum information theory, and atomic-molecular-optical physics and consists of three work packages (WP). The first two WPs will address (I) a description of quantum density matrices and toolbox for measuring observables such as entanglement, which cannot be efficiently accessed in most general settings, and (II) a theory of physical phenomena in quantum matter enabled by the interplay of intrinsic interactions and non-unitary dynamics, such as entangled nonequilibrium steady states and phase transitions, universal aspects of quantum quenches, and phenomena realized in monitored quantum systems with feedback. Results from WPs (I)-(II) are synthesised in WP (III) to guide various atomic and solid-based quantum simulation platforms in realizations of physical phenomena theoretically described in WP (II), and their validation using measurement tools from WP (I).The theory delivered by this project will uncover universal behaviors of nonequilibrium quantum systems beyond unitary dynamics and will help advance our ability to efficiently store and process quantum information.