Cooperative behavior can be understood as the enhanced response of a system of many particles with respect to isolated entities. This collective response is brought about by some mutual coupling among the entities establishing non-local and long-range correlations in space and time. In the classical world it characterizes, for instance, the dynamics of flocking birds, the swarm intelligence of fish, or the development of trends in human societies. In the quantum world, a prominent example for cooperative behavior is superradiance, where quantum interference modifies the response of an ensemble of emitters to radiation in a fundamentally different manner from the scattering properties of individual particles. This modification sets in via entanglement among the emitters induced, e.g., by the observation of outgoing photons or by controlling and tailoring their mutual interactions. Quantum cooperative behavior is present at various length and energy scales, from the subatomic to the macroscopic world, from hard x-rays to visible light down to molecular vibrations, and shows up in a vast multitude of platforms. The experimental control as well as the theoretical description is challenging, especially if noise, disorder and fluctuations are taken into account. The development of a general framework for quantum cooperativity is an open problem in physics.This mindset is the starting point of the research efforts in the CRC-TR Quantum Cooperativity of Light and Matter - QuCoLiMa. Our objective is to characterize, control and eventually utilize cooperativity at the quantum level and to understand the interplay of quantum interference and entanglement in the collective response of many-body quantum systems interacting with light. In particular, the role of the quantum properties of radiation will be explored in establishing and mediating quantum cooperative phenomena in a variety of complex matter systems. This will be accomplished either in a bottom-up approach, where the quantum cooperative behavior is analyzed as the particle number is scaled up in a controlled manner from the microscopic to the mesoscopic regime, or top-down, where in a system with a macroscopic size quantum cooperative behavior of collective degrees of freedom is identified and controlled. To this end, the QuCoLiMa brings together leading theorists and experimentalists with cutting-edge expertise in quantum optics and condensed-matter physics. The successful implementation of this research programme will lead to a systematic understanding of the buildup of spatio-temporal quantum correlations in mesoscopic light-matter systems and identify the key ingredients for exploiting robust quantum dynamics for quantum technological applications such as enhanced sensing, secure communication, and quantum computing.
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