Cooperative quantum phenomena

Quantum cooperativity is evident in light-matter platforms where quantum emitter ensembles are interfaced with confined optical modes and are coupled via the ubiquitous electromagnetic quantum vacuum. Cooperative aspects such as dipole-dipole interactions and subradiance find applications in the design of nanoscale coherent light sources and highly-reflective quantum metasurfaces made up of hundreds of optically trapped atoms, in the implementation of topological quantum optics on subwavelength arrays of emitters, in quantum metrology and quantum information. The quick bursts of radiation from a collection of quasi-indistiguishable emitters provides an alternative approach to standard lasers by introducing superradiant lasers operating at extremely low intracavity power. This tutorial provides a set of theoretical tools to tackle the behavior responsible for the onset of cooperativity in light-matter systems by extending open quantum system dynamics methods, such as the master equation and quantum Langevin equations, to electron-photon interactions in strongly coupled and correlated quantum emitters ensembles. These analytical approaches are then also extended to frequency disordered or vibronically coupled quantum emitter ensembles with wide relevance ranging from atoms in optical lattices, quantum dots in solid state environments or molecular quantum systems.