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.
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.
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 effects can find applications, among other areas, in topological quantum optics, in quantum metrology, or in quantum information.This tutorial provides a set of theoretical tools to tackle the behavior responsible for the onset of cooperativity 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-emitter ensembles.The methods are illustrated on a wide range of current research topics such as the design of nanoscale coherent-light sources, highly reflective quantum metasurfaces, or low intracavity power superradiant lasers.
The interaction between light and matter has captivated physicists for centuries, from early studies of vision and refraction in ancient Greece to the development of quantum mechanics and quantum electrodynamics in the past century. While the response of a single quantum emitter to light is well understood, the radiative properties of an ensemble of closely spaced emitters are far more intricate. Coupling to a shared electromagnetic environment induces coherent and dissipative interactions between emitters, giving rise to a collective response that cannot be captured by treating them independently. In the regime of few excitations, the system hosts delocalized subradiant states, that is, coherent superpositions that are largely decoupled from the electromagnetic field and thus decay at suppressed rates. While this weak coupling makes subradiant states attractive for quantum technologies, it also renders them difficult to manipulate. At higher excitation densities, the intrinsic nonlinearity of emitters and the exponential growth of the Hilbert space make theoretical and numerical descriptions of the system and its dynamics increasingly challenging. This thesis explores two fundamental questions: How can subradiant and dark states be selectively accessed and harnessed for practical applications in quantum technologies? And how can interacting ensembles of quantum emitters be efficiently simulated to uncover their many-body physics? The first part of the thesis develops protocols for controlling and addressing dark states in free-space and waveguide-coupled atomic arrays, demonstrating their utility in quantum storage and the deterministic generation of entangled photonic states. Incorporating atomic motion, we further show that collective subradiant states can enhance cooling in dense atomic arrays, offering new avenues for controlling motional dynamics. In the second part, we introduce cumulant expansions of the equations of motion as a powerful tool to analytically and numerically investigate collective decay in the many-body regime. We first examine the collective decay of fully excited atomic arrays in free space, characterizing the onset and scaling of the superradiant burst across different geometries. In collaboration with experiments on ultracold erbium atoms in optical lattices, we provide the first direct observations of many-body collective effects in free-space ordered arrays, including early-time superradiant bursts, late-time subradiant tails, and the emergence of atomic correlations throughout the dynamics. Finally, we theoretically and numerically explore the transient formation of multi-excitation subradiant states, and demonstrate how the existence of multiple dissipation channels suppresses steady-state superradiance in extended arrays.
Dipole-coupled subwavelength quantum emitter arrays respond cooperatively to external light fields as they may host collective delocalized excitations (a form of excitons) with super- or subradiant character. Deeply subwavelength separations typically occur in molecular ensembles, where in addition to photon-electron interactions, electron-vibron couplings and vibrational relaxation processes play an important role. We provide analytical and numerical results on the modification of super- and subradiance in molecular rings of dipoles including excitations of the vibrational degrees of freedom. While vibrations are typically considered detrimental to coherent dynamics, we show that molecular dimers or rings can be operated as platforms for the preparation of long-lived dark superposition states aided by vibrational relaxation. In closed ring configurations, we extend previous predictions for the generation of coherent light from ideal quantum emitters to molecular emitters, quantifying the role of vibronic coupling onto the output intensity and coherence.
Reduced abstract. This Thesis explores emergent cooperative phenomena in collective light-matter systems. We study ensembles of interacting quantum emitters coherently driven by a laser field and coupled to photonic structures, focusing on the hybrid description of emitters dressed by light. The interplay among quantum emitters, coherent driving, and photonic environments reveals a rich landscape of cooperative effects. While single-emitter dressing has been widely studied, we address collective phenomena in two non-identical emitters modelled as two-level systems. Strong interaction forms a dimer exhibiting superradiant and subradiant states, with two-photon resonances directly connecting ground and doubly excited states. This nonlinear process, central to the Thesis, enables new regimes of cooperative light-matter physics. Analytical studies show how interactions reshape observables such as emission intensity, photon statistics, and spectra, offering implications for quantum metrology. The sensitivity of two-photon processes to emitter distance and driving strength enables high-precision sensing and sub-wavelength imaging. Unexpectedly, we find that off-resonant virtual states may gain population through dissipation, redefining their role in open systems. To capture this, we develop a hierarchical adiabatic elimination method for metastable dynamics. We also analyze entanglement in emitters coupled to a lossy cavity, identifying five mechanisms, including the frequency-resolved Purcell effect introduced here. This selective enhancement stabilizes cooperative states and enables scalable entanglement. Our models, tailored to solid-state platforms such as quantum dots and molecular aggregates, address challenges like inhomogeneous broadening and decoherence, demonstrating the feasibility of harnessing cooperative light-matter effects for quantum technologies.
Coupling between quantum emitters and modes of light is foundational to studies of quantum systems. Coherent interactions between matter and light have greatly advanced the development of quantum technologies. When an ensemble of atoms interacts with light that is confined within a cavity---a resonator for photons---light also mediates atom-atom interactions, leading to collective phenomena that cannot be extrapolated from microscopic behaviors. Understanding how interactions among quantum particles lead to macroscopic phenomena, such as phase transitions and breaking of symmetries, remains a challenge in modern physics. In this dissertation, I present results addressing this challenge in the context of mesoscopic arrays of optical-tweezer-trapped atoms interfaced with a high-finesse optical cavity. In particular, the physics we investigate arises from the collective scattering of light. Utilizing the ability to place atoms with nanometer-scale precision, we engineer superradiant and subradiant states, where control over interference of the emission from multiple atoms leads to collectively enhanced or suppressed amounts of scattered light. Building on this work, we investigate the emergence of optomechanical self-organization, mediated by superradiance in the cavity electromagnetic field. By coupling atoms to the same cavity mode, the atoms exert forces on one another through the exchange of photons, leading them to autonomously order themselves spatially. We characterize mesoscopic fluctuations and their effect on symmetry-breaking dynamics associated with self-organization. Finally, we extend this framework to theoretically investigate how the phase of the atom-cavity coupling can be altered to generate higher symmetries. Our analysis reveals first-order phase transitions and instabilities induced by non-reciprocal forces. Altogether, this work establishes a path towards realizing mesoscopic systems of complex phases of matter in cavity quantum electrodynamics with unprecedented programmability.
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.