Quantum mechanics is fundamentally governed by the Schrödinger equation, which is linear in the wave function. Nevertheless, quantum systems can exhibit highly nonlinear behavior in their observable dynamics. Such nonlinearities can emerge from many-body interactions, nonlinear coupling mechanisms, or the interplay between coherent evolution and dissipation. In the collective limit, microscopic quantum interactions can give rise to qualitatively new macroscopic behavior. Open quantum systems provide a rich setting for such phenomena, as environmental coupling introduces dissipation and fluctuations that compete with coherent dynamics and can alter the steady states and dynamical phases of a system. Combined with nonlinear interactions, this competition can produce behavior with no direct counterpart in conventional linear light--matter systems. In this thesis, I investigate such collective phenomena through nonlinear two-photon light--matter interactions and engineered quantum reservoirs. I first investigate the driven--dissipative two-photon Dicke model and demonstrate the emergence of a dissipative superradiant phase transition. The quadratic light--matter interaction introduces distinct stability requirements in the presence of dissipation. In particular, two-photon loss stabilizes the superradiant phase, allowing its steady states and critical behavior to be characterized. I next investigate photon blockade and transient quadrature-squeezed radiation in the two-photon Tavis--Cummings model. I show that two-photon interactions collectively enhance photon blockade and squeezing, in contrast to the conventional one-photon model, where the effective nonlinearity diminishes in the collective limit. Finally, I consider collective behavior induced by reservoir engineering. Two spatially separated open quantum systems without direct coherent interaction can undergo a nonlocal quantum phase transition when coupled to correlated quantum reservoirs. Remarkably, the transition is hidden from local observables and emerges only through nonlocal correlations and collective observables. Together, these results demonstrate how nonlinear interactions and engineered dissipation can reshape collective behavior in open quantum systems.
Quantum mechanics is fundamentally governed by the Schrödinger equation, which is linear in the wave function. Nevertheless, quantum systems can exhibit highly nonlinear behavior in their observable dynamics. Such nonlinearities can emerge from many-body interactions, nonlinear coupling mechanisms, or the interplay between coherent evolution and dissipation. In the collective limit, microscopic quantum interactions can give rise to qualitatively new macroscopic behavior. Open quantum systems provide a rich setting for such phenomena, as environmental coupling introduces dissipation and fluctuations that compete with coherent dynamics and can alter the steady states and dynamical phases of a system. Combined with nonlinear interactions, this competition can produce behavior with no direct counterpart in conventional linear light--matter systems. In this thesis, I investigate such collective phenomena through nonlinear two-photon light--matter interactions and engineered quantum reservoirs. I first investigate the driven--dissipative two-photon Dicke model and demonstrate the emergence of a dissipative superradiant phase transition. The quadratic light--matter interaction introduces distinct stability requirements in the presence of dissipation. In particular, two-photon loss stabilizes the superradiant phase, allowing its steady states and critical behavior to be characterized. I next investigate photon blockade and transient quadrature-squeezed radiation in the two-photon Tavis--Cummings model. I show that two-photon interactions collectively enhance photon blockade and squeezing, in contrast to the conventional one-photon model, where the effective nonlinearity diminishes in the collective limit. Finally, I consider collective behavior induced by reservoir engineering. Two spatially separated open quantum systems without direct coherent interaction can undergo a nonlocal quantum phase transition when coupled to correlated quantum reservoirs. Remarkably, the transition is hidden from local observables and emerges only through nonlocal correlations and collective observables. Together, these results demonstrate how nonlinear interactions and engineered dissipation can reshape collective behavior in open quantum systems.
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.
The Dicke model is a paradigmatic quantum-optical model describing the interaction of a collection of two-level systems with a single bosonic mode. Effective implementations of this model made it possible to observe the emergence of superradiance, i.e., cooperative phenomena arising from the collective nature of light-matter interactions. Via reservoir engineering and analogue quantum simulation techniques, current experimental platforms allow us not only to implement the Dicke model but also to design more exotic interactions, such as the two-photon Dicke model. In the Hamiltonian case, this model presents an interesting phase diagram characterized by two quantum criticalities: a superradiant phase transition and a spectral collapse, that is, the coalescence of discrete energy levels into a continuous band. Here, we investigate the effects of both qubit and photon dissipation on the phase transition and on the instability induced by the spectral collapse. Using a mean-field decoupling approximation, we analytically obtain the steady-state expectation values of the observables signaling a symmetry breaking, identifying a first-order phase transition from the normal to the superradiant phase. Our stability analysis unveils a very rich phase diagram, which features stable, bistable, and unstable phases depending on the dissipation rate.
Interactions govern the emergence of collective behaviour in classical and quantum many-body systems. While conservative interactions are well known to generate nonlinear phenomena ranging from self-trapping to pattern formation, it remains largely unexplored whether purely dissipative -- i.e., non-Hermitian -- interactions can give rise to similarly rich dynamics and nontrivial system states. Here, we experimentally realise tuneable non-Hermitian interactions in two coupled condensates of light confined within a dye-filled double-well microcavity. Local coupling to molecular reservoirs generates the effective dissipative photon interactions. We show that the interplay between coherent tunnelling and interactions stabilises limit-cycle oscillations, a hallmark of nonlinear dynamics traditionally associated with Hermitian nonlinearities. By tuning the reservoir coupling, we map out the dynamical phase diagram comprising stable fixed points and limit cycles, thereby demonstrating direct control over the interaction strength. Our experimentally validated model reveals both supercritical and subcritical Hopf bifurcations, giving rise to hysteresis, bistability and excitability. These results validate dissipative interactions as a mechanism for organising collective nonlinear dynamics in driven-dissipative systems and pave the way towards exploring nonequilibrium many-body physics through controlled dissipation.
In this work we give an overview on a couple of decades of theoretical and experimental research on the many-body physics of driven-dissipative quantum fluids of light in optical cavities. These systems consist of a large number of photons enclosed in a cavity device where spatial confinement induces a finite photon mass and the Kerr optical nonlinearity of the cavity material mediates finite photon-photon interactions. Differently from standard Bose gases of material particles like liquid Helium or ultracold atomic gases, photons are inevitably subject to radiative and/or non-radiative losses, which must be compensated by some pumping mechanism. As a result, the properties of the steady state are not imposed by a thermal equilibrium condition, but are determined by a dynamical interplay of pumping and losses. Among the many collective phenomena that are observed in these systems, we focus here on the collective excitations around the steady state and we characterize the impact of the driven-dissipative nature of the gas on their properties, in particular on their dispersion relation. Different pumping configurations give very different behaviors: a specific discussion is provided for the most important configurations used in the experiments. Observable consequences of the various forms of the dispersion -gapped, gapless, sonic, band-sticking, diffusive Goldstone- are illustrated with a special eye towards their consequences on the superfluidity properties. We conclude the article with a presentation of a few research avenues that we personally find most exciting for the next years, namely the osbervable consequences of the concurrently superfluid and solid nature of supersolid states of light and the collective dynamics of quantum correlated states of strongly interacting photon gases in the presence of strong nonlinearities, in particular Mott insulator states.
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.
In the vicinity of ground-state phase transitions quantum correlations can display nonanalytic behavior and critical scaling. This signature of emergent collective effects has been widely investigated within a broad range of equilibrium settings. However, under nonequilibrium conditions, as found in open quantum many-body systems, characterizing quantum correlations near phase transitions is challenging. Moreover, the impact of local and collective dissipative processes on quantum correlations is not broadly understood. Here we consider as a paradigmatic setting the superradiant phase transition of the open quantum Dicke model and characterize quantum and classical correlations across the phase diagram. We develop an approach to quantum fluctuations which allows us to show that local dissipation, which cannot be treated within the commonly employed Holstein-Primakoff approximation, rather unexpectedly leads to an enhancement of collective quantum correlations, and to the emergence of a nonequilibrium superradiant phase in which the bosonic and spin degrees of freedom of the Dicke model are entangled.