Harnessing the nonlinear response of a medium is essential for applications including frequency conversion and light amplification, as well as for the generation of quantum many-body correlations of light or matter. However, achieving these effects typically requires high drive intensities and thick samples, which induce undesired heating effects that typically suppress quantum correlations. In this work, we demonstrate that atom-thin arrays of quantum emitters exhibit a robust nonlinear response even at arbitrarily weak drive intensities. This discovery challenges the long-held assumption that weakly driven ensembles behave classically; instead, we reveal that subradiant states provide a dominant nonlinear contribution that persists in the low-intensity limit. Using a Dynamical Mean-Field Theory (DMFT) approach, we predict that these nonlinearities generate a quantum-correlated steady state composed of interacting pairs of subradiant excitations, characterized by long-range correlations and multi-mode squeezing. Our findings establish a new frontier for nonlinear quantum optics at minimal power, and provide a scalable protocol for preparing multimode squeezing, offering potential for applications in quantum metrology.
Harnessing the nonlinear response of a medium is essential for applications including frequency conversion and light amplification, as well as for the generation of quantum many-body correlations of light or matter. However, achieving these effects typically requires high drive intensities and thick samples, which induce undesired heating effects that typically suppress quantum correlations. In this work, we demonstrate that atom-thin arrays of quantum emitters exhibit a robust nonlinear response even at arbitrarily weak drive intensities. This discovery challenges the long-held assumption that weakly driven ensembles behave classically; instead, we reveal that subradiant states provide a dominant nonlinear contribution that persists in the low-intensity limit. Using a Dynamical Mean-Field Theory (DMFT) approach, we predict that these nonlinearities generate a quantum-correlated steady state composed of interacting pairs of subradiant excitations, characterized by long-range correlations and multi-mode squeezing. Our findings establish a new frontier for nonlinear quantum optics at minimal power, and provide a scalable protocol for preparing multimode squeezing, offering potential for applications in quantum metrology.
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.
Typical schemes for generating correlated states of light require a highly nonlinear medium that is strongly coupled to an optical mode. However, unavoidable dissipative processes, which cause photon loss and blur nonlinear quantum effects, often impede such methods. In this talk, I will report on our experimental implementation of the opposite approach. Using a strongly dissipative, weakly coupled medium, we generate and study strongly correlated states of light. Specifically, we study the transmission of resonant light through an ensemble of non-interacting atoms that weakly couple to a guided optical mode. Dissipation removes uncorrelated photons while preferentially transmitting highly correlated photons, created through collectively enhanced nonlinear interactions. As a result, the transmitted light constitutes a strongly correlated many-body state of light, revealed in the second-order correlation function. The latter exhibits strong antibunching or bunching, depending on the optical depth of the atomic ensemble. The demonstrated mechanism opens a new avenue for generating nonclassical states of light and for exploring correlations of photons in non-equilibrium systems using a mix of nonlinear and dissipative processes.
Quantum emitters coupled to nonlinear one-dimensional waveguides provide a route for quantum-state engineering by utilizing parametric gain accumulation along with modified waveguide-mediated interactions. Since the accumulated squeezing depends on propagation distance, different emitter separations can experience different effective gain, making the spatial structure of connected quantum correlations a central feature of the dynamics. Here we investigate the transient and steady-state connected correlations of emitter arrays coupled to a parametrically driven waveguide. Using an effective master equation for nonlinear waveguide QED, we analyze second- and third-order connected correlations as functions of the squeezing parameter and interparticle distance. In the two-emitter limit, accumulated squeezing drives excitation buildup and generates a nonzero connected second-order correlation. For many-emitter arrays, tuning the interparticle distance switches the dominant local second-order correlation between the bulk and boundary regions, and enables an analogous spatial control of genuine third-order connected correlations. In the steady state, the averaged second-order correlation exhibits sign-changing and nonmonotonic behavior in the squeezing--interparticle distance parameter space, whereas the third-order connected correlation is strongly enhanced by increasing the squeezing parameter. These results identify nonlinear waveguide QED as a tunable platform for spatially controlling connected quantum correlations and provide insights into correlation engineering in open quantum optical arrays. We further show that this local contrast remains visible in both odd and even number of atomic arrays.
Enhancing interactions in many-body quantum systems, while protecting them from environmental decoherence, is at the heart of many quantum technologies. Waveguide quantum electrodynamics is a promising platform for achieving this, as it hosts infinite-range interactions and decoherence-free subspaces of quantum emitters. However, as coherent interactions between emitters are typically washed out in the wavelength-spacing regime hosting decoherence-free states, coherent control over the latter becomes limited, and many-body Hamiltonians in this important regime remain out of reach. Here we show that by incorporating emitter arrays with nonlinear waveguides hosting parametric gain, we obtain a unique class of many-body interaction Hamiltonians with coupling strengths that increase with emitter spacing, and persist even for wavelength-spaced arrays. We then propose to use these Hamiltonians to coherently generate decoherence-free states directly from the ground state, using only global squeezing drives, without the need for local addressing of individual emitters. Interestingly, we find that the dynamics approaches a unitary evolution in the limit of weak intrawaveguide squeezing, and we discuss potential experimental realizations of this effect. Our results pave the way towards coherent control protocols in waveguide quantum electrodynamics, with applications including quantum computing, simulation, memory, and nonclassical light generation.
The achievement of sufficiently fast interactions between two optical fields at the few-photon level would provide a key enabler for a broad range of quantum technologies. One critical hurdle in this endeavor is the lack of a comprehensive quantum theory of the generation of nonlinearities by ensembles of emitters. Distinct approaches applicable to different regimes have yielded important insights: i) a semiclassical approach reveals that, for many-photon coherent fields, the contributions of independent emitters add independently allowing ensembles to produce strong optical nonlinearities via EIT; ii) a quantum analysis has shown that in the few-photon regime collective coupling effects prevent ensembles from inducing these strong nonlinearities. Rather surprisingly, experimental results with around twenty photons are in line with the semi-classical predictions. Theoretical analysis has been fragmented due to the difficulty of treating nonlinear many-body quantum systems. Here we are able to solve this problem by constructing a powerful theory of the generation of optical nonlinearities by single emitters and ensembles. The key to this construction is the application of perturbation theory to perturbations generated by subsystems. This theory reveals critical properties of ensembles that have long been obscure. The most remarkable of these is the discovery that quantum effects prevent ensembles generating single-photon nonlinearities only within the rotating-wave regime; outside this regime single-photon nonlinearities scale as the number of emitters. The theory we present here also provides an efficient way to calculate nonlinearities for arbitrary multi-level driving schemes, and we expect that it will prove a powerful foundation for further advances in this area.
High-harmonic generation (HHG) is a prototypical strong-field process in which intense light drives matter to emit radiation at integer multiples of the driving frequency. Extending HHG into the quantum-optical regime offers new opportunities to probe and control strongly nonlinear light-matter interactions using nonclassical states of light. Yet describing this regime requires a fully quantum treatment of the correlated electron-photon dynamics, which becomes computationally challenging for broadband, strongly squeezed fields. Here we solve the quantum-electrodynamical dynamics of a two-level system driven by bright squeezed vacuum in a converged multimode Hilbert space. Both the driving field and emitted harmonics are fully quantized, with the light-matter interaction treated nonperturbatively. This enables direct access to the multimode quantum state and its higher-order correlations beyond semiclassical sampling or perturbative descriptions. We show that squeezed-vacuum driving produces harmonic emission with qualitatively distinct second- and third-order photon correlations compared with coherent excitation. Moreover, back-action from the driven emitter strongly reshapes the incident squeezed field, generating pronounced Wigner-function negativities that evolve on attosecond timescales. Our results establish a fully quantum framework for broadband strong-field dynamics with squeezed light and provide a route to predicting and interpreting quantum-HHG experiments and their extension to more complex emitters.