This review describes an emerging field of waveguide quantum electrodynamics (WQED) studying interaction of photons propagating in a waveguide with localized quantum emitters. In such systems, atoms and guided photons are hybridized with each other and form polaritons that can propagate along the waveguide, contrary to the cavity quantum optics setup. Emerging in such a system collective light-atom interactions result in super-and sub-radiant quantum states, that are promising for quantum information processing, and give rise to peculiar quantum correlations between photons. The review is aimed at both experimentalists and theoreticians from various fields of physics interested in the rapidly developing subject of WQED. We highlight recent groundbreaking experiments performed for different quantum platforms, including cold atoms, superconducting qubits, semiconductor quantum dots, quantum solid-state defects and at the same time provide a comprehensive introduction into various theoretical techniques to study atom-photon interactions in the waveguide.

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A detailed experimental and theoretical study of the linear and nonlinear optical properties of different Fibonacci-spaced multiple-quantum-well structures is presented. Systematic numerical studies are performed for different average spacing and geometrical arrangement of the quantum wells. Measurements of the linear and nonlinear (carrier density dependent) reflectivity are shown to be in good agreement with the computational results. As the pump pulse energy increases, the excitation-induced dephasing broadens the exciton resonances resulting in a disappearance of sharp features and reduction in peak reflectivity.

Topological quantum phases underpin many concepts of modern physics. While the existence of disorder-immune topological edge states of electrons usually requires magnetic fields, direct effects of magnetic field on light are very weak. As a result, demonstrations of topological states of photons employ synthetic fields engineered in special complex structures or external time-dependent modulations. Here, we reveal that the quantum Hall phase with topological edge states, spectral Landau levels and Hofstadter butterfly can emerge in a simple quantum system, where topological order arises solely from interactions without any fine-tuning. Such systems, arrays of two-level atoms (qubits) coupled to light being described by the classical Dicke model, have recently been realized in experiments with cold atoms and superconducting qubits. We believe that our finding will open new horizons in several disciplines including quantum physics, many-body physics, and nonlinear topological photonics, and it will set an important reference point for experiments on qubit arrays and quantum simulators.

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