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We present a theoretical analysis of nearly monochromatic light propagation through a gas of two-level atoms using the Heisenberg-Langevin equation method. Our focus is on the evolution of the photon annihilation operator and its impact on the second-order correlation function, $g^{(2)}({\tau})$, with particular emphasis on photon antibunching behavior. The model accounts for both open and closed atomic system approximations, including Doppler broadening and the influence of pump field detuning. We derive expressions that reproduce known results from scattering theory and extend the analysis to complex systems, such as inhomogeneously broadened media. The theoretical predictions are compared with experimental data from a waveguide QED platform, which show good agreement and thereby demonstrate the power of our approach. Future work will explore extensions to even more complex systems and other quantum light characteristics for practical applications., Comment: 19 pages, 10 figures

We model and investigate the collective nonlinear optical response of an ensemble of two-level emitters that are weakly coupled to a single-mode waveguide. Our approach generalizes the insight that photon-photon correlations in the light scattered by a single two-level emitter result from two-photon interference to the case of many emitters. Using our model, we study different configurations for probing the nonlinear response of the ensemble, e.g., through the waveguide or via external illumination, and derive analytical expressions for the second-order quantum coherence function, $g^{(2)}(\tau)$, as well as for the squeezing spectrum of the output light in the waveguide, $S_\theta(\omega)$. For the transmission of resonant guided light, we recover the same predictions as previously made with far more involved theoretical models when analyzing experimental results regarding $g^{(2)}(\tau)$ (Prasad et al. [1]) and $S_\theta(\omega)$ (Hinney et al. [2]). We also study the transmission of light that is detuned from the transition of the two-level emitter, a situation that we recently studied experimentally (Cordier et al. [3]). Our model predictions show how the collectively enhanced nonlinear response of weakly coupled emitters can be harnessed to generate non-classical states of light using ensembles ranging from a few to many emitters.

We report on the realization and characterization of a novel magic-wavelength nanofiber-based two-color optical dipole trap that allows us to generate a periodic one-dimensional array of trapping sites with a spacing significantly smaller than half of the resonant wavelength of the cesium D2-line. To this end, we launch a blue-detuned partial standing wave and two red-detuned light fields through the nanofiber. We demonstrate the trapping of atoms in the array and characterize the resulting trap configuration by measuring the trap frequencies in three directions and observe good agreement with theoretical predictions. The implementation of this nanofiber-based optical interface with magic trapping wavelengths and sub-$\lambda/2$ spacing is an important step towards the exploration of novel collective radiative effects such as selective radiance in 1D atomic arrays., Comment: 5 pages, 4 figures

The interaction of light with a single two-level emitter is the most fundamental process in quantum optics, and is key to many quantum applications. As a distinctive feature, two photons are never detected simultaneously in the light scattered by the emitter. This is commonly interpreted by saying that a single two-level quantum emitter can only absorb and emit single photons. However, it has been theoretically proposed that the photon anti-correlations can be thought to arise from quantum interference between two possible two-photon scattering amplitudes, which one refers to as coherent and incoherent. This picture is in stark contrast to the aforementioned one, in that it assumes that the atom even has two different mechanisms at its disposal to scatter two photons at the same time. Here, we validate the interference picture by experimentally verifying the 40-year-old conjecture that, by spectrally rejecting only the coherent component of the fluorescence light of a single two-level atom, the remaining light consists of photon pairs that have been simultaneously scattered by the atom. Our results offer fundamental insights into the quantum-mechanical interaction between light and matter and open up novel approaches for the generation of highly non-classical light fields., Comment: 9 pages, 7 figures, updated Methods section