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Nanolasers operating at low power levels are strongly affected by intrinsic quantum noise, affecting both intensity fluctuations and laser coherence. Starting from semi-classical rate equations and making a simple hypothesis for the phase of the laser field, a simple stochastic model for the laser quantum noise is suggested. The model is shown to agree quantitatively with quantum master equations for microscopic lasers with a small number of emitters and with classical Langevin equations for macroscopic systems. In contrast, neither quantum master equations nor classical Langevin equations adequately address the mesoscopic regime. The stochastic approach is used to calculate the linewidth throughout the transition to lasing, where the linewidth changes from being dominated by the particle-like nature of photons below threshold to the wave-like nature above threshold, where it is strongly influenced by index fluctuations enhancing the linewidth., Comment: 6 pages, 4 figures. Submitted for PRL

In this paper, we introduce a numerical framework designed to solve problems within the emerging field of Waveguide Quantum Electrodynamics (WQED). The framework is based on collision quantum optics, where a localized quantum system interacts sequentially with individual time-bin modes. This approach provides a physically intuitive model that allows researchers familiar with tools such as QuTiP in Python, Quantum Optics Toolbox for Matlab, or QuantumOptics.jl in Julia to efficiently set up and execute WQED simulations. Despite its conceptual simplicity, we demonstrate the framework's robust ability to handle complex WQED scenarios. These applications include the scattering of single- or two-photon pulses by quantum emitters or cavities, as well as the exploration of non-Markovian dynamics, where emitted photons are reflected back, thereby introducing feedback mechanisms., Comment: 14 pages, 7 figures

While the semiconductor quantum dot placed in a solid-state material allows for deterministic emission of single photons, the photon indistinguishability is strongly influenced by the intrinsic coupling to lattice vibrations, phonons, of the solid-state environment. This work investigates the phonon-induced decoherence for a quantum dot placed in the one-dimensional system of a homogeneous cylindrical nanowire. Such a structure supports multiple longitudinal phonon branches, and we consider both a linear and a quadratic coupling of the emitter to these modes. Under a polaron approach, we initially derive an analytical expression for the 1D pure dephasing rate, which leads to a reduced pure dephasing rate compared with bulk. By implementing these results into a full cavity quantum electrodynamic model, we demonstrate that multimode coupling is necessary to correctly predict the indistinguishability in a 1D system, which may otherwise be significantly underestimated., Comment: 21 pages, 14 figures

It is shown that the intensity quantum noise of a single-emitter nanolaser can be accurately computed by adopting a stochastic interpretation of the standard rate equation model under the only assumption that the emitter excitation and photon number are stochastic variables with integer values. This extends the validity of rate equations beyond the mean-field limit and avoids using the standard Langevin approach, which is shown to fail for few emitters. The model is validated by comparison to full quantum simulations of the relative intensity noise and second-order intensity correlation function, g(2)({\tau} ). Surprisingly, even when the full quantum model displays vacuum Rabi oscillations, which are not accounted for by rate equations, the intensity quantum noise is correctly predicted by the stochastic approach. Adopting a simple discretization of the emitter and photon populations, thus, goes a long way in describing quantum noise in lasers. Besides providing a versatile and easy-to-use tool for modeling a new generation of nanolasers with many possible applications, these results provide insight into the fundamental nature of quantum noise in lasers., Comment: Revised and resubmitted for review

Phonon interactions are inevitable in cavity quantum electrodynamical systems based on solid-state emitters or fluorescent molecules, where vibrations of the lattice or chemical bonds couple to the electronic degrees of freedom. Due to the non-Markovian response of the vibrational environment, it remains a significant theoretical challenge to describe such effects in a computationally efficient manner. This is particularly pronounced when the emitter-cavity coupling is comparable to or larger than the typical phonon energy range, and polariton formation coincides with vibrational dressing of the optical transitions. In this Article, we consider four non-Markovian perturbative master equation approaches to describe such dynamics over a broad range of light-matter coupling strengths and compare them to numerically exact reference calculations using a tensor network. The master equations are derived using different basis transformations and a perturbative expansion in the new basis is subsequently introduced and analyzed. We find that two approaches are particularly successful and robust. The first of these is suggested and developed in this Article and is based on a vibrational dressing of the exciton-cavity polaritons. This enables the description of distinct phonon-polariton sidebands that appear when the polariton splitting exceeds the typical phonon frequency scale in the environment. The second approach is based on a variationally optimized polaronic vibrational dressing of the electronic state. Both of these approaches demonstrate good qualitative and quantitative agreement with reference calculations of the emission spectrum and are numerically robust, even at elevated temperatures, where the thermal phonon population is significant., Comment: 17 pages, 10 figures

Phonon interactions in solid-state photonics systems cause intrinsic quantum decoherence and often present the limiting factor in emerging quantum technology. Due to recent developments in nanophotonics, exciton-cavity structures with very strong light-matter coupling rates can be fabricated. We show that in such structures, a new regime emerges, where the decoherence is completely suppressed due to decoupling of the dominant phonon process. Using a numerically exact tensor network approach, we perform calculations in this non-perturbative, non-Markovian dynamical regime. Here, we identify a strategy for reaching near-unity photon indistinguishability and also discover an interesting phonon-dressing of the exciton-cavity polaritons in the high-Q regime, leading to multiple phonon sidebands when the light-matter interaction is sufficiently strong., Comment: Accepted for publication in Physical Review B