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We introduce a nanowire-based photonic crystal waveguide system capable of controllably mediating the photon coupling between two quantum dots which are macroscopically separated. Using a rigorous Green-function-based master equation approach, our two-dot system is shown to provide a wide range of interesting quantum regimes. In particular, we demonstrate the formation of long-lived entangled states and study the resonance fluorescence spectrum which contains clear signatures of the coupled quantum dot pair. Depending upon the operating frequency, one can obtain a modified Mollow triplet spectrum or a Mollow nonuplet, namely a spectrum with nine spectral peaks. These multiple peaks are explained in the context of photon-exchange-mediated dressed states. Results are robust with respect to scattering loss, and spatial filtering via propagation allows for each quantum dot's emission to be observed individually.

The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir computing relaxes the need for optimization of intra-network parameters, and is thus particularly attractive for near-term hardware-efficient quantum implementations. However, the complete description of practical quantum reservoir computers requires accounting for their placement in a quantum measurement chain, and its conditional evolution under measurement. Consequently, training and inference has to be performed using finite samples from obtained measurement records. Here we describe a framework for reservoir computing with nonlinear quantum reservoirs under continuous heterodyne measurement. Using an efficient truncated-cumulants representation of the complete measurement chain enables us to sample stochastic measurement trajectories from reservoirs of several coupled nonlinear bosonic modes under strong excitation. This description also offers a mathematical basis to directly compare the information processing capacity of a given physical reservoir operated across classical and quantum regimes. Applying this framework to the classification of Gaussian states of systems that are part of the same measurement chain as the quantum reservoir computer, we uncover its working principles and provide a detailed analysis of its performance as a function of experimentally-controllable parameters. Our results identify the vicinity of bifurcation points as presenting optimal nonlinear processing regimes of an oscillator-based quantum reservoir. The considered models are directly realizable in modern circuit QED experiments, while the framework is applicable to more general quantum nonlinear reservoirs.

We introduce a new platform for realizing on-chip quantum electrodynamics using photoniccrystal waveguide structures comprised of periodic nanowire arrays with embedded semiconductor quantum dots to act as a quantum light sources. These nanowire-based structures, which can now be fabricated with excellent precision, are found to produce waveguide Purcell factors exceeding 100 and on-chip β factors up to 99%. We investigate the fundamental optical properties of photonic crystal waveguides and finite-size structures, using both photonic band structure calculations and rigorous Green function computations which allow us to obtain the modal properties and the local density of photon states. A comparison with slab-based photonic crystals is also made and we highlight a number of key advantages in the nanowire system, including the potential to reduce extrinsic scattering losses and produce high theoretical Purcell factors and β factors on-chip. We also demonstrate that these structures exhibit rich photonic Lamb shifts over broadband frequencies.

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