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We present analytic solutions to the evolution in generalized tight-binding models, which consider complex first-neighbor couplings with equal amplitude and arbitrary phases. Our findings provide a powerful tool for efficiently calculating expectation values and correlations within the system, which are otherwise difficult to compute numerically. We apply our results to relevant examples in quantum light manipulation using N-port linear couplers, describing the evolution of single(multi)-mode squeezing, single photon added (subtracted) Gaussian states, and second-order site-to-site photon correlations. Significantly, our analytic results outperform standard numerical calculations. Our study paves the way for a comprehensive mathematical framework describing the spatial evolution of quantum states across a wide range of physical systems governed by the tight-binding model., Comment: 18 pages, 7 figures. Includes Supplementary Material

Optical nonlinearities are fundamental in several types of optical information processing protocols. However, the high laser intensities needed for implementing phase nonlinearities using conventional optical materials represent a challenge for nonlinear optics in the few-photon regime. We introduce an infrared cavity quantum electrodynamics (QED) approach for imprinting nonlinear phase shifts on individual THz pulses in reflection setups, conditional on the input power. Power-dependent phase shifts on the order of $ 0.1\, \pi$ can be achieved with femtosecond pulses of only a few $\mu$W input power. The proposed scheme involves a small number of intersubband quantum well transition dipoles evanescently coupled to the near field of an infrared resonator. The field evolution is nonlinear due to the dynamical transfer of spectral anharmonicity from material dipoles to the infrared vacuum, through an effective dipolar chirping mechanism that transiently detunes the quantum well transitions from the vacuum field, leading to photon blockade. We develop analytical theory that describes the dependence of the imprinted nonlinear phase shift on relevant physical parameters. For a pair of quantum well dipoles, the phase control scheme is shown to be robust with respect to inhomogeneities in the dipole transition frequencies and relaxation rates. Numerical results based on the Lindblad quantum master equation validate the theory in the regime where the material dipoles are populated up to the second excitation manifold. In contrast with conventional QED schemes for phase control that require strong light-matter interaction, the proposed phase nonlinearity works best in weak coupling, increasing the prospects for its experimental realization using current nanophotonic technology., Comment: 25 pages, 5 figures

Nanoscale infrared (IR) resonators with sub-diffraction limited mode volumes and open geometries have emerged as new platforms for implementing cavity quantum electrodynamics (QED) at room temperature. The use of infrared (IR) nano-antennas and tip nanoprobes to study strong light-matter coupling of molecular vibrations with the vacuum field can be exploited for IR quantum control with nanometer and femtosecond resolution. In order to accelerate the development of molecule-based quantum nano-photonic devices in the mid-IR, we develop a generally applicable semi-empirical quantum optics approach to describe light-matter interaction in systems driven by mid-IR femtosecond laser pulses. The theory is shown to reproduce recent experiments on the acceleration of the vibrational relaxation rate in infrared nanostructures, and also provide physical insights for the implementation of coherent phase rotations of the near-field using broadband nanotips. We then apply the quantum framework to develop general tip-design rules for the experimental manipulation of vibrational strong coupling and Fano interference effects in open infrared resonators. We finally propose the possibility of transferring the natural anharmonicity of molecular vibrational levels to the resonator near-field in the weak coupling regime, to implement intensity-dependent phase shifts of the coupled system response with strong pulses. Our semi-empirical quantum theory is equivalent to first-principles techniques based on Maxwell's equations, but its lower computational cost suggests its use a rapid design tool for the development of strongly-coupled infrared nanophotonic hardware for applications ranging from quantum control of materials to quantum information processing., Comment: 18 pages, 7 figures

The localization of light in flat-band lattices has been recently proposed and experimentally demonstrated in several configurations, assuming a classical description of light. Here, we study the problem of light localization in the quantum regime. We focus on quasi one-dimensional and two-dimensional lattices which exhibit a perfect flat-band inside their linear spectrum. Localized quantum states are constructed as eigenstates of the interaction Hamiltonian with a vanishing eigenvalue and a well defined total photon number. These are superpositions of Fock states with probability amplitudes given by positive as well as negative square roots of multinomial coefficients. The classical picture can be recovered by considering poissonian superpositions of localized quantum states with different total photon number. We also study the separability properties of flat band quantum states and apply them to the transmission of information via multi-core fibers, where these states allow for the total passive suppression of photon crosstalk and exhibit robustness against photon losses. At the end, we propose a novel on-chip setup for the experimental preparation of localized quantum states of light for any number of photons., Comment: 12 pages, 5 figures

We experimentally study the transport prop- erties of dipolar and fundamental modes on one di- mensional (1D) coupled waveguide arrays. By carefully modulating a wide optical beam, we are able to effec- tively excite dipolar or fundamental modes to study discrete diffraction (single-site excitation) and gaussian beam propagation (multi-site excitation plus a phase gradient). We observe that dipolar modes experience a larger spreading area due to an effective larger coupling constant, which is found to be more than two times larger than the one for fundamental modes. Addition- ally, we study the effect of non-diagonal disorder and find that while fundamental modes are already trapped on a weakly disorder array, dipoles are still able to prop- agate across the system., Comment: 6 pages, 4 figures

We study the polarization properties of elliptical femtosecond-laser-written waveguides arrays. A new analytical model is presented to explain the asymmetry of the spatial transverse profiles of linearly polarized modes in these waveguides. This asymmetry produces a polarization dependent coupling coefficient, between adjacent waveguides, which strongly affects the propagation of light in a lattice. Our analysis explains how this effect can be exploited to tune the final intensity distribution of light propagated through the array, and links the properties of a polarizing beam splitter in integrated optical circuits to the geometry of the waveguides., Comment: 6 pages, 6 figures V2: Section V rewritten