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Quantum random number generation (QRNG) harnesses the intrinsic randomness of quantum mechanical phenomena. On-chip photonic circuitry provides a robust and versatile platform that can address and explore fundamental questions in quantum as well as classical physics. Likewise, integrated waveguide-based architectures hold the potential for intrinsically scalable, efficient and compact implementations of photonic QRNG. Here, we harness the quantum emission from the two-dimensional material hexagonal boron nitride an emerging atomically thin medium that can generate single photons on demand while operating at room temperature. By means of a customized splitter arrangement, we achieve true random number generation through the measurement of single photons exiting one of four designated output ports, and subsequently verify the randomness of the sequences in accordance with the National Institute of Standards and Technology benchmark suite. Our results clearly demonstrate the viability and efficiency of this approach to on-chip deterministic random number generators.

Radially self-accelerating beams are rotating shape-invariant solutions of the Helmholtz equation. As such, they exhibit continuous indefinitely spiraling trajectories. Here we present the possibility to tailor those beams to achieve almost any desired beam cross section, without sacrificing the unique propagation characteristics. We discuss analytical tailoring opportunities and highlight their inherent limitations. Following that, by way of example, a genetic optimization algorithm is applied to demonstrate the feasibility of heuristic computer optimization methods in general. The convergence towards several test-targets is demonstrated and the influence of the chosen fitness function is discussed.

We theoretically show that multiport photonic lattices emulating driven quantum harmonic oscillators give rise to Aharonov–Anandan geometric phase, which is proportional to the associated dynamic phase irrespective of the initial state. Consequently, the non-adiabatic geometric phase can be directly measured without the need of complex setups to remove the dynamic phase. Further, we propose the observation of such geometric phases in multiport photonic lattices via integrated interferometry. Our work provides insights into the potential development of integrated photonic platforms for modulation-based topological photonics.

We present a complete and consistent theory of vector radially self-accelerating beams (RSABs). We use this theory as a model for describing the properties of focussed RSABs, and to show, in particular, that only circular polarised RSABs maintain their self-accelerating character upon focussing. Moreover, we also calculate the linear and angular momentum for paraxial vector RSABs, and discuss both their global and local properties.

We discuss the impact of gain and loss on the evolution of photonic quantum states and find that -symmetric quantum optics in gain/loss systems is not possible. Within the framework of macroscopic quantum electrodynamics we show that gain and loss are associated with non-compact and compact operator transformations, respectively. This implies a fundamentally different way in which quantum correlations between a quantum system and a reservoir are built up and destroyed.

We use the concept of two-particle probability amplitude to derive the stochastic evolution equation for two-particle four-point correlations in tight-binding networks affected by diagonal dynamic disorder. It is predicted that in the presence of dynamic disorder, the average spatial wave function of indistinguishable particle pairs delocalizes and populates all network sites including those which are weakly coupled in the absence of disorder. Interestingly, our findings reveal that correlation elements accounting for particle indistinguishability are immune to the impact of dynamic disorder.

We establish theoretically and demonstrate experimentally that photon-pair generation through spontaneous parametric down-conversion in a nonlinear waveguide with scattering or material losses can be effectively emulated by classical laser light propagation through a specially designed linear waveguide circuit. This platform can represent arbitrary photon and pump losses, with a potential for the emulation of non-Markovian decay. We characterize the photon-pair correlation spectrum and observe its characteristic transformation from the well-known sinc-shape in lossless waveguides towards a Lorentzian shape in the presence of photon loss.

Over the last 20 years quantum walks (QWs) have gained increasing interest in the field of quantum information science and processing. In contrast to classical walkers, quantum objects exhibit intrinsic properties like non-locality and non-classical many-particle correlations, which renders QWs a versatile tool for quantum simulation and computation as well as for a deeper understanding of genuine quantum mechanics. Since they are highly controllable and hardly interact with their environment, photons seem to be ideally suited quantum walkers. In order to study and exploit photonic QWs, lattice structures that allow low loss coherent evolution of quantum states are demanded. Such requirements are perfectly met by integrated optical waveguide devices that additionally allow a substantial miniaturization of experimental settings. Moreover, by utilizing the femtosecond direct laser writing technique three-dimensional waveguide structures are capable of analyzing QWs also on higher dimensional geometries. In this context, advances and findings of photonic QWs are discussed in this review. Various concepts and experimental results are presented covering, such as different quantum transport regimes, the Boson sampling problem, and the discrete fractional quantum Fourier transform.

We address the localization of spatio-temporal wave packets in disordered waveguide arrays whereby temporal localization is mediated by nonlinearity while strong disorder provides Anderson statistical spatial localization. This combination of two different mechanisms allows localization to occur outside the range of parameters where diffraction, dispersion, and self-action have similar strengths, as required for the formation of standard spatio-temporal solitons. Under suitable conditions, nonlinearity is shown to weakly affect the statistically averaged spatial intensity distributions. In contrast, the temporal duration of the localized wave packets strongly depends on the level of disorder.

We analyze the transport of light in the bulk and at the edge of photonic Lieb lattices, whose unique feature is the existence of a flat band representing stationary states in the middle of the band structure that can form localized bulk states. We find that transport in bulk Lieb lattices is significantly affected by the particular excitation site within the unit cell, due to overlap with the flat band states. Additionally, we demonstrate the existence of new edge states in anisotropic Lieb lattices. These states arise due to a virtual defect at the lattice edges and are not described by the standard tight-binding model., Comment: 8 pages; 4 figures

The concept of quasi- symmetry in an optical wave-guiding system is elaborated by comparing the evolution dynamics of a -symmetric directional coupler and a passive directional coupler. In particular, we show that in the low-loss regime, apart from an overall exponentially damping factor that can be compensated via a dynamical renormalization of the power flow in the system along the propagation direction, the dynamics of the passive coupler fully reproduce the one in the -symmetric system.

A novel approach to investigate the dynamics of indistinguishable particles in non-Hermitian lattice systems is presented, allowing an efficient calculation of quantum correlations between these particles in the presence of losses. Particular attention is paid to quasi-parity-time-symmetric systems, for which we numerically analyze two-particle quantum random walks for a variety of input states. Our results show how in some scenarios coherence is lost, inducing classical random walks, while in others the characteristic signatures of bosonic and fermionic exchange symmetry prevail.

The rectification of light beams in an optical ratchet is reported. This directed transport is implemented using a photonic mesh lattice consisting of sequences of directional couplers. In such a structure, we observe light propagation at an angle that is independent of the input direction of the injected beam.

Nonlinearity and disorder in discrete systems give rise to fascinating dynamics in various fields of physics. Photonic lattices allow investigation of them in an optical context. The very nature of discrete propagation allows perfect reconstruction of arbitrary initial wave packets by introducing phase shifts to specific lattice sites. We investigate, both numerically and experimentally, the interplay of nonlinearity with this so-called segmentation imaging in the presence of disorder. We find that whereas in the linear regime perfect imaging is achieved for arbitrary amounts of coupling disorder, the onset of nonlinear self- focusing generally destroys imaging. Interestingly, the influence of Anderson localization in strongly disordered lattices renders the imaging significantly more susceptible to nonlinear perturbations.