Photonic waveguides are prime candidates for integrated and parallel photonic interconnects. Such interconnects correspond to large-scale vector matrix products, which are at the heart of neural network computation. However, parallel interconnect circuits realized in two dimensions, for example, by lithography, are strongly limited in size due to disadvantageous scaling. We use three-dimensional (3D) printed photonic waveguides to overcome this limitation. 3D optical couplers with fractal topology efficiently connect large numbers of input and output channels, and we show that the substrate's area and height scale linearly. Going beyond simple couplers, we introduce functional circuits for discrete spatial filters identical to those used in deep convolutional neural networks.

We propose the single-step fabrication of (3+1)D graded-index (GRIN) optical elements by introducing the light exposure as the additional dimension. Following this method, we demonstrate two different optical devices: Volume holograms that are superimposed using angular and peristrophic multiplexing and optical waveguides with a well-defined refractiveindex profile. In the latter, we precisely control the propagating modes via tuning the 3D-printed waveguide parameters and report step-index and graded-index core-cladding transitions.

Two-level emitters are the main building blocks of photonic quantum technologies and are model systems for the exploration of quantum optics in the solid state. Most interesting is the strict resonant excitation of such emitters to control their occupation coherently and to generate close to ideal quantum light, which is of utmost importance for applications in photonic quantum technology. To date, the approaches and experiments in this field have been performed exclusively using bulky lasers, which hinders the application of resonantly driven two-level emitters in compact photonic quantum systems. Here we address this issue and present a concept for a compact resonantly driven single-photon source by performing quantum-optical spectroscopy of a two-level system using a compact high-β microlaser as the excitation source. The two-level system is based on a semiconductor quantum dot (QD), which is excited resonantly by a fiber-coupled electrically driven micropillar laser. We dress the excitonic state of the QD under continuous wave excitation, and trigger the emission of single photons with strong multi-photon suppression () and high photon indistinguishability (V = 57±9%) via pulsed resonant excitation at 156 MHz. These results clearly demonstrate the high potential of our resonant excitation scheme, which can pave the way for compact electrically driven quantum light sources with excellent quantum properties to enable the implementation of advanced quantum communication protocols.

Semiconductor lasers with delayed feedback exhibit two fundamentally different dynamical states: weak and strong chaos. We characterize experimentally the mechanism for the emergence of strong chaos. Based on these insights, we demonstrate similarity properties for long delays, i.e., similar dynamics for different pump currents when adjusting the feedback strength. For different delay times, even the same time-and amplituderescaled version of the dynamics can be generated. Using a simple rate-equation model, these properties can be corroborated. The results have major consequences for the characterization and tailoring of the dynamics for applications.

The unstable emission of semiconductor lasers due to delayed optical feedback is characterized by combined intensity and frequency dynamics. Nevertheless, real-time experimental investigations have so far been restricted to measurements of intensity dynamics only. Detailed analysis and comparison with numerical models, therefore, have suffered from limited experimental information. Here, we report the simultaneous determination of the lasers optical emission intensity and emission frequency with high temporal resolution. The frequency dynamics is made accessible using a heterodyne detection scheme, in which a beat signal between the delayed feedback laser and a reference laser is generated. Our experiment provides insight into the overall spectral drift on nanosecond timescales, the spectral distribution of the unstable pulsations and the role of the individual external cavity modes. This opens new perspectives for the analysis, understanding and functional utilization of delayed feedback semiconductor lasers.

We perform phase-space tomography of semiconductor laser dynamics by simultaneous experimental determination of optical intensity, frequency, and population inversion with high temporal resolution. We apply this technique to a laser with delayed feedback, serving as prominent example for high-dimensional chaotic dynamics and as model system for fundamental investigations of complex systems. Our approach allows us to explore so far unidentified trajectories in phase space and identify the underlying physical mechanism. DOI: 10.1103/PhysRevLett.115.053901 PACS numbers: 42.55.Px, 05.45.Jn, 42.60.Mi, 42.65.Sf Shortly after the initial demonstration of semiconductor lasers in the 1960s, it was discovered that these devices are extremely sensitive to time-delayed back reflections of their own emission [1]: in a range from very weak (40 dB attenuated) to strong delayed feedback, one can observe dramatic modifications of their dynamical behavior [2]. While initially the resulting dynamics was mainly considered to be a major nuisance, soon, fundamental aspects of the observed behavior received increasing interest [3]. Delayed-feedback semiconductor lasers became a prime test bed for the scientific study of nonlinear and highdimensional systems exhibiting chaotic behavior. The dramatic modification to the laser's properties manifests itself in the collapse of the laser's coherence, with an increase of the optical emission linewidth from ∼MHz to easily tens of GHz [4]. This reduction of coherence by up to 5 orders of magnitude is accompanied by corresponding picosecond intensity pulsations [5]. As such, the impact of delayed feedback has to be considered as nontrivial.The state of a free running, single mode semiconductor laser diode biased above threshold is characterized by its carrier inversion (N 0 ), frequency (ν 0 ), and intensity (I 0 ). This solitary laser mode (SLM) usually is a stable fixed point. Delayed feedback strongly modifies the laser's phase-space structure, resulting in a large variety of delay-induced complex phenomena, including narrow linewidth emission or dynamics in the form of limit cycles, quasiperiodic behavior, and deterministic chaos [6,7]. Each of these regimes is characterized by its corresponding phase-space trajectory [8]. Full-bandwidth and realtime measurements of feedback laser intensity [IðtÞ] [5] and frequency [νðtÞ] [9] dynamics already revealed significant new insight; however, this lacked the additional information on the carrier dynamics. Though highly successful, reconstructing complete phase space trajectories from scalar or few-variable via Takens' approach does not allow for the association of different phase-space directions to variables of the physical system [10]. Therefore, it is difficult to identify physical mechanisms from such a reconstructed phase space.Here, we report on the simultaneous experimental determination of the three aforementioned physical phase-space variables with high temporal resolution. Our phase-space tomography therefore allows us to experiment...

We study and analyze the fundamental aspects of noise propagation in recurrent as well as deep, multi-layer networks. The main focus of our study are neural networks in analogue hardware, yet the methodology provides insight for networks in general. The system under study consists of noisy linear nodes, and we investigate the signal-to-noise ratio at the network's outputs which is the upper limit to such a system's computing accuracy. We consider additive and multiplicative noise which can be purely local as well as correlated across populations of neurons. This covers the chief internal-perturbations of hardware networks and noise amplitudes were obtained from a physically implemented recurrent neural network and therefore correspond to a real-world system. Analytic solutions agree exceptionally well with numerical data, enabling clear identification of the most critical components and aspects for noise management. Focusing on linear nodes isolates the impact of network connections and allows us to derive strategies for mitigating noise. Our work is the starting point in addressing this aspect of analogue neural networks, and our results identify notoriously sensitive points while simultaneously highlighting the robustness of such computational systems.

Synchronization of coupled oscillators at the transition between classical physics and quantum physics has become an emerging research topic at the crossroads of nonlinear dynamics and nanophotonics. We study this unexplored field by using quantum dot microlasers as optical oscillators. Operating in the regime of cavity quantum electrodynamics (cQED) with an intracavity photon number on the order of 10 and output powers in the 100 nW range, these devices have high β -factors associated with enhanced spontaneous emission noise. We identify synchronization of mutually coupled microlasers via frequency locking associated with a sub-gigahertz locking range. A theoretical analysis of the coupling behavior reveals striking differences from optical synchronization in the classical domain with negligible spontaneous emission noise. Beyond that, additional self-feedback leads to zero-lag synchronization of coupled microlasers at ultra-low light levels. Our work has high potential to pave the way for future experiments in the quantum regime of synchronization.