Complex systems displaying recurrent spike patterns are ubiquitous in nature. Understanding the organization of these patterns is a challenging task. Here we study experimentally the spiking output of a semiconductor laser with feedback. By using symbolic analysis we unveil a nontrivial organization of patterns, revealing serial spike correlations. The probabilities of the patterns display a well-defined, hierarchical and clustered structure that can be understood in terms of a delayed model. Most importantly, we identify a minimal model, a modified circle map, which displays the same symbolic organization. The validity of this minimal model is confirmed by analyzing the output of the forced laser. Since the circle map describes many dynamical systems, including neurons and cardiac cells, our results suggest that similar correlations and hierarchies of patterns can be found in other systems. Our findings also pave the way for optical neurons that could provide a controllable set up to mimic neuronal activity.

We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fiber laser. Ordinal analysis and the horizontal visibility graph applied to the experimentally measured laser output intensity reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods unveil coherent structures with well-defined time scales and strong correlations both, in the timing of the laser pulses and in their peak intensities. Our approach is generic and may be used in other complex systems that undergo similar transitions involving the generation of extreme fluctuations.

Optical excitable devices that mimic neuronal behavior can be building-blocks of novel, brain-inspired information processing systems. A relevant issue is to understand how such systems represent, via correlated spikes, the information of a weak external input. Semiconductor lasers with optical feedback operating in the low frequency fluctuations regime have been shown to display optical spikes with intrinsic temporal correlations similar to those of biological neurons. Here we investigate how the spiking laser output represents a weak periodic input that is implemented via direct modulation of the laser pump current. We focus on understanding the influence of the modulation frequency. Experimental sequences of inter-spike-intervals (ISIs) are recorded and analyzed by using the ordinal symbolic methodology that identifies and characterizes serial correlations in datasets. The change in the statistics of the various symbols with the modulation frequency is empirically shown to be related to specific changes in the ISI distribution, which arise due to different phase-locking regimes. A good qualitative agreement is also found between simulations of the Lang and Kobayashi model and observations. This methodology is an efficient way to detect subtle changes in noisy correlated ISI sequences and may be applied to investigate other optical excitable devices.

We investigate experimentally a cascade of temperature-compensated unequal-path interferometers that can be used to measure frequency states in a high-dimensional quantum distribution system. In particular, we demonstrate that commercially-available interferometers have sufficient environmental isolation so that they maintain an interference visibility greater than 98.5% at a wavelength of 1550 nm over extended periods with only moderate passive control of the interferometer temperature (< ±0.50 • C). Specifically, we characterize two interferometers that have matched delays: one with a free-spectral range of 2.5 GHz, and the other with 1.25 GHz. We find that the relative path of these interferometers drifts less than 3 nm over a period of one hour during which the temperature fluctuates by < ±0.10 • C. The error in our measurement is largely dominated by the small drift in the frequency and power of the stabilized laser used to perform the measurement. When we purposely heat the interferometers over a temperature range of 20-50 • C, we find that the temperature sensitivity is different for each interferometer, likely due to slight manufacturing errors during the temperature compensation procedure. Over this range, we measure a path-length shift of 26 ± 9 nm/ • C for the 2.5 GHz interferometer. For the 1.25 GHz interferometer, the path-length shift is nonlinear and is locally equal to zero at a temperature of 37.1 • C and is 50 ± 17 nm/ • C at 22 • C. With these devices, we realize a cascade of 1.25 GHz and 2.5 GHz interferometers to measure four-dimensional classical frequency states created by modulating a stable and continuous-wave laser. We observe a visibility > 99% over an hour, which is mainly limited by our ability to precisely generate these states. Overall, our results indicate that these interferometers are well suited for realistic time-frequency quantum distribution protocols. arXiv:1610.04947v1 [quant-ph]