Experimental observations of rare giant pulses or rogue waves were done in the output intensity of an optically injected semiconductor laser. The long-tailed probability distribution function of the pulse amplitude displays clear non-Gaussian features that confirm the rogue wave character of the intensity pulsations. Simulations of a simple rate equation model show good qualitative agreement with the experiments and provide a framework for understanding the observed extreme amplitude events as the result of a deterministic nonlinear process. DOI: 10.1103/PhysRevLett.107.053901 PACS numbers: 42.65.Sf, 05.45.Àa, 42.60.Mi, 42.55.Px According to fishermen tales from a pub in Ireland, rogue waves (RWs) like solid walls of water, higher than 30 m, are more or less common phenomena in deep ocean waters. This fact is in contradiction with the Gaussian models often used to describe fluctuations of the wave height in the sea [1,2]. A recent experience of a luxury ship close to Antarctica is an example that seems to give credit to such tales. Scientific interest on extremely high waves increased substantially during the past decade not only in oceanography but also in other systems such as capillary waves [3], acoustic waves [4], and optical waves [5][6][7][8][9][10]. Both from the theoretical and from the experimental points of view there are several issues still unclear, such as the physical mechanisms that originate the RWs, the way they develop [11], the probability to observe them [12], and the type of system able to generate such extreme events [13].A first problem is defining quantitatively an extreme event. The oceanography community often employs the abnormality index, which is the ratio between the height of the wave and the average wave height among one-third of the highest waves in a time series [14]. Every event whose abnormality index is larger than 2 is considered a rogue wave. An alternative definition is in terms of the standard deviation of the ocean surface variations: any wave whose height is higher than the mean surface value plus 8 is considered a rogue wave [14].These definitions have the advantage of being precise and the drawback of being quite arbitrary. Since they imply that a rogue wave is highly improbable if the probability distribution function (PDF) of the wave amplitude is a Gaussian, the optical community has employed the general criterion that non-Gaussian and long-tailed PDFs signature the existence of RWs [5][6][7][8][9][10].A second problem is determining which type of system might exhibit these rare extreme events. The intrinsic characteristics of a rogue wave (high amplitude, fast rise and fast fall) imply that the system must be highly nonlinear. A mechanism that has been shown to be directly connected to RWs is the existence of a modulational instability [15], as in the nonlinear Schrödinger (NLS) equation. From the theoretical point of view, the formation of ocean rogue waves has been studied using as a framework the NLS equation (see, e.g., Refs. [16,17] and references therei...

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Rogue waves are devastating extreme events that occur in many natural systems, and a lot of work has focused on predicting and understanding their origin. In optically injected semiconductor lasers rogue waves are rare ultra-high pulses that sporadically occur in the laser chaotic output intensity. Here we show that these optical rogue waves can be predicted with long anticipation time, that they are generated by a crisis-like process, and that noise can be employed to either enhance or suppress their probability of occurrence. By providing a good understanding of the mechanisms triggering and controlling the rogue waves, our results can contribute to improve the performance of injected lasers and can also enable new experiments to test if these mechanisms are also involved in other natural systems where rogue waves have been observed. Extreme events are often catastrophic ones, such as tsunamis, earthquakes, supernovas, stock market crashes, etc. [1][2][3][4][5]. Ocean rogue waves, also referred to as freak waves, are several times the average height of surrounding waves and have steep, fast rising, and fast falling sides, like "a wall of water" [6][7][8][9]. They are a topic of intensive research as they can develop suddenly even in calm and apparently safe seas and have been responsible for several boat accidents, representing a major challenge for the design of off-shore platforms for the oil and gas industry.In optics, Solli et al.[10] have shown that extremely broadband radiation can be generated from a narrow-band input, with a long-tailed distribution similar to that of ocean rogue waves. Since then, optical rogue waves have been observed in several systems [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], and their study has advanced the research in the field, in a way that has been compared to the introduction of optical systems to study chaos in the 1980s [26].In lasers, rogue waves occurring in the form of giant intensity pulses capable of producing catastrophic optical damage have been observed in pump-modulated [19], Raman [20], mode-locked [21][22][23], and optically injected lasers [24]. In Ref.[24] the rogue waves were studied in the framework of a simple and deterministic model that exhibits two types of chaos: one in which rogue waves do not appear consistently and one in which they are relatively frequent [24]. Since a deterministic chaotic system possesses some correlation length, the rogue waves in the system should have some degree of predictability.Here we show, experimentally and numerically, that these optical rogue waves can indeed be predicted with a long anticipation time as compared with the laser characteristic time scales. In addition, we show that an external crisis-like process [27,28], in the form of the crossing of the attractor, developed from one fixed point, with the stable manifold of another fixed point, gives rise to an expanded attractor that supports trajectories with rogue waves. We also show that noise can be exploited for either enhancing or suppressing ...

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Abstract

We study the efficiency of different two-photon states of light to induce the simultaneous excitation of two atoms of different kinds when the sum of the energies of the two photons matches the sum of the energies of the two atomic transitions, while no photons are resonant with each individual transition. We find that entangled two-photon states produced by an atomic cascade are indeed capable of enhancing by a large factor the simultaneous excitation probability as compared to uncorrelated photons, as predicted some years ago by Muthukrishnan et al., but that several unentangled, separable, correlated states, produced either by an atomic cascade or parametric down-conversion, or even appropriate combinations of coherent states, have comparable efficiencies. We show that the key ingredient for the increase of simultaneous excitation probability is the presence of strong frequency anticorrelation and neither time correlation nor time-frequency entanglement.

We demonstrate coherence resonance in a dynamical system without external noise. The experimental evidence is reported in the low frequency fluctuations of a chaotic diode laser with optical feedback. The phenomenon is also verified numerically using the Lang-Kobayashi equations for a single solitary mode laser, without noise terms. Fast deterministic dynamics plays the role of an effective exciting noise, narrowing the resonance in the autonomous slow power drop cycles of the laser. This new result is the natural extension of deterministic stochastic resonance and noise induced coherence resonance predicted and observed in recent years.

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