Robustness of replica symmetry breaking phenomenology in random laser

Experimental evidence on the feasibility of employing a replica symmetry breaking classification random laser

Replica symmetry breaking (RSB) has been introduced in a random laser to investigate the interactions between disorder and fluctuations. In this work, the dynamic difference between four non-energy transfer and Förster resonance energy transfer (FRET)-assisted random laser systems is investigated based on RSB. It is found that FRET is one of the key factors influencing RSB, and it is demonstrated that RSB in a random laser is not robust. This dynamic difference can be attributed to the different disorders induced by the gain mechanism in different random laser systems. This provides experimental evidence and theoretical support for the classification feasibility of RL with different emission mechanisms employing RSB.

Replica symmetry breaking in 1D Rayleigh scattering system: theory and validations

Spin glass theory, as a paradigm for describing disordered magnetic systems, constitutes a prominent subject of study within statistical physics. Replica symmetry breaking (RSB), as one of the pivotal concepts for the understanding of spin glass theory, means that under identical conditions, disordered systems can yield distinct states with nontrivial correlations. Random fiber laser (RFL) based on Rayleigh scattering (RS) is a complex disordered system, owing to the disorder and stochasticity of RS. In this work, for the first time, a precise theoretical model is elaborated for studying the photonic phase transition via the platform of RS-based RFL, in which we clearly reveal that, apart from the pump power, the photon phase variation in RFL is also an analogy to the temperature term in spin-glass phase transition, leading to a novel insight into the intrinsic mechanisms of photonic phase transition. In addition, based on this model and real-time high-fidelity detection spectral evolution, we theoretically predict and experimentally observe the mode-asymmetric characteristics of photonic phase transition in RS-based RFL. This finding contributes to a deeper understanding of the photonic RSB regime and the dynamics of RS-based RFL.

Replica symmetry breaking in a colloidal plasmonic random laser with gold-coated triangular silver nanostructures

Plasmonic random lasers have drawn significant attention recently due to their versatility, low threshold, and the possibility of achieving tunable and coherent/incoherent outputs. However, in this Letter, the phenomenon of replica symmetry breaking is reported in intensity fluctuations of a rarely used colloidal plasmonic random laser (RL) illumination. Triangular nanosilver scatter particles produced incoherent RL action when used in a dimethylformamide (DMF) environment in a Rhodamine-6G gain medium. The use of gold-coated triangular nanosilver as the scatterer in place of triangular nanosilver offered a dual contribution of scattering and lower photo-reabsorption, which caused a reduction in the lasing threshold energy of 39% compared to that obtained with the latter. Further, due to its long-term photostability and chemical properties, a phase transition from the photonic paramagnetic to the glassy phase is observed experimentally in the RL system used. Interestingly, the transition occurs at approximately the lasing threshold value, which is a consequence of stronger correlation of modal behaviors at high input pump energies.

Threshold behavior and tunability of a diffusive random laser

In this study, it is shown that the dynamics of the lasing threshold and the intensity saturation of a diffusive random laser can be visualized by one spectral feature: the peak wavelength shift (tunability). The varied ink concentration and pump energy were utilized to experimentally induce the peak shift and the lasing threshold dynamics. It was found that the peak wavelength progressively turns from blueshift to redshift upon crossing the lasing threshold. A unique random laser threshold regime instead of a threshold point is revealed. This threshold regime was also compared with those deduced from the replica symmetry breaking and the Lévy statistics, both are the state-of-the-art methods to predict the behavior of a complex system. All three results show the high agreement in terms of unveiling the lasing nature of the random lasers.

Random lasing and replica symmetry breaking in GeO2-PbO-MgO glass–ceramics doped with neodymium

We investigated the random lasing process and Replica Symmetry Breaking (RSB) phenomenon in neodymium ions (Nd³⁺) doped lead-germanate glass–ceramics (GCs) containing MgO. Glass samples were fabricated by conventional melt-quenching technique and the GCs were obtained by carefully devitrifying the parent glasses at 830 °C for different time intervals. The partial crystallization of the parent glasses was verified by X-ray diffraction. Photoluminescence (PL) enhancement of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx$$\end{document}≈ 500% relative to the parent glasses was observed for samples with a higher crystallinity degree (annealed during 5 h). Powders with grains having average size of 2 µm were prepared by griding the GCs samples. The Random Laser (RL) was excited at 808 nm, in resonance with the Nd³⁺ transition ⁴I_9/2 → {⁴F_5/2, ²H_9/2}, and emitted at 1068 nm (transition ⁴F_3/2 → ⁴I_11/2). The RL performance was clearly enhanced for the sample with the highest crystallinity degree whose energy fluence excitation threshold (EFE_th) was 0.25 mJ/mm². The enhanced performance is attributed to the residence-time growth of photons inside the sample and the higher quantum efficiency of Nd³⁺ incorporated within the microcrystals, where radiative losses are reduced. Moreover, the phenomenon of Replica Symmetry Breaking (RSB), characteristic of a photonic-phase-transition, was detected by measuring the intensity fluctuations of the RL emission. The Parisi overlap parameter was determined for all samples, for excitation below and above the EFE_th. This is the first time, for the best of the authors knowledge, that RL emission and RSB are reported for a glass–ceramic system.

Stabilizing Brillouin random laser with photon localization by feedback of distributed random fiber grating array

Strong scattering random media can localize light and extend photon lifetime through multiple scattering, which offers opportunities for stabilizing random lasers. Here, we demonstrate a frequency stabilized Brillouin random laser with high coherence enabled by photon localization in random fiber grating array (RFGA). Photon trapping is realized due to wave interference in multi-scattering Fabry-Pérot (FP) cavities between random fiber gratings enabling light localization to prolong photon lifetime. The formation of the high finesse peaks of RFGA suppresses multi-longitudinal modes, which offers single-mode operation at high pump power. The RFGA distributed feedback-based Brillouin random fiber laser (BRFL) maintains a small frequency drift with the pump laser (a phase-locked laser with a linewidth of 100 Hz) at 51 kHz/s for a total change of 620 kHz over 12 s. Note there is no locking between the two lasers, and the beat frequency is measured by the optical heterodyne method. The correlation coefficient change of the measured optical beat frequency is maintained at 4.5%. This indicates that the BRFL is capable of maintaining a small optical frequency difference with the phase-locked pump laser over 12 s thanks to the RFGA capable of trapping photons in the same path, which is a remarkable feature for a random fiber laser. Furthermore, we confirm the single-mode lasing with a long lifetime in the stabilizing BRFL by the replica symmetry behavior and ultralow intensity noise at high pump power. Our findings explore a new approach to stabilize the frequency of Brillouin random lasers passively without commonly used active phase locking laser themes, which makes a simple and cost-effective system.

Direct Measurement of the Reduced Scattering Coefficient by a Calibrated Random Laser Sensor

The research in optical sensors has been largely encouraged by the demand for low-cost and less or non-invasive new detection strategies. The invention of the random laser has opened a new frontier in optics, providing also the opportunity to explore new possibilities in the field of sensing, besides several different and peculiar phenomena. The main advantage in exploiting the physical principle of the random laser in optical sensors is due to the presence of the stimulated emission mechanism, which allows amplification and spectral modification of the signal. Here, we present a step forward in the exploitation of this optical phenomenon by a revisitation of a previous experimental setup, as well as the measurement method, in particular to mitigate the instability of the results due to shot-to-shot pump energy fluctuations. In particular, the main novelties of the setup are the use of optical fibers, a reference sensor, and a peristaltic pump. These improvements are devoted to: eliminating optical beam alignment issues; improving portability; mitigating the variation in pump energy and gain medium performances over time; realizing an easy and rapid change of the sensed medium. The results showed that such a setup can be considered a prototype for a portable device for directly measuring the scattering of liquid samples, without resorting to complicated numerical or analytic inversion procedures of the measured data, once the suitable calibration of the system is performed.

Simultaneous evaluation of intermittency effects, replica symmetry breaking and modes dynamics correlations in a Nd:YAG random laser

Random lasers (RLs) are remarkable experimental platforms to advance the understanding of complex systems phenomena, such as the replica-symmetry-breaking (RSB) spin glass phase, dynamics modes correlations, and turbulence. Here we study these three phenomena jointly in a Nd:YAG based RL synthesized for the first time using a spray pyrolysis method. We propose a couple of modified Pearson correlation coefficients that are simultaneously sensitive to the emergence and fading out of photonic intermittency turbulent-like effects, dynamics evolution of modes correlations, and onset of RSB behavior. Our results show how intertwined these phenomena are in RLs, and suggest that they might share some common underlying mechanisms, possibly approached in future theoretical models under a unified treatment.

Replica symmetry breaking in coherent and incoherent random lasing modes

We investigate intensity fluctuations of a weakly scattering optofluidic random laser having coherent and incoherent emission fractions. The coherent part comprises random spikes, whereas the incoherent part forms a broad pedestal in the emission spectra. Evaluating the fractional ratio of the coherent and incoherent parts of the emission, a replica symmetry breaking phase transition is observed independently in both coherent and incoherent parts of the intensity. Also, the incoherent component has higher non-zero correlation values compared to those of the coherent part, implying a larger contribution to mode coupling. Moreover, survival function analysis reveals a significant contribution of the incoherent part on determining the decay profile of lasing intensity.

Effect of Active Photons on Dynamical Frustration in Cavity QED

We study the far-from-equilibrium dynamical regimes of a many-body spin-boson model with disordered couplings relevant for cavity QED and trapped ion experiments, using the discrete truncated Wigner approximation. We focus on the dynamics of spin observables upon varying the disorder strength and the frequency of the photons, finding that the latter can considerably alter the structure of the system's dynamical responses. When the photons evolve at a similar rate as the spins, they can induce qualitatively distinct frustrated dynamics characterized by either logarithmic or algebraically slow relaxation. The latter illustrates resilience of glassylike dynamics in the presence of active photonic degrees of freedom, suggesting that disordered quantum many-body systems with resonant photons or phonons can display a rich diagram of nonequilibrium responses, with near future applications for quantum information science.

Monolayer 2D ZrTe2 transition metal dichalcogenide as nanoscatter for random laser action

We demonstrate random laser emission from Rhodamine 6G with ZrTe2 transition metal dichalcogenide (TMD) as nanoscatters, both in powder and 2D nanoflakes liquid suspension. The 2D semimetal ZrTe2 was synthesized by a modified redox exfoliation method to provide single layer TMD, which was employed for the first time as the scatter medium to provide feedback in an organic gain medium random laser. In order to exploit random laser emission and its threshold value, replica symmetry breaking leading to a photonic paramagnetic to photonic spin glass transition in both 2D and 3D (powder) ZrTe2 was demonstrated. One important aspect of mixing organic dyes with ZrTe2 is that there is no chemical reaction leading to dye degradation, demonstrated by operating over more than 2 hours of pulsed (5 Hz) random laser emission.

Nonlinear effects and photonic phase transitions in Nd3+-doped nanocrystal-based random lasers

The interplay between gain and scattering of light propagating in disordered media allows operation of random lasers (RLs)-lasers without conventional optical cavities. In the present paper, we review our recent contributions in this area, which include the demonstration of self-second-harmonic and self-sum-frequency generation, the characterization of Lévy's statistics of the output intensity fluctuations, and replica symmetry breaking (analogue to the spin-glass phase transition) by RLs based on nanocrystals containing trivalent neodymium ions.

Replica Symmetry Breaking in a Weakly Scattering Optofluidic Random Laser

We report the observation of replica symmetry breaking (RSB) in a weakly scattering optofluidic random laser (ORL). Coherent random lasing is indicated by the presence of narrow peaks rising out of the spectral background. This coherence helps to identify a random laser threshold, which is expected to be gradual with weak scattering. We find that lasing action initiated using optical pulsed pumping coincides with the onset of both RSB and Lévy flight statistics. However, the transition from the photonic paramagnetic to photonic glass phase is more subtle in that the Parisi overlap function broadens instead of completely changing shape. This subtlety is balanced by an accompanying result of identical experimental conditions giving rise to lasing or no lasing depending on the shot. Additional statistical calculations and investigations into the fundamental physical mechanisms present in the ORL support this conclusion. Using simple numerical models, we study the critical spectral properties required for RSB to occur, as indicated by the Parisi overlap function. The simplicity of the models helps demonstrate the sensitive nature of this tool and the necessity of additional verification of the physical mechanisms present in the experiment.

Large-Scale Photonic Ising Machine by Spatial Light Modulation

Quantum and classical physics can be used for mathematical computations that are hard to tackle by conventional electronics. Very recently, optical Ising machines have been demonstrated for computing the minima of spin Hamiltonians, paving the way to new ultrafast hardware for machine learning. However, the proposed systems are either tricky to scale or involve a limited number of spins. We design and experimentally demonstrate a large-scale optical Ising machine based on a simple setup with a spatial light modulator. By encoding the spin variables in a binary phase modulation of the field, we show that light propagation can be tailored to minimize an Ising Hamiltonian with spin couplings set by input amplitude modulation and a feedback scheme. We realize configurations with thousands of spins that settle in the ground state in a low-temperature ferromagneticlike phase with all-to-all and tunable pairwise interactions. Our results open the route to classical and quantum photonic Ising machines that exploit light spatial degrees of freedom for parallel processing of a vast number of spins with programmable couplings.

Evidence of a Floquet Phase in a Photonic System

The ground breaking extension of the key concept of phase structure to nonequilibrium regimes was only recently achieved in Floquet systems, characterized by a time-dependent quantum Hamiltonian with a periodic driving source. However, despite the theoretical advances, only very few systems are known to display experimental Floquet phases, not one of them employing a laser emission-based mechanism. Here we report the first experimental observation of a Floquet phase in a photonic system, a disordered fiber laser with spatial eigenmode localization. We apply a periodically oscillating cw pumping source that drives the random couplings of the Floquet Hamiltonian. A photonic Floquet spin-glass phase is demonstrated in the random-lasing regime by extensive measurements of the Parisi overlap parameter and asymmetry properties of its distribution. In contrast, in the fluorescent regime below threshold, the absence of mode localization prevents the stabilization of a Floquet phase. Our results are nicely described by theoretical arguments.

Coexistence of turbulence-like and glassy behaviours in a photonic system

Coexistence of physical phenomena can occur in quite unexpected ways. Here we demonstrate the first evidence in any physical system of the coexistence in the same set of measurements of two of the most challenging phenomena in complex systems: turbulence and spin glasses. We employ a quasi-one-dimensional random fibre laser, which displays all essential ingredients underlying both behaviours, namely disorder, frustration and nonlinearity, as well as turbulent energy cascades and intermittent energy flux between fluctuation scales. Our extensive experimental results are theoretically supported by a newly defined photonic Pearson correlation coefficient that unveils the role of the intermittency and describes remarkably well both the spin-glass Parisi overlap parameter and the distribution of turbulent-like intensity increments. Our findings open the way to unravel subtle connections with other complex phenomena, such as disordered nonlinear wave propagation, Lévy statistics of intensity fluctuations, and rogue waves.

Observation of replica symmetry breaking in disordered nonlinear wave propagation

A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics. The most fascinating concept is the breaking of replica symmetry: identical copies of the randomly interacting system that manifest completely different dynamics. Replica symmetry breaking has been predicted in nonlinear wave propagation, including Bose-Einstein condensates and optics, but it has never been observed. Here, we report the experimental evidence of replica symmetry breaking in optical wave propagation, a phenomenon that emerges from the interplay of disorder and nonlinearity. When mode interaction dominates light dynamics in a disordered optical waveguide, different experimental realizations are found to have an anomalous overlap intensity distribution that signals a transition to an optical glassy phase. The findings demonstrate that nonlinear propagation can manifest features typical of spin-glasses and provide a novel platform for testing so-far unexplored fundamental physical theories for complex systems.

Turbulence hierarchy in a random fibre laser

Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a continuous-wave-pumped erbium-based random fibre laser, with random Bragg grating scatterers. The distribution of intensity fluctuations in an extensive data set exhibits three qualitatively distinct behaviours: a Gaussian regime below threshold, a mixture of two distributions with exponentially decaying tails near the threshold and a mixture of distributions with stretched-exponential tails above threshold. All distributions are well described by a hierarchical stochastic model that incorporates Kolmogorov’s theory of turbulence, which includes energy cascade and the intermittence phenomenon. Our findings have implications for explaining the remarkably challenging turbulent behaviour in photonics, using a random fibre laser as the experimental platform.

Random fibre lasers constitute a class of lasers where the optical feedback is provided by multiple scattering in a disordered system. Here, González et al. theoretically and experimentally study the statistical turbulence behaviour in relation to the lasing transition in such lasers.