Observation of replica symmetry breaking in disordered nonlinear wave propagation

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.

Observation and all-optical manipulation of replica symmetry breaking dynamics in a multi-Stokes-involved Brillouin random fiber laser photonic system

In this paper, we propose and demonstrate an all-optical control of RSB transition in a multi-wavelength Brillouin random fiber laser (MWBRFL). Multi-order Stokes light components can be subsequently generated by increasing the power of the Erbium-doped fiber amplifier (EDFA) inside the MWBRFL, providing additional disorder as well as multiple Stokes-involved interplay. It essentially allows diversified laser mode landscapes with adjustable average mode lifetime and random mode density of the 1st order Stokes, which benefits the switching between replica symmetry breaking (RSB) and replica symmetry (RS) states in an optically controlled manner. Results show that the average mode lifetime of the 1st order Stokes component gradually decreases from 250.0 ms to 1.2 ms as high orders from the 2nd to the 5th of Stokes components are activated. Meanwhile, the order parameter q of the 1st order Stokes random lasing emission presents distinct statistical distributions within the selective sub-window under various EDFA optical powers. Consequently, all-optical dynamical control of the 1st Stokes random laser mode landscapes with adjustable average mode lifetime turns out to be attainable, facilitating the RSB transition under an appropriate observation time window. These findings open a new avenue for exploring the underlying physical mechanisms behind the occurrence of the RSB phenomenon in photonic complex systems.

Two-photon synthetic aperture microscopy for minimally invasive fast 3D imaging of native subcellular behaviors in deep tissue

Holistic understanding of physio-pathological processes requires noninvasive 3D imaging in deep tissue across multiple spatial and temporal scales to link diverse transient subcellular behaviors with long-term physiogenesis. Despite broad applications of two-photon microscopy (TPM), there remains an inevitable tradeoff among spatiotemporal resolution, imaging volumes, and durations due to the point-scanning scheme, accumulated phototoxicity, and optical aberrations. Here, we harnessed the concept of synthetic aperture radar in TPM to achieve aberration-corrected 3D imaging of subcellular dynamics at a millisecond scale for over 100,000 large volumes in deep tissue, with three orders of magnitude reduction in photobleaching. With its advantages, we identified direct intercellular communications through migrasome generation following traumatic brain injury, visualized the formation process of germinal center in the mouse lymph node, and characterized heterogeneous cellular states in the mouse visual cortex, opening up a horizon for intravital imaging to understand the organizations and functions of biological systems at a holistic level.

Interplay of Thermalization and Strong Disorder: Wave Turbulence Theory, Numerical Simulations, and Experiments in Multimode Optical Fibers

We address the problem of thermalization in the presence of a time-dependent disorder in the framework of the nonlinear Schrödinger (or Gross-Pitaevskii) equation with a random potential. The thermalization to the Rayleigh-Jeans distribution is driven by the nonlinearity. On the other hand, the structural disorder is responsible for a relaxation toward the homogeneous equilibrium distribution (particle equipartition), which thus inhibits thermalization (energy equipartition). On the basis of the wave turbulence theory, we derive a kinetic equation that accounts for the presence of strong disorder. The theory unveils the interplay of disorder and nonlinearity. It unexpectedly reveals that a nonequilibrium process of condensation and thermalization can take place in the regime where disorder effects dominate over nonlinear effects. We validate the theory by numerical simulations of the nonlinear Schrödinger equation and the derived kinetic equation, which are found in quantitative agreement without using any adjustable parameter. Experiments realized in multimode optical fibers with an applied external stress evidence the process of thermalization in the presence of strong disorder.

Intense Wave Formation from Multiple Soliton Fusion and the Role of Extra Dimensions

We experimentally and numerically explore the role of dimensionality in multiple (three or more) soliton fusion supported by nonreciprocal energy exchange. Three-soliton fusion into an intense wave is found when an extra dimension, with no broken inversion symmetry, is involved. The phenomenon is observed for 2+1D spatial waves in photorefractive crystals, where solitons are supported by a spatially local saturated Kerr-like self-focusing and fusion is driven by the leading nonlocal correction, the spatial analog of the nonlinear Raman effect.

Controlling Nonlinear Interaction in a Many-Mode Laser by Tuning Disorder

A many-mode laser with nonlinear modal interaction could serve as a model system to study many-body physics. However, precise and continuous tuning of the interaction strength over a wide range is challenging. Here, we present a unique method for controlling lasing mode structures by introducing random phase fluctuation to a nearly degenerate cavity. We show numerically and experimentally that as the characteristic scale of phase fluctuation decreases by two orders of magnitude, the transverse modes become fragmented and the reduction of their spatial overlap suppresses modal competition for gain, allowing more modes to lase. The tunability, flexibility, and robustness of our system provides a powerful platform for investigating many-body phenomena.

Statistical mechanics of beam self-cleaning in GRIN multimode optical fibers

Since its first demonstration in graded-index multimode fibers, spatial beam self-cleaning has attracted a growing research interest. It allows for the propagation of beams with a bell-shaped spatial profile, thus enabling the use of multimode fibers for several applications, from biomedical imaging to high-power beam delivery. So far, beam self-cleaning has been experimentally studied under several different experimental conditions. Whereas it has been theoretically described as the irreversible energy transfer from high-order modes towards the fundamental mode, in analogy with a beam condensation mechanism. Here, we provide a comprehensive theoretical description of beam self-cleaning, by means of a semi-classical statistical mechanics model of wave thermalization. This approach is confirmed by an extensive experimental characterization, based on a holographic mode decomposition technique, employing laser pulses with temporal durations ranging from femtoseconds up to nanoseconds. An excellent agreement between theory and experiments is found, which demonstrates that beam self-cleaning can be fully described in terms of the basic conservation laws of statistical mechanics.

Evaluation of Pearson correlation coefficient and Parisi parameter of replica symmetry breaking in a hybrid electronically addressable random fiber laser

The hybrid electronically addressable random (HEAR) laser is a novel type of random fiber laser that presents the remarkable property of selection of the fiber section with lasing emission. Here we present a joint analysis of the correlations between intensity fluctuations at distinct wavelengths and replica symmetry breaking (RSB) behavior of the HEAR laser. We introduce a modified Pearson coefficient that simultaneously comprises both the Parisi overlap parameter and standard Pearson correlation coefficient. Our results highlight the contrast between the correlations and presence or not of RSB phenomenon in the spontaneous emission behavior well below threshold, replica-symmetric ASE regime slightly below threshold, and RSB phase with random lasing emission above threshold. In particular, in the latter we find that the onset of RSB behavior is accompanied by a stochastic dynamics of the lasing modes, leading to competition for gain intertwined with correlation and anti-correlation between modes in this complex photonic phase.

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.

Dramatic Acceleration of Wave Condensation Mediated by Disorder in Multimode Fibers

Classical nonlinear waves exhibit a phenomenon of condensation that results from the natural irreversible process of thermalization, in analogy with the quantum Bose-Einstein condensation. Wave condensation originates in the divergence of the thermodynamic equilibrium Rayleigh-Jeans distribution, which is responsible for the macroscopic population of the fundamental mode of the system. However, achieving complete thermalization and condensation of incoherent waves through nonlinear optical propagation is known to require prohibitive large interaction lengths. Here, we derive a discrete kinetic equation describing the nonequilibrium evolution of the random wave in the presence of a structural disorder of the medium. Our theory reveals that a weak disorder accelerates the rate of thermalization and condensation by several order of magnitudes. Such a counterintuitive dramatic acceleration of condensation can provide a natural explanation for the recently discovered phenomenon of optical beam self-cleaning. Our experiments in multimode optical fibers report the observation of the transition from an incoherent thermal distribution to wave condensation, with a condensate fraction of up to 60% in the fundamental mode of the waveguide trapping potential.

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.