Category: Random Lasers

Optical Spin Glasses

https://opg.optica.org/aop/abstract.cfm?URI=aop-18-2-421

Spin-glass theory emerged in the 1980s as a merger between theoretical physics and condensed matter. Soon, physicists realized that spin glasses serve as a paradigm for complex systems, as underscored by the 2021 Nobel Prize in Physics, and for applications in machine learning and neuroscience, with a profound connection with the Hopfield model and Boltzmann machines, subjects of the 2024 Nobel Prize in Physics. However, the connection with optics and photonics is even more profound and fundamental; this connection was identified as early as 1982, with the first realizations of optical neural networks. Thirty years later, the first experimental demonstration of a pillar of spin-glass theory, the replica symmetry breaking, was reported in photonics. Nowadays, many scientists consider photonics as an effective solution for new hardware in artificial intelligence, capable of reducing energy consumption in training large machine-learning modules, and also more suitable for realizing fully connected models that underpin modern data-driven analysis. The substantial equivalence between linear optical propagation and a system of interacting binary spins is now well recognized, triggering the development of a new family of devices for both classical and quantum computing. This review is intended to detail the work of the past twenty years concerning the link between spin-glass theory and optics. After a simple introduction to the main ideas of spin glasses, we start from the first works aimed at finding a direct experimental proof of ideas such as the landscape and ultrametricity; then we report on “linear optical spin glasses,” which refer to the photonic simulation of various Ising models for combinatorial optimization and interlinked with quantum computers; finally, we discuss the emerging field of “nonlinear optical spin glasses,” driven by the impressive progress in the realization of coherent Ising machines with parametric oscillators, that opened an new research direction driven by the cross-fertilization of advanced theoretical physics, artificial intelligence, classical and quantum nonlinear optics.

The First Experimental Observation of Ultrametricity

https://www.researchsquare.com/article/rs-5433512/v1

Ultrametricity is a fundamental mathematical concept that describes a particular metric space in which every triplet of points in the space forms an isosceles triangle. The ultrametric space differs from the usual Archimedean metric, where three points are allowed from any triangle.

Ultrametricity is the topology of hierarchical architectures. Examples can be found in taxonomy, where phylogenetic trees are ultrametric, mathematics with p-adic numbers, geography for measuring landscape complexity, and physics, where complex systems have intrinsically an ultrametric structure.

The Noble Prize Giorgio Parisi demonstrated this within the theory of spin glasses, where the overlap between spins exhibits ultrametricity, with the mathematical solution given by the full replica symmetry breaking.

An experimental demonstration of this is still lacking due to the difficulty of finding measurable physical observables.

In 2015, we introduced random lasers as photonic counterparts of spin glasses, and we demonstrated the replica symmetry breaking by directly measuring the overlap between spins, known as the order parameter in the description of glass phase transitions.

In the work, we clearly show the hierarchical organization of the overlap matrix reproducing the Parisi Ansatz, and we experimentally prove the ultrametric nature of the replica states.

For the first time, we measure the distance between any three replicas forming a triangle, and we report the growth of the distribution of isosceles tringles when the system enters the glassy regime. This is an unambiguous way to demonstrate ultrametricity and has been previously done only in numerical simulations.

In addition, from the hierarchical structure of the spin states, illustrated as dendrograms, and the distances between replicas, we attain the first topological energy landscape of a complex system from experiments.

The great potentiality of our research is the ability to access measurable spins from emission spectra and to quantify the overlap parameter. Random lasers are photonic spin glasses, as they manifest a clear phase transition from a paramagnetic ordered state to a glassy disordered one by increasing the system’s energy. Thanks to this powerful asset, we demonstrate the ultrametricity of the replica space. We report the experimental energy landscape with a topology that changes from a flat large basin to the coexistence of many metastable minima and the braking of ergodicity in the glassy state.

Biosensing with free space whispering gallery mode microlasers

Highly accurate biosensors for few or single molecule detection play a central role in numerous key fields, such as healthcare and environmental monitoring. In the last decade, laser biosensors have been investigated as proofs of concept, and several technologies have been proposed. We here propose a demonstration of polymeric whispering gallery microlasers as biosensors for detecting small amounts of proteins down to 400 pg. They have the advantage of working in free space without any need for waveguiding for input excitation or output signal detection. The photonic microsensors can be easily patterned on microscope slides and operate in air and solution. We estimate the limit of detection up to 148 nm/RIU for three different protein dispersions. In addition, the sensing ability of passive spherical resonators in the presence of dielectric nanoparticles that mimic proteins is described by massive ab initio numerical simulations.

https://doi.org/10.1364/PRJ.477139

Parisi Nobel lecture mentioning our experiments

This is the extended version of the Giorgio Parisi Nobel lecture mentioning our experiments in nonlinear optics and random laser with the first observation of Replica Symmetry Breaking

https://arxiv.org/abs/2304.00580