Anomalous diffusion in two-dimensional Anderson-localization dynamics

Localization of plasmon modes in a 2D photonic nanostructure with a controlled disorder

In this paper, we focus on the optical properties of disordered hole arrays etched in a gold thin film. The disorder is induced and controlled using hole displacements following a Gaussian distribution and starting from a periodic array. The nanostructures present a transition from ordered arrays to short-range ordered arrays and random arrays by increasing the disorder amount. The associated optical properties are characterized in far and near fields by complementary approaches (absorption spectroscopy, classical scanning near field optical microscopy (SNOM) and Finite Difference Time Domain (FDTD) simulations). By increasing the disorder, a broadened absorption up to 30% in the far-field is achieved. Experiments in agreement with FDTD simulations point out the energy localization induced by the disorder and the dependence on the amount of disorder and on the excitation wavelength. By using a controlled disorder, we also show that the effect of these two parameters is also closely linked.

Anomalous Diffusion and Localization in a Positionally Disordered Quantum Spin Array

Disorder in quantum systems can lead to the disruption of long-range order in the ground state and to the localization of the elementary excitations. Here we exhibit an alternative paradigm, by which disorder preserves long-range order in the ground state, while it localizes the elementary excitations above it, introducing a stark dichotomy between static properties-mostly sensitive to the density of states of excitations-and nonequilibrium dynamical properties-sensitive to the spatial structure of excitations. We exemplify this paradigm with a positionally disordered 2d quantum Ising model with r^{-6} interactions, capturing the internal-state physics of Rydberg-atom arrays. Disorder is found to lead to multifractality and localization of the spin-wave excitations above a ferromagnetic ground state; as a result, the spreading of entanglement and correlations starting from a factorized state exhibits anomalous diffusion with a continuously varying dynamical exponent, interpolating between ballistic and arrested transport. Our findings are directly relevant for the low-energy dynamics in quantum simulators of quantum Ising models with power-law decaying interactions.

CO2 -Assisted Conversion of Crystal Two-Dimensional Molybdenum Oxide to Amorphism with Plasmon Resonances

Localized surface plasmon resonances (LSPRs) of ultra-thin two-dimensional (2D) nanomaterials have opened up a new regime in plasmonics in the last several years. 2D plasmonic materials are currently concentrated on the crystal structure, with amorphous materials hardly being reported because of their limited preparation methods rather than undesired plasmonic properties. Taking molybdenum oxides as an example, herein, we elaborate the 2D amorphous plasmons prepared with the assistance of supercritical CO₂ . In brief, we examine the reported characteristic plasmonic properties of molybdenum oxides, and applications of supercritical CO₂ in formations of 2D layer materials as well as introduced phase and disorder engineering based on our research. Furthermore, we propose our perspective on the development of 2D plasmons, especially for amorphous layer materials in the future.

Photon management in two-dimensional disordered media

Elaborating reliable and versatile strategies for efficient light coupling between free space and thin films is of crucial importance for new technologies in energy efficiency. Nanostructured materials have opened unprecedented opportunities for light management, notably in thin-film solar cells. Efficient coherent light trapping has been accomplished through the careful design of plasmonic nanoparticles and gratings, resonant dielectric particles and photonic crystals. Alternative approaches have used randomly textured surfaces as strong light diffusers to benefit from their broadband and wide-angle properties. Here, we propose a new strategy for photon management in thin films that combines both advantages of an efficient trapping due to coherent optical effects and broadband/wide-angle properties due to disorder. Our approach consists of the excitation of electromagnetic modes formed by multiple light scattering and wave interference in two-dimensional random media. We show, by numerical calculations, that the spectral and angular responses of thin films containing disordered photonic patterns are intimately related to the in-plane light transport process and can be tuned through structural correlations. Our findings, which are applicable to all waves, are particularly suited for improving the absorption efficiency of thin-film solar cells and can provide a new approach for high-extraction-efficiency light-emitting diodes.

Experimental observation of speckle instability in Kerr random media

In a disordered nonlinear medium the transmitted speckle pattern was predicted to become unstable as a result of the positive feedback between intensity fluctuations and local variations of the refractive index. We show experimental evidence of speckle instability for light transversally scattered in a liquid crystal cell, where a two-dimensional controlled disorder is imprinted by suitable illumination of a photoconductive wall and nonlinearity is obtained through optical reorientation of the liquid crystal molecules. The speckle pattern spontaneously oscillates at discrete frequencies above a critical threshold, whose dependence on the scattering mean free path confirms the crucial role of disorder in the feedback process.

Dynamics of wave packets in two-dimensional random systems with anisotropic disorder

A theoretical model is proposed to describe narrowband pulse dynamics in two-dimensional systems with arbitrary correlated disorder. In anisotropic systems with elongated cigarlike inhomogeneities, fast propagation is predicted in the direction across the structure where the wave is exponentially localized and tunneling of evanescent modes plays a dominant role in typical realizations. Along the structure, where the wave is channeled as in a waveguide, the motion of the wave energy is relatively slow. Numerical simulations performed for ultra-wide-band pulses show that even at the initial stage of wave evolution, the radiation diffuses predominantly in the direction along the major axis of the correlation ellipse. Spectral analysis of the results relates the long tail of the wave observed in the transverse direction to a number of frequency domain "lucky shots" associated with the long-living resonant modes localized inside the sample.

Self-consistent transport dynamics for localized waves

We find that the Vollhardt and Wolfle self-consistent theory of Anderson localization makes simple predictions for transport dynamics in unbounded one- and two-dimensional media. These predictions are derived and explored and compared with direct numerical simulations.

Anderson localized state as a predissipative state: irreversible emission of thermalized quanta from a dynamically delocalized state

It was shown that localization in one-dimensional disordered (quantum) electronic system is destroyed against coherent harmonic perturbations and the delocalized electron exhibits an unlimited diffusive motion [Yamada and Ikeda, Phys. Rev. E 59, 5214 (1999)]. The appearance of diffusion implies that the system has potential for irreversibility and dissipation. In the present paper, we investigate dissipative property of the dynamically delocalized state, and we show that an irreversible quasistationary energy flow indeed appears in the form of a "heat" flow when we couple the system with another dynamical degree of freedom. In the concrete we numerically investigate dissipative properties of a one-dimensional tight-binding electronic system perturbed by time-dependent harmonic forces, by coupling it with a quantum harmonic oscillator or a quantum anharmonic oscillator. It is demonstrated that if the on-site potential is spatially irregular an irreversible energy transfer from the scattered electron to the test oscillator occurs. Moreover, the test oscillator promptly approaches a thermalized state characterized by a well-defined time-dependent temperature. On the contrary, such a relaxation process cannot be observed at all for periodic potential systems. Our system is one of the minimal quantum systems in which a distinct nonequilibrium statistical behavior is self-induced.

Dynamical delocalization in one-dimensional disordered systems with oscillatory perturbation

The effect of dynamical perturbation on the quantum localization phenomenon in a one-dimensional disordered quantum system (1DDS) is investigated systematically by a numerical method. The dynamical perturbation is modeled by an oscillatory driving force containing M independent (mutually incommensurate) frequency components. For M>or=2 a diffusive behavior emerges and in the presence of the finite localization length of the asymptotic wave packet can no longer be detected numerically. The diffusive motion obeys a subdiffusion law characterized by the exponent alpha as xi(t)(2) proportional t(alpha), where xi(t)(2) is the mean square displacement of the wave packet at time t. With an increase in M and/or the perturbation strength, the exponent alpha rapidly approaches 1, which corresponds to normal diffusion. Moreover, the space-time (x-t) dependence of the distribution function P(x,t) is reduced to a scaled form decided by alpha and another exponent beta such that P(x,t) approximately exp(-constx(x/t(alpha/2))(beta)), which contains the two extreme limits, i.e., the localization limit (alpha=0, beta=1) and the normal-diffusion limit (alpha=1, beta=2) in a unified manner. Some 1DDSs driven by the oscillatory perturbation in different ways are examined and compared.