Wave phenomena in disordered systems contributions

In this work we present an unexpected example of fluctuation induced forces caused by classical light propagating in a scattering medium. In weakly disordered media, light intensity has long ranged spatial fluctuations (speckle) associated to mesoscopic coherent effects. These intensity fluctuations induce a new type of measurable radiation forces.

The effect is fully understood and characterized by means of an effective Langevin description of the light flow, where coherent mesoscopic effects are the source of the noise.

This approach is of particular interest since it maps the problem of coherent multiple light scattering onto an effective non equilibrium light flow. A clear asset of this type of approach is in its dependence upon two parameters only, thus making it a candidate to efficient machine learning algorithms.

Recently, it has been shown that disordered dielectrics can show a photonic band gap in the presence of structural correlations [1], but 30 years after John's seminal proposal on the interplay between the photonic pseudo band gap in disordered photonic crystals and Anderson localization [2], a controlled experimental study of the transport properties in between ordered and disordered states is still lacking. In this talk, I present new experimental and numerical results obtained for a 2D system composed of high index dielectric cylinders in air [3] placed according to stealthy hyperuniform point patterns [1]. Measurements are performed in the microwave range (1 to 10 GHz). In addition to the (local) density of states and the Thouless conductance, we can access experimentally the field amplitude which allows us to unambiguously visualize single eigenmodes in finite size open systems for all the transport regimes such as stealthy-transparent, diffusion, Anderson-localization and the band gap [4], as a function of the degree of stealthiness $\chi$. Our observations are supported by the analysis of the spreading of the wave in the time domain.

[1] M. Florescu, S. Torquato, and P. J. Steinhardt, Designer disordered materials with large, complete photonic band gaps PNAS 106, 20658 (2009)

[2] S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486 (1987).

[3] D. Laurent et al. Localized Modes in a Finite-Size Open Disordered Microwave Cavity, Phys. Rev. Lett. 99, 253902 (2007).

[4] L. Froufe-Pérez et al., Band gap formation and Anderson licalization in disordered photonic materials with structural correlations PNAS 114, 9570 (2017).

Anderson localization of 3D light has eluded definitive experimental proofs for many years, both for technical and fundamental reasons. Apart from the difficulty of producing highly scattering samples, a major challenge is identifying an unambiguous signature of the phase transition in experimentally feasible situations. We here discuss the correspondence between the collapse of the conductance, the increase in intensity fluctuations at the localization transition and the Ioffe-Regel criterion, thus connecting the macroscopic and microscopic approaches of localization. Intensity fluctuations thus appear as a proper signature to study the localization transition in 3D.

We experimentally study the brownian motion of an optically trapped micrometric particle in liquids at ultrashort timescales in order to reveal the effects of fluid compressibility on its dynamics.

To that purpose, standard trapping and detection schemes are coupled to femtosecond "pump-probe" experiment to take advantage of the high temporal resolution of time resolved ultrafast spectroscopy experiments. The goal is to achieve a proper measurement of the instantaneous velocity of the brownian particle beyond the ballistic regime to probe the influence of compressibility effects on the motion of the trapped sphere, measurement that has never been made and remains elusive. The expected spatial and temporal resolutions ($0.15$ fm at $1$ ps) provided by these techniques will allow us to measure the Velocity Auto Correlation Function to obtain an evidence of compressibility effects on the particle dynamic.

This type of study provides new features into investigations of non equilibrium physics related to brownian motion and optical tweezers.

We study experimentally the dynamics of a cold gas of particles confined in a single plane. We prepare uniformly-filled clouds with different shapes (disk, squares, triangles) and monitor the time evolution of their density profile when applying an isotropic harmonic confinement. We operate in a regime where the gas is well described by a classical field whose evolution is given by the Gross-Pitaevskii (GP) equation. We show that the presence of a dynamical symmetry, described by the SO(2,1) group, leads to conserved quantities in the time evolution and allows us to relate different experimental situations by a scaling transform. Suprisingly, we also observe, for specific shapes, time periodic solutions of the GP equation, that we identify as breathers. Reference : arXiv:1903:04528

This talk will present recent experiments that we performed on the study of near-resonance light scattering in dense laser-cooled and hot atomic vapors. In both cases, the large density results in a strong influence of the interactions between light-induced dipoles. We will compare our measurements of the coherent scattering on both systems to theoretical models and show that while the qualitative behaviors are correctly reproduced for hot and cold vapors, the quantitative agreement is only achieved in the hot vapor case. The talk will also come back to the origin of the collective Lamb shift in hot atomic vapors and present it as an indirect consequence of the dipole-dipole interactions between atoms.

Transmission eigenchannels are building blocks of coherent wave transport through multiple-scattering media. High transmission eigenchannel can have near unity transmittance. Wavefront shaping techniques have been developed to selectively couple light into such channels to enhance light transmittance through multiple-scattering media. It has been shown that coupling light into high-transmission channels not only enhances the transmittance, but also modifies the depth profile of energy density inside the medium.

We discover that the transmission eigenchannels of a wide multiple-scattering slab exhibit transversely localized incident and outgoing intensity profiles, even in the diffusive regime far from Anderson localization. Such transverse localization can be understood with optical reciprocity, local coupling of spatial modes, and non-local intensity correlations of multiply-scattered light. Experimentally, we observe transverse localization of high-transmission channels with finite illumination area. Transverse localization of high-transmission channels enhances optical energy densities inside and on the back surface of the turbid media, which will be important for imaging and sensing applications.

We further demonstrate that selective coupling of light into a single transmission eigenchannel modifies the range of angular memory effect. High-transmission channels have a broader range of memory effect than a plane wave or a Gaussian beam. Thus will provide a wider field-of-view for memory-effect-based imaging through multiple-scattering media.

Focusing and imaging through inhomogeneous, disordered media challenges many applications in optics. Examples range from focusing through atmospheric turbulence in optical communication and LIDAR applications, to focusing through biological tissues in optical microscopy and laser nano-surgery applications. Wavefront shaping with spatial light modulators can focus light through a disordered medium but finding the desired wavefront requires long acquisition times. Here, we exploit an all optical feedback in order to image and focus light through a disordered media at much shorter time scales.

We experimentally demonstrate that by placing the scattering medium directly inside the laser cavity, the appropriate wavefront, which focuses and images the light through the medium, is chosen by the laser itself. This occurs as a result of mode competition and without the need for complicated computer controlled phase modulators and electronic feedback algorithms. The optimal wavefront is found by the laser in less than 500 ns, which is orders of magnitude faster than the reported wavefront shaping record.

When a wavepacket is launched with a finite velocity in free space, it follows a balistic motion, both in classical and quantum mechanics. In the presence of a disordered potential, the generic classical behavior, described by the Boltzman equation, is a random walk - that is a diffusive motion at long time - whose charateristic length is the mean free path. The center of mass of the classical "wavepacket" first drifts balistically in the direction of the initial velocity, slowly slows down and ends up at long time displaced by one mean free path. The quantum dynamics is drastically different: the center of mass first drifts balistically, but rapidly performs a U-turn and slowly returns to its initial position. I will describe this "Quantum Boomerang" effect both numerically and analytically in dimension 1, and show that it is partially destroyed by weak particle interactions which act as a decoherence process. The Quantum Boomerang effect is also present in higher dimensions, provided the dynamics is Anderson localized.

Quantum fluids of light merge many-body physics and nonlinear optics, revealing quantum hydrodynamic features of light when it propagates in nonlinear media. One of the most outstanding evidence of light behaving as an interacting fluid is its ability to carry itself as a superfluid. Here, we report a direct experimental detection of the transition to superfluidity in the flow of a fluid of light past an obstacle in a bulk nonlinear crystal. In this cavityless all-optical system, we extract a direct optical analog of the drag force exerted by the fluid of light and measure the associated displacement of the obstacle. Both quantities drop to zero in the superfluid regime characterized by a suppression of long-range radiation from the obstacle. The experimental capability to shape both the flow and the potential landscape paves the way for simulation of quantum transport in complex systems.

Ultracold atoms offer a unique platform to study the interaction of near-resonant light with an ensemble of resonant emitters. Our experiments probe an ensemble of alkali atoms cooled to a temperature where the inhomogeneous Doppler broadening is negligible and a two-level system can be isolated, so that cooperative scattering effects take place. We study in particular the dense regime where the interatomic distance is shorter than the wavelength of the light. In this regime the atoms interact strongly via the resonant dipole-dipole interactions, and their collective response is significantly modified with respect to the individual one. The geometrical arrangement plays in addition a crucial role in the enhancement of cooperative effects. We will present our recent experimental progress towards tailoring atomic ensembles with sub-wavelength interatomic distance, as well as perspectives in the short term for light-matter interaction experiments in such ensembles.

The study of fluctuations and correlations often gives access to information not contained in averaged values. Among the many statistical properties of a fluctuating field, the intensity correlation function is largely used in a number of areas, from astronomy, to quantum optics, particle physics, and to mesoscopic optics. In the latter, it has been applied to the fluctuations of light scattered by a disordered medium. First used in the single-scattering regime with a technique known as dynamic light scattering or quasielastic light scattering, it was then extended to strong multiple-scattering regime.

In this talk, I will present different results obtained with intensity correlation measurements on light scattered by a cold atomic cloud. We first applied this technique to cold atoms under purely ballistic motion and we investigate the transition between the single and the multiple-scattering regime. When the atoms are driven by a strong laser field, one measures the well-known Mollow triplet, a fundamental signature of quantum optics. Finally, by coupling the intensity correlation to the beat note technique, one has access to the first and second order correlation functions, allowing in particular to test the validity of the Siegert relation in different configurations.

Superfluids like liquid helium or ultracold atomic Bose-Einstein condensates are an exotic state of matter in which quantum effects appear on a macroscopic scale. One of the main features of superfluids is the presence of topological defects with quantised circulation, known as quantum vortices. These vorticity filaments can reconnect dissipating energy through sound emission and thus they play a central role in superfluid turbulence. At the same time, helicoidal waves (called Kelvin waves) can propagate along the vortex filaments and interact nonlinearly among themselves, contributing to the energy transfer towards small scales. An important experimental breakthrough occurred in 2006, when quantum vortices were directly visualised by using micrometer-sized hydrogen particles. Since these particles are trapped inside the vortex core they can be used to track the motion of vortices themselves. Thanks to this method, quantum vortex reconnections and Kelvin wave propagation have been observed. Nowadays, particles are still the main experimental tool used to visualise quantum vortices and to study their dynamics. Our aim is to study the propagation of waves along a superfluid vortex filament, when active particles are trapped inside its core. We perform numerical simulations of a self-consistent model based on the Gross-Pitaevskii (GP) equation, in which particles are described as localised potentials depleting the superfluid and following a Newtonian dynamics. In a former work we have shown that this model is able to reproduce the capture of a particle by a quantum vortex line. Now we study how the dynamics of a collection of particles (impurities) already set inside the vortex reflects the motion of the vortex itself. We measure the spatiotemporal spectra of the system, showing how the presence of particles induces a nontrivial modification of the vortex wave dispersion relation. In order to explain the numerical results, we develop a theory that mixes hydrodynamic equations and basic solid-state concepts. In particular, we point out a remarkable analogy with the propagation of electrons in a crystal lattice.

Adding disorder to a system of quantum particles or excitations can lead to dramatic changes of their properties, including Anderson localization. While there are effective approximations to describe consequences of disorder, such as the Born approximation, they generally fail at large disorder. Here will we review an approach based on a non-linear approximation, which can be applied to arbitrary correlated potentials and which is also effective at high disorder strengths. This formalism leads to interesting results in experimental systems, such as speckle potentials, disordered quantum wires and vibrational topological states in graphene, which will be discuss in this talk.

The universal features of the spectra of chaotic systems are well reproduced by the corresponding quantities of the random matrix ensembles [1]. Depending on symmetry with respect to time reversal and the presence or absence of a spin 1/2 there are three ensembles: the Gaussian orthogonal (GOE), the Gaussian unitary (GUE), and the Gaussian symplectic ensemble (GSE). With a further particle-antiparticle symmetry there are in addition the chiral variants of these ensembles [2]. Relativistic quantum mechanics is not needed to realize the latter symmetry. A tight-binding system made up of two subsystems with only interactions between the subsystems but no internal interactions, such as a graphene lattice with only nearest neighbor interactions, will do it as well. First results of a microwave realization of the chiral GOE (the BDI in Cartan's notation) will be presented, where the tight-binding system has been constructed by a lattice made up of dielectric cylinders [3].

[1] O. Bohigas, M. J. Giannoni, and C. Schmit. Characterization of chaotic spectra and universality of level fluctuation laws. PRL 52, 1 (1984).

[2] C. W. J. Beenakker. Random-matrix theory of Majorana fermions and topological superconductors. Rev. Mod. Phys. 87, 1037 (2015).

[3] S. Barkhofen, M. Bellec, U. Kuhl, and F. Mortessagne. Disordered graphene and boron nitride in a microwave tight-binding analog. PRB 87, 035101 (2013).

Band theory has been one of the major achievements of condensed matter physics during the second half of the last century. Tight-binding model and Bloch theorem give a clear understanding of electronic dispersion relations in metals and semiconductors. The discovery of quantum Hall effect in the 80’s marks the emergence of topology in transport properties: The recognition that the Hall conductance at the plateaus can be understood in terms of topological invariants known as Chern numbers. Playing the role of an order parameter in a “topological phase transition“, Chern number and others topological invariants are nowadays intensively studied in the active field of topological insulators. These concepts extend far beyond the scope of solid-state physics, and several research groups proposed alternative experimental platforms using cold atoms, photons, polaritons, and other classical waves. The Waves in Complex Systems group in Nice has developed artificial condensed-matter systems by means of microwave resonator lattices. I will present a selection of results obtained the last 5 years.

An array of closely spaced, dipole coupled quantum emitters exhibits collective energy shifts as well as super- and subradiance with characteristic tailorable spatial radiation patterns. Ring shape configurations exhibit exponential suppression of spontaneous emission and lossless excitation transport. Optimizing the geometry with respect to the spatial profile of a near resonant optical structures allows to increase the ratio between light scattering into the cavity mode and free space by orders of magnitude. This comes with very distinct nonlinear particle number scaling for the strength of coherent light-matter interactions versus collective decay. In particular, for subradiant states the collective cooperativity increases much faster than the linear ~N dependence of independent emitters in the low excitation regime. This extraordinary collective enhancement is manifested both, in the intensity and phase profile of the sharp collective emitter anti-resonances detectable at the cavity output port via transmission spectroscopy. Subradiant atomic excitations show a much larger effective cooperativity than superradiant states.

References:

Plankensteiner, David, et al. "Cavity antiresonance spectroscopy of dipole coupled subradiant arrays." Physical review letters 119.9 (2017): 093601,

M Moreno-Cardoner, et. Al. “Extraordinary subradiance with lossless excitation transfer in dipole-coupled nano-rings of quantum emitters” arXiv preprint arXiv:1901.10598, 2019.

Abstract: In my talk I will present the concept of random anti-lasing, i.e., the time-reverse of random lasing. In the same way as a random laser emits a spatially complex but coherent wave at its first lasing threshold, the random anti-laser absorbs such a complex incoming field perfectly. We recently implemented this concept in a microwave experiment, where an absorber is embedded in the middle of a disordered medium [1]. Measuring the 8x8 scattering matrix of this structure allows us to calculate and then generate an incoming wave field that gets absorbed by more then 99.7 % inside the disorder. Our setup is scalable in the number of involved modes and can easily be transferred to other wave scattering systems. I will conclude with an outlook on the possible applications of this novel technology.

[1] Pichler, Kühmayer, Böhm, Brandstötter, Ambichl, Kuhl, and Rotter, Nature 567, 351 (2019)

We report on the fabrication and characterization of disordered hyperuni- form photonic materials in two and three dimensions. We first discuss the fabrication of polymer templates of network structures using direct laser writing (DLW) lithography. Next we demonstrate how these mesoscopic polymer networks can be converted into silicon materials by infiltration and double-inversion. The resulting hyperuniform photonic materials display a pronounced pseudo gap in the optical transmittance in the short-wave infrared. To obtain a deeper understanding of the physical parameters dictating the properties of disordered photonic materials we investigate band gaps, and we report Anderson localization in hyperuniform structures using numerical simulations of the density of states and optical transport. Our results show that, depending on the frequency of in- cident radiation, a disordered, but highly correlated, dielectric material can transition from photon diffusion to Anderson localization and to a bandgap. In two dimensions we can also identify a regime, near the gap, dominated by tunnelling between weakly coupled states.

1) N. Muller, J. Haberko, C. Marichy, and F. Scheffold, Silicon Hyper- uniform Disordered Photonic Materials with a Pronounced Gap in the Shortwave Infrared, Adv. Optical Mater. 2, 115?119 (2014)

2) Luis S. Froufe-Pérez, M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, and F. Scheffold, Role of short-range order and hyperuni- formity in the formation of band gaps in disordered photonic materials, Phys. Rev. Lett. 117, 053902 (2016)

3) Luis S. Froufe-Pérez, M. Engel, J.J. S’aenz, F. Scheffold, Band gap formation and Anderson localization in disordered photonic materials with structural correlations, Proceedings of the National Academy of Sciences, 114 (36), 05130 (2017)

4) J. Haberko,Luis S. Froufe-Pérez,and F. Scheffold, https://arxiv.org/abs/1812.02095

Topological photonics aims to replicate fermionic symmetries as feats of precision engineering. Here I show how to enhance these systems via effects such as gain, loss and nonlinearities that do not have a direct electronic counterpart. This leads to a topological mechanism of mode selection [1,2,3], formation of compactons in flat band condensates [4], and topological excitations in lasers when linearized around their working point [5]. The resulting effects show a remarkable practical robustness against disorder, which arises from the increased spectral isolation of the manipulated states.

[1] Topologically protected midgap states in complex photonic lattices, H. Schomerus, Opt. Lett. 38, 1912 (2013).

[2] Selective enhancement of topologically induced interface states in a dielectric resonator chain, C. Poli, M. Bellec, U.Kuhl, F. Mortessagne, H. Schomerus, Nat. Commun. 6, 6710 (2015).

[3] Topological Hybrid Silicon Microlasers, H. Zhao et al., Nat. Commun. 9, 981 (2018)

[4] Exciton-polaritons in a two-dimensional Lieb lattice with spin-orbit coupling, C. E. Whittaker et al., Phys. Rev. Lett. 120, 097401 (2018).

[5] Topological dynamics and excitations in lasers and condensates with saturable gain or loss, S. Malzard, E. Cancellieri, and H. Schomerus, Opt. Express 26, 22506-22518 (2018).

We review a number of intriguing predictions regarding the dynamics of plasmonic nanoparticles under crossed laser fields [1]. As a recent example, we will discuss the self-organized collective behavior of gold nanoparticles moving in aqueous solution under a non-conservative optical vortex lattice. As we will see, above a critical field intensity and concentration, the interplay between optical forces, thermal fluctuations and hydrodynamic pairing leads to a spontaneous transition towards synchronized motion [2].

Light induced forces are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic van der Waals and, in general, Casimir-Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. It has been recently shown that non-equilibrium, quasi-monochromatic, random fluctuating light fields can be used to induce and control isotropic, translational invariant, dispersion forces between small colloidal particles [3]. Interestingly, when the light frequency of a quasi-monochromatic isotropic random field is tuned to an absorption line (at the so-called Fröhlich resonance) we will see that the attractive force between two identical molecules or resonant nanoparticles follows a gravity-like inverse square distance law [4]. Our results generalize Lorentz’s [5] (and Spitzer-Gamow’s “Mock Gravity” [6]) electromagnetic version of the remarkable Fatio-LeSage’s corpuscular theory of gravity introduced as early as in 1690.

[1] Albaladejo, S., et al., Nano letters, 9, 3527 (2009); Zapata I, et al., Phys. Rev. E 93, 062130 (2016); Luis-Hita J. et al., ACS Photonics, 3, pp.1286 (2016); Meléndez. M. et al., Phys. Rev. E 99, 022603 (2019).

[2] Delgado-Buscalioni, R. et al., Phys. Rev. E 00, 002600 (2018)

[3] Brügger, G. et al., Nat. Commun., 6, 7460 (2015)

[4] Luis-Hita, J. et al., arXiv:1802.05648 (2018)

[5] Lorentz, H.A., Lectures on Theoretical Physics. (1927)

[6] Gamow, G., Rev. Mod. Phys., 21, 367 (1949)

We experimentally and numerically study the subradiant decay in an ensemble of cold atoms as a function of the temperature. In the experiment we are recording the temporal switch-off dynamics of the light scattered by a cold-atom sample driven by a weak laser pulse (linear-optics regime). As subradiance is usually interpreted as an interference effect, it is not obvious that the finite temperature of the sample and for this the atomic motion don't introduce a source of dephasing with direct impact on the decay dynamics. We observe that subradiance is rather robust against an increase of the temperature, the measurements show only a slight decrease of the subradiant decay time when increasing the temperature up to several millikelvins, and in particular we measure subradiant decay rates that are much smaller than the Doppler broadening, which might be counter-intuitive. In the numerical simulations we can observe a complete breakdown of subradiance, which occurs at high temperature, when the Doppler broadening is larger than the natural decay rate of a single atom.

It is well known that spontaneous emission, typically assumed to be an independent process for each atom, can be correlated due to the interference of light emitted by different atoms. Cooperative radiation phenomena such as Dicke's superradiance has been explored in systems ranging from individual atoms to black holes. Recently, such cooperative radiation emerged as a promising method for manipulating systems ranging from unordered gases to ordered atomic arrays to two-dimensional semiconductor materials. I will discuss several theoretical ideas relating to super- and subradiance as well as potential applications of such effects.