arXiv subjects

E. Akkermans

Publications and source records attributed to E. Akkermans.

At least 19 recordsLinked to original sources

arXiv2021

Roles of cooperative effects and disorder in photon localization: The case of a vector radiation field

We numerically study photon escape rates from three-dimensional atomic gases and investigate the respective roles of cooperative effects and disorder in photon localization, while taking into account the vectorial nature of light. A scaling behavior is observed for the escape rates, and photons undergo a crossover from delocalization toward localization as the optical thickness of the cloud is increased. This result indicates that light localization is dominated by cooperative effects rather than disorder. We compare our results with those obtained in the case of a scalar radiation field and find no significant differences. We conclude that the scalar model constitutes an excellent approximation when considering photon escape rates from atomic gases.

physics.atom-ph↗

arXiv2017

Revealing the topology of quasicrystals with a diffraction experiment

Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly observe, using an interferometric approach, all the topological invariants of finite-length Fibonacci chains in their diffraction pattern. We also demonstrate quantitatively the stability of these topological invariants with respect to structural disorder.

cond-mat.mes-hall↗

arXiv2017

Observing a scale anomaly and a universal quantum phase transition in graphene

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe 'Efimov physics'. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive $1/r$ Coulomb potential. The purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realised in graphene.

cond-mat.mes-hall↗

arXiv2017

Measuring topological invariants from generalized edge states in polaritonic quasicrystals

We investigate the topological properties of Fibonacci quasicrystals using cavity polaritons. Composite structures made of the concatenation of two Fibonacci sequences allow investigating generalized edge states forming in the gaps of the fractal energy spectrum. We employ these generalized edge states to determine the topological invariants of the quasicrystal. When varying a structural degree of freedom (phason) of the Fibonacci sequence, the edge states spectrally traverse the gaps, while their spatial symmetry switches: the periodicity of this spectral and spatial evolution yields direct measurements of the gap topological numbers. The topological invariants that we determine coincide with those assigned by the gap-labeling theorem, illustrating the direct connection between the fractal and topological properties of Fibonacci quasicrystals.

cond-mat.mes-hall↗

arXiv2016

Topological properties of Fibonacci quasicrystals : A scattering analysis of Chern numbers

We report on a study of topological properties of Fibonacci quasicrystals. Chern numbers which label the dense set of spectral gaps, are shown to be related to the underlying palindromic symmetry. Topological and spectral features are related to the two independent phases of the scattering matrix: the total phase shift describing the frequency spectrum and the chiral phase sensitive to topological features. Conveniently designed gap modes with spectral properties directly related to the Chern numbers allow to scan these phases. An effective topological Fabry-Perot cavity is presented.

physics.optics↗

arXiv2014

Cooperative effects and disorder: A scaling analysis of the spectrum of the effective atomic Hamiltonian

We study numerically the spectrum of the non-Hermitian effective Hamiltonian that describes the dipolar interaction of a gas of $N\gg 1$ atoms with the radiation field. We analyze the interplay between cooperative effects and disorder for both scalar and vectorial radiation fields. We show that for dense gases, the resonance width distribution follows, both in the scalar and vectorial cases, a power law $P(Γ) \sim Γ^{-4/3}$ that originates from cooperative effects between more than two atoms. This power law is different from the $ P(Γ) \sim Γ^{-1}$ behavior, which has been considered as a signature of Anderson localization of light in random systems. We show that in dilute clouds, the center of the energy distribution is described by Wigner's semicircle law in the scalar and vectorial cases. For dense gases, this law is replaced in the vectorial case by the Laplace distribution. Finally, we show that in the scalar case the degree of resonance overlap increases as a power law of the system size for dilute gases, but decays exponentially with the system size for dense clouds.

cond-mat.mes-hall↗

arXiv2013

Cooperative effects and photon localization in atomic gases: The two-dimensional case

We study photon escape rates from two-dimensional atomic gases while taking into account cooperative effects between the scatterers. Based on the spectrum of the random Euclidean matrix Uij = Jo(xij), where xij is the dimensionless random distance between any two atoms, a scaling behavior for the escape rates is obtained. This behavior is similar to the one obtained in the three-dimensional case, but qualitatively different from the result obtained in one dimension.

cond-mat.mes-hall↗

arXiv2013

Cooperative effects in one-dimensional random atomic gases: Absence of single atom limit

We study superradiance in a one-dimensional geometry, where N>>1 atoms are randomly distributed along a line. We present an analytic calculation of the photon escape rates based on the diagonalization of the N x N coupling matrix Uij = cos xij, where xij is the dimensionless random distance between any two atoms. We show that unlike a three-dimensional geometry, for a one- dimensional atomic gas the single-atom limit is never reached and the photon is always localized within the atomic ensemble. This localization originates from long-range cooperative effects and not from disorder as expected on the basis of the theory of Anderson localization.

cond-mat.mes-hall↗

arXiv2008

Photon localization and Dicke superradiance in atomic gases

Photon propagation in a gas of N atoms is studied using an effective Hamiltonian describing photon mediated atomic dipolar interactions. The density P(Γ) of photon escape rates is determined from the spectrum of the N x N random matrix Γ_{ij} = \sin (x_{ij}) / x_{ij}, where x_{ij} is the dimensionless random distance between any two atoms. Varying disorder and system size, a scaling behavior is observed for the escape rates. It is explained using microscopic calculations and a stochastic model which emphasizes the role of cooperative effects in photon localization and provides an interesting relation with statistical properties of "small world networks".

cond-mat.mes-hall↗

arXiv2007

Conservation of energy in coherent backscattering of light

Although conservation of energy is fundamental in physics, its principles seem to be violated in the field of wave propagation in turbid media by the energy enhancement of the coherent backscattering cone. In this letter we present experimental data which show that the energy enhancement of the cone is balanced by an energy cutback at all scattering angles. Moreover, we give a complete theoretical description, which is in good agreement with these data. The additional terms needed to enforce energy conservation in this description result from an interference effect between incident and multiply scattered waves, which is reminiscent of the optical theorem in single scattering.

cond-mat.dis-nn↗

arXiv2007

Superradiance and multiple scattering of photons in atomic gases

We study the influence of cooperative effects such as superradiance and subradiance, on the scattering properties of dilute atomic gases. We show that cooperative effects lead to an effective potential between pairs of atoms that decays like $1/r$. In the case of superradiance, this potential is attractive for close enough atoms and can be interpreted as a coherent mesoscopic effect. We consider a model of multiple scattering of a photon among superradiant pairs and calculate the elastic mean free path and the group velocity. We study first the case of a scalar wave which allows to obtain and to understand basic features of cooperative effects and multiple scattering. We then turn to the general problem of a vector wave. In both cases, we obtain qualitatively similar results and derive, for the case of a scalar wave, analytic expressions of the elastic mean free path and of the group velocity for an arbitrary (near resonance) detuning.

cond-mat.mes-hall↗

arXiv2006

Intensity correlations and mesoscopic fluctuations of diffusing photons in cold atoms

We study the angular correlation function of speckle patterns that result from multiple scattering of photons by cold atomic clouds. We show that this correlation function becomes larger than the value given by Rayleigh law for classical scatterers. These large intensity fluctuations constitute a new mesoscopic interference effect specific to atom-photon interactions, that could not be observed in other systems such as weakly disordered metals. We provide a complete description of this behavior and expressions that allow for a quantitative comparison with experiments.

cond-mat.mes-hall↗

arXiv2006

Interference of diffusing photons and level crossing spectroscopy

We show that a new interference effect appears in the intensity fluctuations of photons multiply scattered by an atomic gas of large optical depth b. This interference occurs only for scattering atoms that are Zeeman degenerate and it leads to a deviation from the Rayleigh law. The fluctuations measured by their variance, display a resonance peak as a function of an applied magnetic field. The resonance width is proportional to the small factor 1/b. We derive closed analytic expressions for all these physical quantities which are directly accessible experimentally.

cond-mat.mes-hall↗

arXiv2006

Effect of superradiance on transport of diffusing photons in cold atomic gases

We show that in atomic gases cooperative effects like superradiance and subradiance lead to a potential between two atoms that decays like $1/r$. In the case of superradiance, this potential is attractive for close enough atoms and can be interpreted as a coherent mesoscopic effect. The contribution of superradiant pairs to multiple scattering properties of a dilute gas, such as photon elastic mean free path and group velocity, is significantly different from that of independent atoms. We discuss the conditions under which these effects may be observed and compare our results to recent experiments on photon transport in cold atomic gases.

cond-mat.mes-hall↗

arXiv2005

Mesoscopic scattering of spin s particles

Quantum effects in weakly disordered systems are governed by the properties of the elementary interaction between propagating particles and impurities. Long range mesoscopic effects due to multiple scattering are derived by iterating the single scattering vertex, which has to be appropriately diagonalized. In the present contribution, we present a systematic and detailed diagonalisation of the diffuson and cooperon vertices responsible for weak localisation effects. We obtain general expressions for eigenvalues and projectors onto eigenmodes, for any spin and arbitrary elementary interaction with impurities. This description provides a common frame for a unified theory of mesoscopic spin physics for electrons, photons, and other quantum particles. We treat in detail the case of spin-flip scattering of electrons by freely orientable magnetic impurities and briefly review the case of photon scattering from degenerate dipole transitions in cold atomic gases.

cond-mat.mes-hall↗

arXiv2002

Phase coherence times in the multiple scattering of photons by cold atoms

We present an analysis of the dephasing present in the multiple scattering of photons by atoms with a quantum internal structure. The corresponding phase coherence times $τ_ϕ$ are obtained as a function of the Zeeman degeneracy of the atomic dipole transition and the polarization state of the photons. These results allow for an explanation of the recent experiments on coherent backscattering of photons from a gas of cold rubidium atoms where the height of the backscattering cone depends on the atomic internal degrees of freedom coupled to the polarization of the photons. Some consequences of these results are presented, and analogies with the case of electronic systems are highlighted.

cond-mat.mes-hall↗

arXiv2000

Mesoscopic superconductors in the London limit: equilibrium properties and metastability

We present a study of the behaviour of metastable vortex states in mesoscopic superconductors. Our analysis relies on the London limit within which it is possible to derive closed analytical expressions for the magnetic field and the Gibbs free energy. We consider in particular the situation where the vortices are symmetrically distributed along a closed ring. There, we obtain expressions for the confining Bean-Livingston barrier and for the magnetization which turns out to be paramagnetic away from thermodynamic equilibrium. At low temperature, the barrier is high enough for this regime to be observable. We propose also a local description of both thermodynamic and metastable states based on elementary topological considerations; we find structural phase transitions of vortex patterns between these metastable states and we calculate the corresponding critical fields.

cond-mat.supr-con↗

arXiv2000

A dual point description of mesoscopic superconductors

We present an analysis of the magnetic response of a mesoscopic superconductor, i.e. a system of sizes comparable to the coherence length and to the London penetration depth. Our approach is based on special properties of the two dimensional Ginzburg-Landau equations, satisfied at the dual point $(κ= \frac{1}{\sqrt{2}}).$ Closed expressions for the free energy and the magnetization of the superconductor are derived. A perturbative analysis in the vicinity of the dual point allows us to take into account vortex interactions, using a new scaling result for the free energy. In order to characterize the vortex/current interactions, we study vortex configurations that are out of thermodynamical equilibrium. Our predictions agree with the results of recent experiments performed on mesoscopic aluminium disks.

cond-mat.supr-con↗