School on Anderson Localization: landscape theory, experiments with ultracold atoms

Anderson localization model

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Organizers: T. Bourdel & P. Pelletier 

  • Start date: Wednesday, Oct. 7, 2020
  • End date: Friday, Oct. 9, 2020
  • Location: Held virtually
    • Zoom
    • Gather Town (poster session)

View speaker abstracts and slides here



Schedule, Recorded Video Links, and Poster Information

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October 7, 2020

  • 07:00 CDT / 14:00 CEST: Opening Remarks
  • 07:00 CDT / 14:05 CEST: Anderson localization: Introduction and known results — Dominique Delande (CNRS)
  • 08:10 CDT / 15:10 CEST:Break
  • 08:15 CDT / 15:15 CEST: The Landscape theory of localization — Marcel Filoche (École Polytechnique)
  • 09:20 CDT / 16:20 CEST: Break
  • 09:30 CDT / 16:30 CEST: Anderson localization of light by cold atoms — Sergei Skipetrov (CNRS)
  • 10:05 CDT / 17:05 CEST: Break
  • 10:10 CDT / 17:10 CEST: Quantum fluids of light in quasi-periodic potential — Jacqueline Bloch (Université Paris-Saclay)
  • 10:45 CDT / 17:45 CEST: End of day


October 8, 2020


October 9, 2020


WAVE-20-101 — Arjun Ashoka, University of Cambridge

  • Subgroup: Organics
  • Title: Ultrafast Microscopy as a Tool for Direct Observation of Localization of Electrons and Excitons in Semiconductors
  • Abstract: Unlike the ultra-pure macroscopically coherent cold atom systems, coherence of optical excitations in real condensed matter systems are typically only locally coherent and very short lived due to interactions with the phonon bath. The direct observation of these excitations in their coherent regime therefore requires high spatial and temporal resolution. We discuss the use of optical pump-probe spectroscopy in a microscope geometry for energy-resolved spatiotemporal detection of photoexcited states with 10 fs temporal and 10 nm spatial precision. We discuss a forward optical model for the microscope as well as a model for coherent transport in our excitation framework. We show that we are able to directly observe coherent/ballistic transport in both 3D inorganic semiconducting and 1D polaritonic cavity systems, paving the way for the direct investigation of localization as function of energy, disorder and temperature in semiconducting systems.

WAVE-20-102 — Lucas Lavoine, Laboratoire Charles Fabry, Institut d'Optique Paris Saclay

  • Subgroup: Cold Atoms
  • Title: Observation of the algebraic localization-delocalization transition in a one-dimensional disordered potential with a bias force
  • Abstract: One-dimensional (1D) Anderson localization phenomena are strongly affected by a bias force or equivalently a voltage in electronic systems. We experimentally study this case, launching a noninteracting 39K Bose-Einstein condensate in a 1D disordered potential induced by a far-off-resonance laser speckle, while controlling a bias force. In agreement with theoretical predictions, we observe a transition between algebraic localization and delocalization as a function of our control parameter that is the relative strength of the disorder against the bias force. We also demonstrate that the transition is intrinsically energy independent and that the initial velocity of the wave packet only plays a role through an effective disorder strength due to the correlation of the disorder.

WAVE-20-103 — Thibault Scoquart, Laboratoire Kastler Brossel

  • Subgroup: Cold Atoms
  • Title: Dynamics of weakly interacting disordered Bose gases
  • Abstract: This poster will present a quick review of my theoretical work on the out-of-equilibrium dynamics of Bose gases after a disorder and interaction quench. In this context, I will first show how weak interactions affect the well-known mesoscopic phenomena emerging from coherent multiple scattering in momentum space : a background of diffusive particles, and the Coherent Backscattering peak (or CBS, a direct consequence of weak localization). Using a diagrammatic transport theory, we find that the dynamics is governed by coupled kinetic equations that describe the thermalization of the diffusive and coherent components of the gas. This phenomenon leads to a destruction of CBS which can, at short time, be approximated  by an effective relaxation mechanism, whose rate is controlled by the particle collision time [1]. Then, as the interaction strength grows (so that the scattering time becomes way larger that the particle collision time), scattering on the disorder has negligible effect and particle interactions govern the dynamics of the gas. The gas is quickly driven towards a pre-thermalized state, which exhibits algebraic correlations spreading within a light cone.

WAVE-20-104 – Pierre Pelletier, Ecole Polytechnique

  • Subgroup: Cold Atoms
  • Title: Computing the spectral functions of ultracold atoms in disorder using the localization landscape
  • Abstract: Ultracold atoms systems are very often used to study experimentally the Anderson localization phenomena. One of the key quantity to characterize the results of the experiments in such disordered media is the spectral function. It is a building block for theoretical works as well, as it describes the scattering properties. We discuss the recent experiments to measure it, and the possibility of using the Localization Landscape theory to compute this function.

WAVE-20-105 — Filippo Stellin and Giuliano Orso, Université de Paris

  • Subgroup: Cold Atoms
  • Title : Two-body metal-insulator transitions in the Anderson-Hubbard model
  • Abstract: While the occurrence of Anderson transitions in one-particle systems is well known, a fundamental question is whether and how they survive in the presence of interactions. Here we consider a minimal model of two quantum particles in a disordered lattice and subject to short-range mutual interactions. The two-body problem is exactly mapped into an effective single-particle equation for the center-ofmass motion. Based on transmission-amplitude calculations through the Green’s function numerical method, we show that two-particle Anderson transitions do occur in three dimensions and that their universality class is still the orthogonal one. For zero total energy of the pair, the transition occurs in a regime where all single-particle states are localized, and the critical disorder strength is a nonmonotonic function of the interaction strength. Besides, for finite total energy, the phase diagram in the space of energy, disorder and interaction, presents a rich and counterintuitive structure, characterized by a doubly reentrant behaviour, which is caused by the competition between scattering and bound states of the pair. We also prove that, even if interactions can enhance the localization length by three orders of magnitude, no Anderson transition in 2D occurs and previous claims were affected by severe finite-size effects.

WAVE-20-106 — Jean-Philippe Banon, M. Sauty , A. Thayil , M. Filoche, École Polytechnique, École Polytechnique

  • Subgroup: Cold Atoms
  • Title: Localization landscape approximation of the Poisson-Schrödinger system, application to semiconductor devices
  • Abstract: Simulating charge carrier transport in semiconductor devices taking into account quantum localization effects is a challenging task. Despite its limited range of validity, the classical drift-diffusion, or van Roosbroeck system [1], is widely used for modeling charge carrier transport in semiconductor devices due to its relatively low complexity compared to more rigorous models such as hydrodynamic models for example [2, 3]. For three dimensional devices, the drift-diffusion equations remains the most practical numerical option. The drift-diffusion system is a nonlinear system of equations composed of the Poisson equation, two transport equations, and a model for charge carrier densities. In order to account for quantum confinement and localization effects, a model for the charge carrier densities as a function of the electric potential and quasi-Fermi levels based on the eigenstates of the Schrödinger operator may in principle be used. However, the associated computational cost is impractically large for realistic 3D devices. We present here a model of semiconductors based on the localization landscape theory, allowing to account for quantum effects at the nanoscale [4–6]. As a first step towards the resolution of the full localization-landscape-drift-diffusion system, we consider the case of zero applied bias. In this case, the drift-diffusion equations reduce to the nonlinear Poisson equation in which the model for charge carrier density is given by the landscape theory. We illustrate effects of quantum confinement and of alloy composition disorder by comparing solutions to the classical Poisson equation and to the landscape-Poisson equation for three dimensional devices.   
    • [1] W. V. Roosbroeck, Bell System Technical Journal 29, 560 (1950). [2] P. Markowich, C. Ringhofer, and C. Schmeiser, Semiconductor Equations (Springer Vienna, 2012). [3] A. J¨ungel, Transport Equations for Semiconductors, Lecture Notes in Physics, Vol. 773 (Springer, Berlin, 2009). [4] M. Filoche and S. Mayboroda, Proceedings of the National Academy of Sciences 109, 14761 (2012). [5] D. N. Arnold, G. David, D. Jerison, S. Mayboroda, and M. Filoche, Physical Review Letters 116, 056602 (2016). [6] M. Filoche, M. Piccardo, Y.-R. Wu, C.-K. Li, C. Weisbuch, and S. Mayboroda, Physical Review B 95, 144204 (2017).  

About the School on Anderson Localization

While Anderson localization is more than 60 years old, it is still an active subject both in theory and experiments. In this school, we intend to review both the usual theory of Anderson localization as well as the novel landscape theory. Experimentally, we will focus on clean systems enabling accurate measurements with a specific emphasis on the ultracold atom experiments.

The question of ergodicity and many-body localization in disordered systems will also be addressed. The goal is to foster knowledge in order to tackle the open problems in the field. This school is organized and financed by the Simons collaboration the localization of waves. It will include tutorials, invited, and contributed talks.

Doctoral students and young researchers are very welcome, however, the school is a priori open to anyone interested. Participation will be free of charge, including lodging and full board. If you wish to participate, please send an email to the organizing committee ( and include your profile (name, working position and place, birth date) and one or two lines about your motivation. If you wish to present a poster please specify so—some posters could be selected for oral presentation. The organizing and scientific committee (A. Aspect and M. Filoche) will then select the participants and confirm participation as space is limited.

Tutorial lectures will be presented by:

  • M. Filoche (landscape theory of localization)
  • V. Josse (Anderson localization with cold atoms)
  • D. Delande (Anderson localization, state of the art and perspectives), to be confirmed

Confirmed invited speakers include: J. Bloch, N. Cherroret, J.-C. Garreau, M. Hoogerland, S. Skipetrov