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Quantum Transport in Disorder



  • Student : Vasiliki Angeloupoulou (1 year internship - M2 Heidelberg)
  • Ex Members: Mukhtar Mussawadah, Vincent Denechaud (CIFRE/DGA -SAFRAN grant), Valentin Volchkov (Marie Sklodowska-Curie Grant No. 655933), Jérémie Richard, Kilian Müller, Fred Jendrzejewski, Alain Bernard, Patrick Cheinet, Juliette Billy, William Guerin, Jean Felix Riou, Marie Fauquembergue
  • Ex Visitors: Raymond Santoso, Valentin Volchkov, Aditya Date, Chris Vo

URGENT: PhD and Post Doc positions available (Simons foundation)

PhD Position 2019 (PDF / 447,22 kB)
Postdoc position 2019 (PDF / 17,90 kB)

Anderson localization with ultracold atoms (see below for further details)


Our team study the transport properties of matter waves in well controlled disordered potentials, focusing especially on the celebrated Anderson localization. Landmarks results has been obtained in the team, such as the direct observation of 1D and 3D Anderson Localization or Coherent Backscattering (which is a direct signature of phase coherent effect in disorder media). Using a novel method (based on spectroscopy) our current goal is to investigate in detail the Anderson transition that occurs in 3D, which constitutes an utmost challenge in the field.

Main publications

1D Localization Nature 2008 (PDF / 448,13 kB)
CBS - PRL 2012 (PDF / 645,61 kB)
CBS revival PRL 2015 (PDF / 1,45 MB)
Spectral Functions PRL 2018 (PDF / 983,17 kB)
Elastic Scattering PRL 2019 (PDF / 658,64 kB)

Complete list of communications: HAL


Details on research activities

Anderson Localization of ultracold atoms in optical disorder

General Motivations:

Disorder lies at the heart of many fundamental phenomena in condensed matter systems, such as metal-insulator transition in amorphous electronic conductors, superfluidity in porous media, and possibly high-Tc superconductivity.

The celebrated Anderson localization (P. W. Anderson Phys. Rev. 109, 1492, 1958) is one of the most emblematic effect of the disorder. Indeed, it predicts that the disorder can completely freeze the motion of quantum particles, leading to a genuine metal-insulator transition. This intriguing effect results from the destructive quantum interferences between many scattering paths and is ubiquituous to wave physics. To date, Anderson localization has been observed with differents systems, for electronic or classical waves ( Lagendijk et al. Phys. Today August 2009, for a recent review). However, despite extensive theoretical and experimental efforts over the past 50 years, the precise understanding of this localization effect remains an exciting but formidable task, both for experiment and theory (see e.g. the webpage of the theory team in our group).

Ultracold atomic systems offers new approaches to these issues. In particular, their great promises have been demonstrated in our group by two landmarks experiments: the first demonstrations of Anderson localization with matter waves (1D and 3D) and direct signature of coherence via the coherent backscattering signal. We are currently working on a new method that will allow us to investigate the localization-delocalization quantum phase transition (Anderson transition) that occurs in 3D, the "graal" of the domain.


Main results:



Elastic Scattering Time of Matter-Waves in Disordered Potentials (Phys. Rev. Lett. 122, 100403, 2019). We report on an extensive study of the elastic scattering time $\tauS$ of matter-waves in optical disordered potentials. Using direct experimental measurements, numerical simulations and comparison with first-order Born approximation based on the knowledge of the disorder properties, we explore the behavior of $\tauS$ over more than three orders of magnitude, spanning from the weak to the strong scattering regime. We study in detail the location of the crossover and, as a main result, we reveal the strong influence of the disorder statistics, especially on the relevance of the widely used Ioffe-Regel-like criterion $k\lS\sim 1$. While it is found to be relevant for Gaussian-distributed disordered potentials, we observe significant deviations for laser speckle disorders that are commonly used with ultracold atoms. Our results are crucial for connecting experimental investigation of complex transport phenomena, such as Anderson localization, to microscopic theories.



Measurement of Spectral Functions of Ultracold atoms in Disordered Potentials (Phys. Rev. Lett. 120, 060404, 2018). We report on the measurement of the spectral functions of non-interacting ultra-cold atoms in a three-dimensional disordered potential resulting from an optical speckle field. Varying the disorder strength by two orders of magnitude, we observe the crossover from the "quantum" perturbative regime of low disorder to the "classical" regime at higher disorder strength, and find an excellent agreement with numerical simulations. The method relies on the use of state-dependent disorder and the controlled transfer of atoms to create well-defined energy states. This opens new avenues for experimental investigations of three-dimensional Anderson localization.



Suppression and Revival of Weak Localization Through Control of Time Reversal Symmetry (Phys. Rev. Lett. 114, 205310, 2015). We report on the observation of suppression and revival of coherent backscattering of ultra-cold atoms launched in an optical disorder in a quasi-2D geometry and submitted to a short dephasing pulse, as proposed in T. Micklitz et al., Phys. Rev. B 91, 064203 (2015). This observation demonstrates a novel and general method to study weak localization by manipulating time reversal symmetry in disordered systems.In future experiments, this scheme could be extended to investigate higher order localization processes at the heart of Anderson (strong) localization.



Coherent Backscattering of Ultracold atoms (Phys. Rev. Lett. 109, 195302, 2012). We report on the direct observation of coherent backscattering (CBS) of ultra-cold atoms, in a quasi two dimensional configuration. Launching atoms with a well defined momentum in a laser speckle disordered potential, we follow the progressive build up of the momentum scattering pattern, consisting of a ring associated with multiple elastic scattering, and the CBS peak in the backward direction. The observation of CBS can be considered a direct signature of coherence in quantum transport of particles in disordered media. It is responsible for the so called weak localization phenomenon, which is the precursor of Anderson localization.



First evidence of 3D Anderson localization with ultracold atoms (Jendrzejewski et al. Nature Physics 8, 392 2012, arXiv:1108.0137). A BEC, suspended against gravity by a magnetic levitation, is allowed to expand in a 3D laser speckle disorder. This disorder is created by crossing two coherent speckle fields at 90°, resulting in short correlation lengths in all directions in space. A phenomenological analysis of our data distinguishes a localized component of the resulting density profile from a diffusive component. The observed localization cannot be interpreted as the classical trapping of particles with energy below the classical percolation threshold in the disorder, nor can it be understood as quantum trapping in local potential minima. Instead, our data are compatible with the self-consistent theory of Anderson localization tailored to our system. This experiment paves the way towards an utmost challenge : the precise inspection of metal-insulator phase transition (between localized and diffusive states) in 3D.



Direct observation of 1D Anderson localization of matter wave (Billy et al. Nature 493, 891 (2008)). A very dilute BEC is released in a 1D waveguide in presence of laser speckle disorder. We observed that the propagation is stopped by a very weak amount of disorder (i.e. without any classical trapping). The inspection of the localized density profiles reveal an exponential decay in the wings, i.e. the emblematic signatures of Anderson localization. The localization lengths have been measured and were found to be in good agreement with theoretical predictions (L. Sanchez-Palencia et al. Phys. Rev. Lett. 98, 210401 (2007)).

Past research activity:

The Guided Atom Laser: a new tool for quantum transport phenomena

General Motivations:

The Bose-Einstein condensation of atoms in the lowest level of a trap represents the matter-wave analogue to the accumulation of photons in a single mode of a laser cavity. In analogy to photonic lasers, coherent atom lasers can then be obtained by outcoupling a part of the atoms from a trapped Bose-Einstein condensate (which acts as a reservoir) to free space. Such atomic outcouplers (for instance realized by applying a radio frequency field that spin flips the atoms from an initial trapped state to a final free state) play the role of the partially transmitting mirror in optics. For the first realization of atom lasers, the atoms were however simply falling under gravity, leading to the rapid increase in energy, i.e. an important decrease of the de Broglie wavelength.

In the Atom Optics group, we develop a new type of atom laser: the guided atom laser (see Fig. 3). In this configuration the atoms are directly outcoupled in a horizontal waveguide, in close analogy with ‘pig-tailed’ photonic lasers. This scheme permits (i) a better control of the atomic motion and, in particular, to create a large and constant de Broglie wavelength along the propagation and (ii) to control the intra-laser interactions (analogous to photonic Kerr non-linearities) by tuning the atom laser flux.

Thus, this guided atom laser opens new prospects to study quantum transport phenomena past obstacles, both in the linear (with low interactions) and the nonlinear regime (with strong interactions).



First demonstration of a quasi-continuous horizontal guided atom laser (W. Guerin et al., Phys. Rev. Lett. 97, 200402 (2006)). A BEC is produced in a hybrid opto-magnetic trap composed of a horizontal optical waveguide for the transverse confinement and a shallow magnetic trap that provides the longitudinal one. The atom laser is directly outcoupled by a rf field into the waveguide. Cancelling the gravity allows us to create large and constant de Broglie (around 1µm) along the propagation.



Characterization of the flux properties of a guided atom laser (A. Bernard et al., New. J. Phys. 13, 065015 (2011)). We investigated here both the outcoupling spectrum (flux of the atom laser versus rf frequency of the outcoupler) and the flux limitations imposed to obtain a quasicontinuous emission. This work has allowed us to identify the operating range of the guided atom laser and to confirm its promises for studying quantum transport phenomena.



Beam quality of an atom laser (J. F. Riou et al. Phys. Rev. Lett. 96, 070404 (2006)). In analogy to photon lasers, we generalized here the M2 factor to characterize the quality of nonideal atom-laser beams. Indeed the atom laser wavefront can be distorted by the strong lensing effect of the Bose-Einstein condensate (BEC) from which it is outcoupled, In this work the M2 factor is predicted theorically for different lensing effects. These predictions are found in good agreement with the observations.