# Quantum Transport in Disorder

## Members

Permanent Staff: Vincent Josse, Alain Aspect

PhD Student: Yukun Guo, Baptiste Lecoutre

Postdoc: Azer Trimeche (SIMONS Wave project)

Ex members: Vasiliki Angelopoulou  , Adrien Signoles (SIRTEQ fellowship), 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

## Main activity: Anderson localization with ultracold atoms

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. This work is supported by the SIMONS foundation via the multidisplinary WAVE project that gathers physicists and mathematiciansto study this celebrated phenomenon in a renewed perspective.

## Main publications

Complete list of communications available here : 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.

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

Ultracold atoms in disordered potentials: elastic scattering time in the strong scattering regime (A. Signoles et al., New. J. Phys. 21, 105002, 2019). We study the elastic scattering time $\tauS$ of ultracold atoms propagating in optical disordered potentials in the strong scattering regime, going beyond the recent work of J. Richard \emph{et al.} \textit{Phys. Rev. Lett.} \textbf{122} 100403 (2019). There, we identified the crossover between the weak and the strong scattering regimes by comparing direct measurements and numerical simulations to the first order Born approximation. Altogether our study characterizes the validity range of usual theoretical methods to predict the elastic scattering time of matter waves, which is essential for future close comparison between theory and experiments, for instance regarding the ongoing studies on Anderson localization.

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 τS 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 τS 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 klS~~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)).