Observation of the Anderson metal-insulator transition with atomic matter waves: Theory and experiment

Lemarié, Gabriel; Chabé, Julien; Szriftgiser, Pascal; Garreau, Jean Claude; Grémaud, Benoît; Delande, Dominique

doi:10.1103/physreva.80.043626

Cited by 111 publications

(192 citation statements)

References 71 publications

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“…This 1D stroboscopic model could become a competitive alternative to the 2D network model for numerical studies of the quantum Hall phase transition, 4 similarly to how the 1D quantum kicked rotator is an alternative to the 3D Anderson model of the metal-insulator transition. 9 Since quantum kicked rotators can be realized using cold atoms, 10,11,39,46 the stroboscopic model might also provide a way to study the quantum Hall effect using atomic matter waves. Cold atoms represent clean and controllable experimental quantum systems, owing to the ability to tune interaction strengths and external potentials.…”

Section: Discussionmentioning

confidence: 99%

“…47 Since, in the kicked rotator, momentum plays the role of coordinate, in this way the diffusion coefficient could be measured, and the critical exponent of the metal-insulator transition was obtained from its time dependence. 10,11,39 To realize the stroboscopic model of the quantum Hall effect, a controllable spin-1/2 degree of freedom is needed. Hyperfine levels in alkali or earth-alkali atoms can be used for that purpose, 47 and arbitrary rotations of this pseudospin have been demonstrated in Cs.…”

Section: Discussionmentioning

confidence: 99%

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Quantum Hall effect in a one-dimensional dynamical system

Dahlhaus

Edge²,

Tworzydło³

et al. 2011

Phys. Rev. B

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We construct a periodically time-dependent Hamiltonian with a phase transition in the quantum Hall universality class. One spatial dimension can be eliminated by introducing a second incommensurate driving frequency, so that we can study the quantum Hall effect in a one-dimensional (1D) system. This reduction to 1D is very efficient computationally and would make it possible to perform experiments on the 2D quantum Hall effect using cold atoms in a 1D optical lattice.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Quantum Hall effect in a one-dimensional dynamical system

Dahlhaus

Edge²,

Tworzydło³

et al. 2011

Phys. Rev. B

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“…At much longer times (t = 10 4 = 400T ), a CFS peak replicating the CBS peak at x 0 is clearly visible. ‡ Note that if ω 2 is incommensurable with 2π, the KR becomes quasi-periodic in time and its dynamics is effectively 2D [69,38,39]. …”

Section: Cbs/cfs Peaks For the Atomic Kicked Rotormentioning

confidence: 99%

Coherent backscattering and forward-scattering peaks in the quantum kicked rotor

et al. 2017

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Abstract. We propose and analyze an experimental scheme using the quantum kicked rotor to observe the newly-predicted coherent forward scattering peak together with its long-known twin brother, the coherent backscattering peak. Contrary to coherent backscattering, which arises already under weak-localization conditions, coherent forward scattering is only triggered by Anderson or strong localization. So far, coherent forward scattering has not been observed in conservative systems with elastic scattering by spatial disorder. We propose to turn to the quantum kicked rotor, which has a long and succesful history as an accurate experimental platform to observe dynamical localization, i.e., Anderson localization in momentum space. We analyze the coherent forward scattering effect for the quantum kicked rotor by extensive numerical simulations, both in the orthogonal and unitary class of disordered quantum systems, and show that an experimental realization involving phase-space rotation techniques is within reach of state-of-the-art cold-atom experiments.arXiv:1612.02091v1 [cond-mat.quant-gas] 7 Dec 2016Coherent back and forward scattering peaks in the quantum kicked rotor 2

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“…The effect of interactions is also being studied experimentally [19][20][21]. Finally, the Anderson metal-insulator transition is being actively studied with a cold atom "quantum simulator" of the 3D Anderson model [22], including, the experimental determination of its critical exponent [7,23,24] and the study of its critical state [25].…”

Section: Introductionmentioning

confidence: 99%

Interacting ultracold bosons in disordered lattices: Sensitivity of the dynamics to the initial state

Vermersch

Garreau

2012

Phys. Rev. E

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We study the dynamics of a nonlinear one-dimensional disordered system obtained by coupling the Anderson model with the Gross-Pitaevskii equation. An analytical model provides us with a single quantity globally characterizing the localization of the system. This quantity obeys a scaling law with respect to the width of the initial state, which can be used to characterize the dynamics independently of the initial state.

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Observation of the Anderson metal-insulator transition with atomic matter waves: Theory and experiment

Cited by 111 publications

References 71 publications

Quantum Hall effect in a one-dimensional dynamical system

Quantum Hall effect in a one-dimensional dynamical system

Coherent backscattering and forward-scattering peaks in the quantum kicked rotor

Interacting ultracold bosons in disordered lattices: Sensitivity of the dynamics to the initial state

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