Semiclassical spectral function and density of states in speckle potentials

Prat, Tony; Delande, Dominique

doi:10.1103/physreva.94.022114

Cited by 15 publications

(31 citation statements)

References 41 publications

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“…[19,20]). This induces a non-trivial annular shape of the incoherent background in momentum space [24] that complicates the precise observation of coherence peaks.…”

Section: Theoretical Descriptionmentioning

confidence: 99%

“…However the critical properties the 3D AT remain difficult to analyze by only using these real-space observables [16,17,18]. Indeed, the main challenge is to circumvent the large disorderinduced energy broadening of the initial state [19,20] and to select a sufficiently narrow energy window to avoid blurring the energy dependence of the diffusion constant and of the localization length near the critical point [21]. Though energy-filtering methods have been proposed for cold atoms [22], their successful experimental implementation is still lacking.…”

Section: Introductionmentioning

confidence: 99%

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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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“…[19,20]). This induces a non-trivial annular shape of the incoherent background in momentum space [24] that complicates the precise observation of coherence peaks.…”

Section: Theoretical Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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“…For the strongest disorder amplitude = -V 4008 kHz R , the green dashed line indicates the distribution ( ) P V sp . of this peak is related to an accumulation of bound states around the averaged ground state harmonic oscillator energy [46][47][48].…”

Section: Comparison With Measured Spectral Functionsmentioning

confidence: 97%

“…For our parameters, one hass E h 460 Hz. disorder) [46,47]. In that case, the FWHM  D of the spectral function is always proportional to | | V R , with a factor that depends on the specific profile of P(V ), yielding the limit t µ | | V 1 s sf,cl R at large disorder.…”

Section: Generalities About Spectral Functionsmentioning

confidence: 99%

“…Determining the self energy is a complex task and it is in general not possible to have an exact expression. Various theoretical approaches render possible its estimate in certain regimes, such as perturbative treatments using a Born expansion [14,45], self-consistent approximations [16,17] or semi-classical considerations [46,47]. Without going further on the derivation of the self-energy (see below for the perturbative treatment and the self-consistent approach), it is nevertheless possible to gain some physical insight on the expected profiles of the spectral function in the different regimes of scattering.…”

Section: Generalities About Spectral Functionsmentioning

confidence: 99%

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Ultracold atoms in disordered potentials: elastic scattering time in the strong scattering regime

et al. 2019

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We study the elastic scattering time t s of ultracold atoms propagating in optical disordered potentials in the strong scattering regime, going beyond the recent work of Richard et al (2019 Phys. Rev. Lett. 122 100403). 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. Here we focus specifically on the strong scattering regime, where the first order Born approximation is not valid anymore and the scattering time is strongly influenced by the nature of the disorder. To interpret our observations, we connect the scattering time t s to the profiles of the spectral functions that we estimate using higher order Born perturbation theory or self-consistent Born approximation. The comparison reveals that self-consistent methods are well suited to describe t s for Gaussiandistributed disorder, but fails for laser speckle disorder. For the latter, we show that the peculiar profiles of the spectral functions, as measured independently in Volchkov et al (2018 Phys. Rev. Lett. 120 060404), must be taken into account. 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. s OPEN ACCESS RECEIVED

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Supervised machine learning of ultracold atoms with speckle disorder

Pilati

Pieri

2019

Sci Rep

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We analyze how accurately supervised machine learning techniques can predict the lowest energy levels of one-dimensional noninteracting ultracold atoms subject to the correlated disorder due to an optical speckle field. Deep neural networks with different numbers of hidden layers and neurons per layer are trained on large sets of instances of the speckle field, whose energy levels have been preventively determined via a high-order finite difference technique. The Fourier components of the speckle field are used as the feature vector to represent the speckle-field instances. A comprehensive analysis of the details that determine the possible success of supervised machine learning tasks, namely the depth and the width of the neural network, the size of the training set, and the magnitude of the regularization parameter, is presented. It is found that ground state energies of previously unseen instances can be predicted with an essentially negligible error given a computationally feasible number of training instances. First and second excited state energies can be predicted too, albeit with slightly lower accuracy and using more layers of hidden neurons. We also find that a three-layer neural network is remarkably resilient to Gaussian noise added to the training-set data (up to 10% noise level), suggesting that cold-atom quantum simulators could be used to train artificial neural networks.

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Semiclassical spectral function and density of states in speckle potentials

Cited by 15 publications

References 41 publications

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

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

Ultracold atoms in disordered potentials: elastic scattering time in the strong scattering regime

Supervised machine learning of ultracold atoms with speckle disorder

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