Long-time expansion of a Bose-Einstein condensate: Observability of Anderson localization

Donsa, Stefan; Hofstätter, Harald; Koch, Othmar; Burgdörfer, Joachim; Březinová, Iva

doi:10.1103/physreva.96.043630

Cited by 15 publications

(18 citation statements)

References 73 publications

(127 reference statements)

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“…The role which interactions play in Anderson localisation has been richly debated in the literature 3 , 19 , 20 , 44 – 46 . This experiment is conducted with 1.6 × 10 4 atoms, resulting in an average density of ~1 atom/μm 2 .…”

Section: Resultsmentioning

confidence: 99%

Observation of two-dimensional Anderson localisation of ultracold atoms

et al. 2020

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Anderson localisation —the inhibition of wave propagation in disordered media— is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased. Here, we report the results of an experiment measuring the 2D transport of ultracold atoms between two reservoirs, which are connected by a channel containing pointlike disorder. The design overcomes many of the technical challenges that have hampered observation of localisation in previous works. We experimentally observe exponential localisation in a 2D ultracold atom system.

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Section: Resultsmentioning

confidence: 99%

Observation of two-dimensional Anderson localisation of ultracold atoms

et al. 2020

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“…Now, a very common solution to this problem -heavily used in the literature (e.g. [14,16,[58][59][60][61][62]) -is to compute the spatial variance of the localised states instead. Since we are working in 2D, we could tentatively examine the quantity…”

Section: Exact Diagonalisationmentioning

confidence: 99%

“…Understandably, this method is inaccurate for strong disorder. Exact time-dependent simulations with the Schrödinger [6,8,13,14] or Gross-Pitaevskii [15,16] equations can be used instead, but this approach is very time-consuming and yields little insight into the physics. Finally, access to the localisation length directly through the eigenstates of the Hamiltonian is hampered by practical considerations (as we shall show below).…”

Section: Introductionmentioning

confidence: 99%

“…Out of the studies above, one-dimensional (1D) [6, 13, 17-19, 21-23, 30, 31, 34, 35, 37, 38] and two-dimensional (2D) [6-8, 10, 12, 14, 15, 20-28, 36] models have been numerically explored far more thoroughly than three-dimensional (3D) [6,27,34], simply because of the increased computational requirements of higher-dimensional spaces. Possibly the most heavily studied model of localisation is the Anderson model, also known as a tight-binding Hamiltonian [4, 10, 12, 13, 22-27, 29, 30, 32, 34-37, 39-44], but other examples include the kicked rotor [19] (formally equivalent to the Anderson model), the Lloyd model [13,21], the Peierls chain [38], a quantum walker [31], and the continuous Schrödinger equation [13,14,17], with either a speckle potential [7,16], delta-function point scatterers [6,10], or more realistic Gaussian scatterers [8,15].…”

Section: Introductionmentioning

confidence: 99%

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Computing the eigenstate localisation length at very low energies from Localisation Landscape Theory

et al. 2021

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While Anderson localisation is largely well-understood, its description has traditionally been rather cumbersome. A recently-developed theory -Localisation Landscape Theory (LLT) -has unparalleled strengths and advantages, both computational and conceptual, over alternative methods. To begin with, we demonstrate that the localisation length cannot be conveniently computed starting directly from the exact eigenstates, thus motivating the need for the LLT approach. Then, we confirm that the Hamiltonian with the effective potential of LLT has very similar low energy eigenstates to that with the physical potential, justifying the crucial role the effective potential plays in our new method. We proceed to use LLT to calculate the localisation length for very low-energy, maximally localised eigenstates, as defined by the length-scale of exponential decay of the eigenstates, (manually) testing our findings against exact diagonalisation. We then describe several mechanisms by which the eigenstates spread out at higher energies where the tunnelling-in-the-effective-potential picture breaks down, and explicitly demonstrate that our method is no longer applicable in this regime. We place our computational scheme in context by explaining the connection to the more general problem of multidimensional tunnelling and discussing the approximations involved. Our method of calculating the localisation length can be applied to (nearly) arbitrary disordered, continuous potentials at very low energies.

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“…In quantum systems, a paradigmatic instance of a highly controlled system is that of a Bose Einstein Condensate (BEC). It was shown that BEC with tunable interactions, are promising systems to study a number of diffusionrelated phenomena, such as Anderson Localization (AL) in disordered media [15][16][17], the expansion of 1D BEC in disordered speckle potentials [15][16][17][18][19][20][21][22][23], the subdiffusive behavior of the expansion of a wave packet of a 1D quantum, chaotic and nonlinear system [15,22,[24][25][26][27][28][29][30][31][32][33], the Brownian motion of solitons in BEC [34], as well as the superdiffusive motion of an impurity in a BEC studied in [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Control of anomalous diffusion of a Bose polaron

Charalambous

García-March

Muñoz-Gil

et al. 2020

Quantum

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We study the diffusive behavior of a Bose polaron immersed in a coherently coupled two-component Bose-Einstein Condensate (BEC). Polaron superdiffuses if it couples in the same manner to both components, i.e. either attractively or repulsively to both of them. This is the same behavior as that of an impurity immersed in a single BEC. Conversely, the polaron exhibits a transient nontrivial subdiffusive behavior if it couples attractively to one of the components and repulsively to the other. The anomalous diffusion exponent and the duration of the subdiffusive interval can be controlled with the Rabi frequency of the coherent coupling between the two components, and with the coupling strength of the impurity to the BEC.

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Long-time expansion of a Bose-Einstein condensate: Observability of Anderson localization

Cited by 15 publications

References 73 publications

Observation of two-dimensional Anderson localisation of ultracold atoms

Observation of two-dimensional Anderson localisation of ultracold atoms

Computing the eigenstate localisation length at very low energies from Localisation Landscape Theory

Control of anomalous diffusion of a Bose polaron

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