Diffusion of cold-atomic gases in the presence of an optical speckle potential

Beilin, Leonid; Gurevich, E.; Shapiro, Boris

doi:10.1103/physreva.81.033612

Cited by 11 publications

(24 citation statements)

References 23 publications

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“…For a weak external potential, however, all the terms introduced by g − ν in Eq. (25) are at least of second order in V R [see Eq. (B16) and the discussion below], so that we can neglect the second term on the right-hand side (r.h.s.)…”

Section: Effective Schrödinger Equationmentioning

confidence: 99%

“…Besides, the terms proportional to in Eqs. (25) and (26) are at least of second order in the disorder amplitude V R (see Sec. III A1), and can also be neglected in a first-order approach.…”

Section: Effective Schrödinger Equationmentioning

confidence: 99%

“…While details of the derivation can be found in Appendix C, here we just outline the approach. The starting point is again the set of BdGEs (25) and (26) in the decoupling basis g ± . Retaining terms up to second order in the potential amplitude V R , we find a new approximate Schrödinger-like equation for g + :…”

Section: E Beyond the Born Approximationmentioning

confidence: 99%

“…So far much attention has been devoted to studies of the disorder-induced damping of motion in Bose [5][6][7][8][9][10] and Fermi [11] gases, classical localization [12][13][14][15][16][17][18][19][20], spatial diffusion [19][20][21][22][23][24][25], and Anderson localization in regimes where interactions can be neglected [18,21,24,[26][27][28][29][30][31][32][33][34][35][36][37][38][39]. The effects of disorder in interacting quantum systems have also been studied in a variety of contexts, such as transport in weakly interacting Bose-Einstein condensates [40][41][42][43][44][45][46][47]…”

Section: Introductionmentioning

confidence: 99%

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Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

Lugan

Sanchez-Palencia

2011

Phys. Rev. A

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Published versionInternational audienceWe study the Anderson localization of Bogoliubov quasiparticles (elementary many-body excitations) in a weakly interacting Bose gas of chemical potential $\mu$ subjected to a disordered potential $V$. We introduce a general mapping (valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov-de Gennes equations onto a single-particle Schrödinger-like equation with an effective potential. For disordered potentials, the Schrödinger-like equation accounts for the scattering and localization properties of the Bogoliubov quasiparticles. We derive analytically the localization lengths for correlated disordered potentials in the one-dimensional geometry. Our approach relies on a perturbative expansion in $V/\mu$, which we develop up to third order, and we discuss the impact of the various perturbation orders. Our predictions are shown to be in very good agreement with direct numerical calculations. We identify different localization regimes: For low energy, the effective disordered potential exhibits a strong screening by the quasicondensate density background, and localization is suppressed. For high-energy excitations, the effective disordered potential reduces to the bare disordered potential, and the localization properties of quasiparticles are the same as for free particles. The maximum of localization is found at intermediate energy when the quasicondensate healing length is of the order of the disorder correlation length. Possible extensions of our work to higher dimensions are also discussed

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Section: Effective Schrödinger Equationmentioning

confidence: 99%

“…Besides, the terms proportional to in Eqs. (25) and (26) are at least of second order in the disorder amplitude V R (see Sec. III A1), and can also be neglected in a first-order approach.…”

Section: Effective Schrödinger Equationmentioning

confidence: 99%

Section: E Beyond the Born Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

Lugan

Sanchez-Palencia

2011

Phys. Rev. A

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“…Cherroret and Skipetrov 2009 [17] had shown the typical diffusion coefficient of the Bose-Einstein Condensate in a three-dimensional random potential. Beilin et al 2010 [18] considered diffusion of cold-atomic Fermi gas in the presence of a random optical speckle potential. [19] numerically studied the dynamics regimes of classical transport of cold atoms gases in a twodimensional anisotropic disorder potential.…”

Section: Introductionmentioning

confidence: 99%

Evaluated Excited-State Time-Independent Correlation Function and Eigenfunction of the Harmonics Oscillator Cosine Asymmetric Potential via Numerical Shooting Method

Hutem

Moonsri

2015

Physics Research International

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We aimed to evaluate the ground-state and excite-state energy eigenvalue (En), wave function, and the time-independent correlation function of the atomic density fluctuation of a particle under the harmonics oscillator Cosine asymmetric potential (Saad et al. 2013). Instead of using the 6-point kernel of 4 Green's function (Cherroret and Skipetrov, 2008), averaged over disorder, we use the numerical shooting method (NSM) to solve the Schrödinger equation of quantum mechanics system with Cosine asymmetric potential. Since our approach does not use complicated formulas, it requires much less computational effort when compared to the Green functions techniques (Cherroret and Skipetrov, 2008). We show that the idea of the program of evaluating time-independent correlation function of atomic density is underdamped motion for the Cosine asymmetric potential from the numerical shooting method of this problem. Comparison of the time-independent correlation function obtained from numerical shooting method by and correlation function experiment by Kasprzak et al. (2008). We show the intensity of atomic density fluctuation ( ( ) =̃( ) −̃( )) in harmonics oscillator Cosine asymmetric potential by numerical shooting method.

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Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder

Pezzé

Robert-De-Saint-Vincent²,

Bourdel

et al. 2011

New J. Phys.

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We numerically study the dynamics of cold atoms in a two-dimensional disordered potential. We consider an anisotropic speckle potential and focus on the classical dynamics, which is relevant to some recent experiments. Firstly, we study the behavior of particles with a fixed energy and identify different transport regimes. For low energy, the particles are classically localized due to the absence of a percolating cluster. For high energy, the particles undergo normal diffusion and we show that the diffusion coefficients scale algebraically with the particle energy, with an anisotropy factor which significantly differs from that of the disordered potential. For intermediate energy, we find a transient sub-diffusive regime, which is relevant to the time scale of typical experiments. Secondly, we study the behavior of a cold-atomic gas with an arbitrary energy distribution, using the above results as a groundwork. We show that the density profile of the atomic cloud in the diffusion regime is strongly peaked and, in particular, that it is not Gaussian. Its behavior at large distances allows us to extract the energy-dependent diffusion coefficients from experimental density distributions. For a thermal cloud released into the disordered potential, we show that our numerical predictions are in agreement with experimental findings. Not only does this work give insights to recent experimental results, but it may also serve interpretation of future experiments searching for deviation from classical diffusion and traces of Anderson localization.

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Diffusion of cold-atomic gases in the presence of an optical speckle potential

Cited by 11 publications

References 23 publications

Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

Evaluated Excited-State Time-Independent Correlation Function and Eigenfunction of the Harmonics Oscillator Cosine Asymmetric Potential via Numerical Shooting Method

Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder

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