Bosons in a random potential: condensation and screening in a dense limit

Lee, Derek K. K.; Gunn, John M.

doi:10.1088/0953-8984/2/38/004

Cited by 48 publications

(64 citation statements)

References 21 publications

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“…37. The present study is complementary to the analysis of bosonic excitations within long-range ordered, but strongly inhomogeneous phases, [38][39][40][41][42] where a substantial amount of literature has discussed the localization properties of Goldstone modes, spin waves and phonons at low energies. Here, we focus instead on understanding the insulating, quantum disordered phase of random bosonic systems.…”

Section: 4-7mentioning

confidence: 98%

Localization of disordered bosons and magnets in random fields

Müller

2013

Annals of Physics

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We study localization properties of disordered bosons and spins in random fields at zero temperature. We focus on two representatives of different symmetry classes, hard-core bosons (XY magnets) and Ising magnets in random transverse fields, and contrast their physical properties. We describe localization properties using a locator expansion on general lattices. For 1d Ising chains, we find non-analytic behavior of the localization length as a function of energy at ω = 0, ξ −1 (ω) = ξ −1 (0) + A|ω| α , with α vanishing at criticality. This contrasts with the much smoother behavior predicted for XY magnets. We use these results to approach the ordering transition on Bethe lattices of large connectivity K, which mimic the limit of high dimensionality. In both models, in the paramagnetic phase with uniform disorder, the localization length is found to have a local maximum at ω = 0. For the Ising model, we find activated scaling at the phase transition, in agreement with infinite randomness studies. In the Ising model long range order is found to arise due to a delocalization and condensation initiated at ω = 0, without a closing mobility gap. We find that Ising systems establish order on much sparser (fractal) subgraphs than XY models. Possible implications of these results for finite-dimensional systems are discussed.

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Section: 4-7mentioning

confidence: 98%

Localization of disordered bosons and magnets in random fields

Müller

2013

Annals of Physics

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“…In the early 90's, disordered Bose condensates were studied using the Bogoliubov approximation [344][345][346]. In [344], the screening of the random potential in a twodimensional dense Bose gas in a lattice due to the short-range repulsive interactions was addressed.…”

Section: Disordered Interacting Bosonic Lattice Models In Condensed Mmentioning

confidence: 99%

“…In [344], the screening of the random potential in a twodimensional dense Bose gas in a lattice due to the short-range repulsive interactions was addressed. This screening is effective when the healing length is short enough so that the condensate can adjust to the variations of the random potential.…”

Section: Disordered Interacting Bosonic Lattice Models In Condensed Mmentioning

confidence: 99%

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

Lewenstein

Sanpera

Ahufinger

et al. 2007

Advances in Physics

2,049

2,338

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We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in "artificial" magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed.

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“…Asĉ 2 is a positive function by virtue of the Wiener-Khinchin theorem, we always have (2) > 0, i.e., μ < gn c in the presence of an external potential (see also Ref. [94]). In Fig.…”

Section: First Correction To the Mean-field Equation Of Statementioning

confidence: 99%

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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Bosons in a random potential: condensation and screening in a dense limit

Cited by 48 publications

References 21 publications

Localization of disordered bosons and magnets in random fields

Localization of disordered bosons and magnets in random fields

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

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