Superfluid-insulator transition of ultracold bosons in disordered one-dimensional traps

Vosk, Ronen; Altman, Ehud

doi:10.1103/physrevb.85.024531

Cited by 25 publications

(31 citation statements)

References 29 publications

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“…For the quasiperiodic lattice we estimate indeed an upper bound E c 0.7J. The observation is however not incompatible with the prediction α = α(U) < 1 found in disorder models that include the corrections beyond mean-field [51].…”

Section: Transport In Disordered Latticessupporting

confidence: 41%

“…The summary of these measurements in Fig.8 shows a clear increase of Δ c with U, indicating that the critical momentum of more strongly interacting systems is less affected by the disorder. The increase of Δ c is actually fully justified, since the critical disorder strength to enter the Bose glass phase from the superfluid in the regime of weak interactions is expected to scale as Δ c /J = A(E int /J) α , where E int νU is the total interaction energy per atom, while A and α are coefficients of the order of unity [49,50,51]. In the absence of an analytical model for the superfluid-Bose glass transition in a quasiperiodic lattice, we fit the experimental data with (Δ c − 2)/J = A(νU/J) α to account for the critical Δ 2J for localization in the non-interacting system.…”

Section: Transport In Disordered Latticesmentioning

confidence: 99%

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Transport of an interacting Bose gas in 1D disordered lattices

D’Errico¹,

Chaudhuri²,

Gori³

et al. 2014

AIP Conference Proceedings

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Abstract. We use ultracold atoms in a quasiperiodic lattice to study two outstanding problems in the physics of disordered systems: a) the anomalous diffusion of a wavepacket in the presence of disorder, interactions and noise; b) the transport of a disordered superfluid. a) Our results show that the subdiffusion, observed when interaction alone is present, can be modelled with a nonlinear diffusion equation and the peculiar shape of the expanding density profiles can be connected to the microscopic nonlinear diffusion coefficients. Also when noise alone is present we can describe the observed normal diffusion dynamics by existing microscopic models. In the unexplored regime in which noise and interaction are combined, instead, we observe an anomalous diffusion, that we model with a generalized diffusion equation, where noise-and interaction-induced contributions add each other. b) We find that an instability appearing at relatively large momenta can be employed to locate the fluid-insulator crossover driven by disorder. By investigating the momentum-dependent transport, we observe a sharp crossover from a weakly dissipative regime to a strongly unstable one at a disorder-dependent critical momentum. The set of critical disorder and interaction strengths for which such critical momentum vanishes, can be identified with the separation between a fluid regime and an insulating one and can be related to the predicted zero-temperature superfluid-Bose glass transition.

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Section: Transport In Disordered Latticessupporting

confidence: 41%

Section: Transport In Disordered Latticesmentioning

confidence: 99%

Transport of an interacting Bose gas in 1D disordered lattices

D’Errico¹,

Chaudhuri²,

Gori³

et al. 2014

AIP Conference Proceedings

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“…Similar ideas have been discussed for disordered bosons in one dimension in Ref. 47,48. We defer an investigation of these ideas to future work.…”

Section: B Disorder In the Bcs Couplingmentioning

confidence: 63%

Superconductivity of disordered Dirac fermions

et al. 2013

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We study the effect of disorder on massless, spinful Dirac fermions in two spatial dimensions with attractive interactions, and show that the combination of disorder and attractive interactions is deadly to the Dirac semimetal phase. First, we derive the zero temperature phase diagram of a clean Dirac fermion system with tunable doping level (µ) and attraction strength (g). We show that it contains two phases: a superconductor and a Dirac semimetal. Then, we add disorder, and show that arbitrarily weak disorder destroys the Dirac semimetal, turning it into a superconductor instead. Thus for Dirac fermions near charge neutrality, disorder actually assists superconductivity. We discuss the strength of the superconductivity for both long range and short range disorder. For long range disorder, the superconductivity is exponentially weak in the disorder strength. For short range disorder, a uniform mean field analysis predicts that superconductivity should be doubly exponentially weak in the disorder strength. However, a more careful treatment of mesoscopic fluctuations suggests that locally superconducting puddles should form at a much higher temperature, and should establish global phase coherence at a temperature that is only exponentially small in weak disorder. Thus, mesoscopic fluctuations exponentially enhance the superconducting critical temperature. We also discuss the effect of disorder on the quantum critical point of the clean system, building in the effect of disorder through a replica field theory. We show that disorder is a relevant perturbation to the supersymmetric quantum critical point. We expect that in the presence of attractive interactions, the flow away from the critical point ends up in the superconducting phase, although firm conclusions cannot be drawn since the renormalization group analysis flows to strong coupling. We argue that although we expect the quantum critical point to get buried under a superconducting phase, signatures of the critical point may be visible in the finite temperature quantum critical regime. Our results have implications for experiments on proximity induced superconductivity in Dirac fermion systems, where they imply an enormous disorder-enhancement of the superconducting susceptibility. As a result, the proximity induced superconductivity in dirty systems is expected to be much stronger than that in clean systems at the Dirac point.

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“…The scaling of the superfluid-insulator phase boundary as a function of the strength of disorder and interactions was established at the mean-field level [49][50][51][52][53], and shown to depend in an essential way on the microscopic disorder correlations. For the 1D geometry, the fragmentation mechanisms driving the transition were analyzed by means of Bogoliubov theory [54], while universal features of the transition and many-body corrections at intermediate disorder strengths were worked out with real-space renormalization group (RG) techniques [25,55]. In the latter approach, making contact with experiments is a challenging task [55], and the method itself is not generalized to higher dimensions in a straightforward way [24].…”

Section: Introductionmentioning

confidence: 99%

Superfluid–insulator transition in weakly interacting disordered Bose gases: a kernel polynomial approach

Saliba¹,

Lugan

Savona³

2013

New J. Phys.

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Abstract. An iterative scheme based on the kernel polynomial method is devised for the efficient computation of the one-body density matrix of weakly interacting Bose gases within Bogoliubov theory. This scheme is used to analyze the coherence properties of disordered bosons in one and two dimensions. In the one-dimensional geometry, we examine the quantum phase transition between superfluid and Bose glass at weak interactions, and we recover the scaling of the phase boundary that was characterized using a direct spectral approach by Fontanesi et al (2010 Phys. Rev. A 81 053603). The kernel polynomial scheme is also used to study the disorder-induced condensate depletion in the twodimensional geometry. Our approach paves the way for an analysis of coherence properties of Bose gases across the superfluid-insulator transition in two and three dimensions.

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Superfluid-insulator transition of ultracold bosons in disordered one-dimensional traps

Cited by 25 publications

References 29 publications

Transport of an interacting Bose gas in 1D disordered lattices

Transport of an interacting Bose gas in 1D disordered lattices

Superconductivity of disordered Dirac fermions

Superfluid–insulator transition in weakly interacting disordered Bose gases: a kernel polynomial approach

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