The superfluid insulator transition of ultra-cold bosons in disordered 1d traps

Abstract

We derive an effective quantum Josephson array model for a weakly interacting one-dimensional condensate that is fragmented into weakly coupled puddles by a disorder potential. The distribution of coupling constants, obtained from first principles, indicate that weakly interacting bosons in a disorder potential undergo a superfluid insulator transition controlled by a strong randomness fixed point [Phys. Rev. Lett. 93, 150402 (2004)]. We compute renormalization group flows for concrete realizations of the disorder potential to facilitate finite size scaling of experimental results and allow comparison to the behavior dictated by the strong randomness fixed point. The phase diagram of the system is obtained with corrections to mean-field results.

10 pages, 6 figures, expanded version including a calculation of a global phase diagram

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• Transport of a Bose gas in 1D disordered lattices at the fluid-insulator transition
• Strong disorder renormalization group primer and the superfluid-insulator transition
• Disordered bosons in one dimension: from weak to strong randomness criticality
• Numerical evidence for strong randomness scaling at a superfluid-insulator transition of one-dimensional bosons
• Superfluid-insulator transition of two-dimensional disordered Bose gases
• Quench-induced delocalization
• Mixtures of ultra-cold atoms in 1D disordered potentials
• Strongly interacting bosons in 1D disordered lattice: phase coherence of distorted Mott phases
• Kane-Fisher weak link physics in the clean scratched-XY model
• Full distribution of the superfluid fraction and extreme value statistics in a one dimensional disordered Bose gas
• Bose-Einstein condensation in a minimal inhomogeneous system
• Superfluid-insulator transition in weakly interacting disordered Bose gases: a kernel polynomial approach