Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates

Abstract

We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andre models in the non-interacting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.

15 pages, 7 figures

References in corpus (11)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Spectroscopy of ultracold atoms by periodic lattice modulations
• Density modulations in an elongated Bose-Einstein condensate released from a disordered potential
• Mean-field phase diagram of cold lattice bosons in disordered potentials
• Delocalization and Heisenberg's uncertainty relation
• Quantum phase transitions in an interacting atom-molecule boson model
• Localization and delocalization of ultracold bosonic atoms in finite optical lattices
• Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasi-periodic optical lattices
• Disorder-enhanced phase coherence in trapped bosons on optical lattices
• Bosons in Disordered Optical Potentials