Selective state spectroscopy and multifractality in disordered Bose-Einstein condensates: a numerical study

Abstract

We propose to apply a modified version of the excitation scheme introduced by Volchkov et al. on bosons experiencing hyperfine state dependent disorder to address the critical state at the mobility edge of the Anderson localization transition, and to observe its intriguing multifractal structure. An optimally designed, spatially focused external radio frequency pulse can be applied to generate transitions to eigenstates in a narrow energy window close to the mobility edge, where critical scaling and multifractality emerge. Alternatively, two-photon laser scanning microscopy is proposed to address individual localized states even close to the transition. The projected image of the cloud is shown to inherit multifractality and to display universal density correlations. Interactions – unavoidably present – are taken into account by solving the Gross-Pitaevskii equations, and their destructive effect on the spectral resolution and the multifractal spectrum is analyzed. Time of flight images of the excited states are predicted to show interference fringes in the localized phase, while they allow one to map equal energy surfaces deep in the metallic phase.

Bichromatic state-dependent disordered potential for Anderson localization of ultracold atoms

“…It is worth noting that this scheme could be extended to other kind of optical potentials used to study disordered systems, such as those created by spatial light modulators as well as quasi-periodic lattices 4 , see, e.g., [ 49 , 50 ]. It opens also many prospects to address fundamental questions related to the Anderson transition, such as the observation of multifractalilty [ 51 ], comparison with new theoretical approaches such as the one based on the “hidden landscape” [ 21 , 31 ], or general Anderson transition with different universality class [ 52 ], dimensions [ 53 ], or even in the presence of non-Hermitian disorder [ 54 ].…”

Localisation of weakly interacting bosons in two dimensions: disorder vs lattice geometry effects

“…From the theoretical perspective, there has been an extensive amount of work addressing the study of transport in disordered optical lattices 15,37–40 . Additionally, proposals to investigate fractal structure induced by disorder 41 and measurement of system replicas simultaneously 42 have been put forward. The interplay of disorder with spin-orbit coupling 43 , spin degrees of freedom 44,45 , supersolidity 46 , and Dirac fermions 47 are being explored.…”