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

Abstract

We investigate the effects of disorder and lattice geometry against localisation phenomena in a weakly interacting ultracold bosonic gas confined in a 2D optical lattice. The behaviour of the quantum fluid is studied at the mean-field level performing computational experiments, as a function of disorder strength for lattices of sizes similar to current experiments. Quantification of localisation, away from the Bose glass phase, was obtained directly from the stationary density profiles through a robust statistical analysis of the condensate component, as a function of the disorder amplitude. Our results show a smooth transition, or crossover, to localisation induced by disorder in square and triangular lattices. In contrast, associated to its larger tunneling amplitude, honeycomb lattices show absence of localisation for the same range of disorder strengths and same lattice amplitude, while also exhibiting partial localisation for large disorder amplitudes. We also conclude that the coordination number z have a partial influence on how fast this smooth transition occurs as the system size increases. Signatures of disorder are also found in the ground state energy spectrum, where a continuous distribution emerges instead of a distribution of sharp peaks proper to the system in the absence of disorder.

Anderson localisation in two dimensions: insights from Localisation Landscape Theory, exact diagonalisation, and time-dependent simulations

“…Several studies have approached the question of interactions in the presence of disorder in cold-atom systems via the Gross-Pitaevskii equation, e.g., [137] in 2D and [138,139,51] in 1D. Reference [51] is particularly interesting, predicting that 1D experiments would not be able to clearly detect Anderson localisation due to the presence of interactions.…”

Relaxation of ferromagnetic domains in a disordered lattice in 2D

“…Since the prepared initial state is non-stationary, the hyperfine spin populations will evolve under the influence of both, disorder and interactions. Previous analysis of a single BEC component confined in a disordered square in 2D have shown that, in the weakly interacting regime, the net effect of the disorder is to localize the condensate density in bounded regions [19]. As a matter of fact, the size of those bounded regions become shorter and shorter as the amplitude of the disorder strength is increased.…”

“…Thus, besides the contribution of the harmonic confinement, the potential depth at each point (x, y) is the result of adding/subtracting a random number δ (x, y) to the amplitude of the potential defining the square lattice at zero disorder. Several previous studies have shown that the mean-field approximation describes the main effects of weakly interacting disordered systems [19,[21][22][23][24].…”

“…1). This arrangement together with a recent study, performed at mean field level, where the effect of disorder is to induce the emergence of spatially localized densities, as a function of the disorder magnitude [19], are our starting point to study the dynamics of the double spin domain. The idea here presented can be extended to other geometrical configurations, like those considered in [19] that can be useful for practical purposes as for instance the design of spin based magnetic protocols with complex configurations.…”

Localization and Delocalization of Ground States of Bose--Einstein Condensates Under Disorder

“…Despite plenty of numerical evidence (cf. [GGCBP19] and the references therein for a recent overview), to the best of our knowledge there has not yet been any direct experimental observation of the localization of ground states under disorder.…”