Localization and hybridization across an effective mobility edge in periodically driven speckle potentials

Abstract

Disorder in a 1D quantum lattice induces Anderson localization of the eigenstates and drastically alters transport properties of the lattice. In the original Anderson model, the addition of a periodic driving increases, in a certain range of the driving's frequency and amplitude, localization length of the appearing Floquet eigenstates. We go beyond the uncorrelated disorder case and address the experimentally relevant situation when spatial correlations are present in the lattice potential. Their presence induces the creation of an effective mobility edge in the energy spectrum of the system. We find that a slow driving leads to resonant hybridization of the Floquet states, by increasing both the participation numbers and effective widths of the states in the strongly localized band and decreasing values of these characteristics for the states in the quasi-extended band. Strong driving homogenizes the bands, so that the Floquet states loose compactness and tend to be spatially smeared. In the basis of the stationary Hamiltonian, these states retain localization in terms of participation number but become de-localized and spectrum-wide in term of their effective widths. Signatures of thermalization are also observed.Anderson localization in disordered systems is a fundamental phenomenon that is still posing new puzzles and bringing new surprises [1][2][3]. The original problem of non-interacting quantum particles [4] was studied thoroughly and has been placed in a broad context, resulting in experimental observations of the localization with matter [5][6][7][8], electromagnetic [9], and acoustic waves [10].The effect of periodic modulations on the localization also received considerable attention. It was found that the localization length increases under the low frequency driving (though non-monotonously with the driving amplitude) and decreases in the opposite limit of the fast driving [11]. The increase of the localization length was attributed to the induced interaction between the particle path channels, with those characterized by weakest localization properties making a dominant contribution. In contrast, the high-frequency driving diminishes timeaveraged hopping amplitudes [11][12][13] and enhance the localization, an effect reminiscent of the dynamic localization [14,15]. Recently, it has been shown that the multifrequency driving can substantially increase the localization length [16], and the complete de-localization can be achieved with driven quasi-periodic potentials [17].The existing results, however, address the original Anderson set-up, with on-site energies being random and uncorrelated variables. At the same time, the presence of correlations is inherent to the optical speckle potentials, used in the experiments with atomic Bose-Einstein condensates [18]. Importantly, a finite correlation length leads to emergence of an effective mobility edge separating the bands with localization lengths differing by orders of magnitude [19][20][21].Application of periodic modulations to a system with correla...

Anomalous localization and multifractality in a kicked quasicrystal

“…Namely, the mixing causes multiple mini bands of different localization properties to appear alternatingly, and multiple mobility edges to appear in the Floquet Brillouin zone. At the same time, this coupling mixes Floquet eigenstates with different localization character [41]. Such states with a mixed character are essential in causing delocalization behavior when the initial states are prepared in a localized region.…”

Localization of matter waves in lattice systems with moving disorder

“…As would be demonstrated, such a moving disordered potential with tunable velocity can be readily achieved in the cold atomic systems, even though it is unrealistic in solid-state settings. Contrary to the periodicallydriven disordered systems which are generally delocalized by low-frequency perturbations [12,18,19,21,22], in the proposed model, a sliding localized phase (SLP) was observed at a sufficiently low velocity of the moving potential. Even though the center of mass (COM) of the matter wave adiabatically follows the moving potential, it does not cause diffusion.…”

“…Owing to its unique features such as the perfect isolation from the environment and high degree of parameter tunability [7], the coldatom system represents a new perspective for studying of localization [8][9][10]. For instance, it allows the exploration of localization physics in a far-from-equilibrium system within a strong driving regime inaccessible in conventional solid-state settings [11][12][13], and thus is beyond the scope of the linear response theory derived by Mott [14].…”