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arXiv:1102.5299 · The European Physical Journal D

Localization of a non interacting quantum wave packet in one-dimensional disordered potentials

M. Moratti, Michele Modugno

Published May 1, 2012• 9 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2012-30132-3

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Considering the discrete nonlinear Schrödinger model with dipole-dipole interactions (DDIs), we comparatively and numerically study the effects of contact interaction, DDI and disorder on the properties of diffusion of dipolar condensate in one-dimensional quasi-periodic potentials. Due to the coupled effects of the contact interaction and the DDI, some new and interesting mechanisms are found: both the DDI and the contact interaction can destroy localization and lead to a subdiffusive growth of the second moment of the wave packet. However, compared with the contact interaction, the effect of DDI on the subdiffusion is stronger. Furthermore and interestingly, we find that when the contact interaction (λ 1 ) and DDI (λ 2 ) satisfy λ 1 ≳ 2λ 2 , the property of the subdiffusion depends only on contact interaction; when λ 1 ≳ 2λ 2 , the property of the subdiffusion is completely determined by DDI. Remarkably, we numerically give the critical value of disorder strength v* for different values of contact interaction and DDI. When the disorder strength v ≥ v*, the wave packet is localized. On the contrary, when the disorder strength v ≤ v*, the wave packet is subdiffusive.
We consider the evolution of an initially localized wave packet after a sudden change in the Hamiltonian, i.e.\ a quench. When both bound and scattering eigenstates exist in the post-quench Hamiltonian, one might expect partial delocalization of the wave packet to ensue. Here we show that if the quench consists of a sudden switching-off of short-range inter-particle interactions, then Tan's universal relations guarantee delocalization through the high-momentum tail of the momentum distribution. Furthermore, we consider the influence of the range of the interaction and show how a finite range alters the coupling to highly excited states. We illustrate our results using numerical simulations of externally trapped particles in one dimension. If the external potential is both disordered and correlated, then the interaction quench leads to transport via delocalized states, showing that localization in disordered systems is sensitive to non-adiabatic changes in the interactions between particles.
We theoretically demonstrate features of Anderson localization in a Tonks-Girardeau gas confined in one-dimensional potentials with controlled disorder. That is, we investigate the evolution of the single-particle density and correlations of a Tonks-Girardeau wave packet in such disordered potentials. The wave packet is initially trapped, the trap is suddenly turned off, and after some time the system evolves into a localized steady state due to Anderson localization. The density tails of the steady state decay exponentially, while the coherence in these tails increases. The latter phenomenon corresponds to the same effect found in incoherent optical solitons.