Coherent Forward Scattering Peak Induced by Anderson Localization

Abstract

Numerical simulations show that, at the onset of Anderson localization, the momentum distribution of a coherent wave packet launched inside a random potential exhibits, in the forward direction, a novel interference peak that complements the coherent backscattering peak. An explanation of this phenomenon in terms of maximally crossed diagrams predicts that the signal emerges around the localization time and grows on the scale of the Heisenberg time associated with the localization volume. Together, coherent back and forward scattering provide evidence for the occurrence of Anderson localization.

Dynamics of localized waves in one-dimensional random potentials: Statistical theory of the coherent forward scattering peak

“…Indeed, observing the CBS effect [23] ensures that interference is at work and that phase coherence is preserved, while observing the CFS effect [24] makes sure that the bulk system has entered the AL regime. To date, while detection and characterization of the CBS peak in momentum space have been quickly reported for matter waves [25,26], the CFS peak still calls for an experimental observation.…”

“…Recently we have proposed to monitor AL for matter waves in momentum space [23,24]. Indeed, observing the CBS effect [23] ensures that interference is at work and that phase coherence is preserved, while observing the CFS effect [24] makes sure that the bulk system has entered the AL regime.…”

Coherent forward scattering as a signature of Anderson metal-insulator transitions

“…dimension and two dimensions [15,17,21], but not in three dimensions where an Anderson MIT takes place. In this article, we numerically demonstrate that the CFS contrast constitutes a reliable and measurable order parameter for MITs: (i) it jumps abruptly from zero in the metallic phase to a finite value in the insulating phase, (ii) obeys the one-parameter scaling hypothesis and gives access to the critical exponents of the transition, and (iii) directly controls the spectral compressibility at the transition, where eigenfunctions are multifractal.…”

“…The solid curve is a cut along kx. Right: time evolution of the normalized CFS contrast Λ in the three phases.dimension and two dimensions [15,17,21], but not in three dimensions where an Anderson MIT takes place. In this article, we numerically demonstrate that the CFS…”

“…We also discover that the critical CFS peak directly controls the spectral compressibility at the transition where eigenfunctions are multifractal, and we demonstrate the universality of this property with respect to various types of disorder. Related to Anderson localization (AL), coherent forward scattering (CFS) is a robust interference effect which triggers a macroscopic peak in the forward direction of the momentum distribution n(k, t) obtained after an initial plane wave |k 0 has evolved through a bulk disordered system [15][16][17]. While CFS resembles the well-known coherent backscattering (CBS) effect, which is due to the pair interference of time-reversed scattering sequences and yields a peak in the backward direction [18], the two effects turn out to be fundamentally different.…”