Coherent forward scattering in two-dimensional disordered systems

Abstract

We present a detailed numerical and theoretical analysis of the recently discovered phenomenon of coherent forward scattering. This effect manifests itself as a macroscopic interference peak in the forward direction of the momentum distribution of a matter wave launched with finite velocity in a random potential. Focusing on the two-dimensional case, we show that coherent forward scattering generally arises due the confinement of the wave in a finite region of space, and explain under which conditions it can be seen as a genuine signature of Anderson localization.

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…”

“…The evolution of the CBS peak is simple: whatever W , this peak becomes sizable after a few mean free times τ [20] and its amplitude shows no discontinuity as the mobility edge is crossed. To analyze the dynamics of CFS, we use the CFS and CBS contrasts C F and C B (defined as the peak height above the background of the momentum distribution at ±k 0 over the background) [17]. As shown below, the CFS contrast C F is a smoking gun of Anderson localization, as it vanishes at long times in the localized regime and grows to a large value -of the order of unity -in the localized regime.…”

“…We then evolve this filtered state with U(t) = exp(−iĤt/ ). Our numerical scheme uses an expansion of the filtering and evolution operators in terms of Chebyshev polynomials ofĤ, see [17] for details. This procedure is repeated for 6000 different disorder configurations to compute the disorder-average…”

“…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.…”