Quantum boomeranglike effect of wave packets in random media

Abstract

We unveil an original manifestation of Anderson localization for wave packets launched with a finite average velocity: after an initial ballistic motion, the center of mass of the wave packet experiences a retroreflection and slowly returns to its initial position, an effect that we dub "Quantum Boomerang" and describe numerically and analytically in dimension 1. In dimension 3, we show numerically that the quantum boomerang is a genuine signature of Anderson localization: it exists if and only if the quantum dynamics if localized.

Observation of the Quantum Boomerang Effect

“…In this work we have presented the first experimental evidence for the quantum boomerang effect in an Anderson-localized system. The measurements confirm theoretical predictions [13,15] and demonstrate that boomerang dynamics can occur from a variety of initial conditions including even a homogeneous density distribution. These experimental results, along with the analytical theory we present in the appendices, elucidate the crucial role of parity and time-reversal symmetry in determining the presence or absence of the quantum boomerang effect.…”

“…Figure 1b illustrates the main result of this work: we experimentally observe the departure from and return to zero average momentum which is the key signature of the quantum boomerang effect [13]. Here V 0 = 38 E R , T = 8 µs, φ ≡ 2k L x 0 = π/2 and α = 0.47, which correspond to k = 10, K = 9.…”

“…Disordered lattice models enjoy a robust theoretical proof of localization and remain a hotbed for discovery even today. While transport in disordered media has been studied for more than 50 years, a fundamental dynamical feature of Anderson-localized matter known as the "quantum boomerang" effect was only recently theoretically predicted [13][14][15]. The central prediction of the quantum boomerang is that, for an appropriate average over disorder realizations, a wavepacket launched with any nonzero momentum will return to and localize at its initial position [13].…”

“…While transport in disordered media has been studied for more than 50 years, a fundamental dynamical feature of Anderson-localized matter known as the "quantum boomerang" effect was only recently theoretically predicted [13][14][15]. The central prediction of the quantum boomerang is that, for an appropriate average over disorder realizations, a wavepacket launched with any nonzero momentum will return to and localize at its initial position [13]. This surprising phenomenon can be understood as a consequence of both Anderson localization and time-reversal symmetry: the long-time density distribution for a wavepacket with an initial momentum k 0 is (i) time-independent because of localization and (ii) does not depend on the sign of k 0 because of time-reversal symmetry.…”

“…The quantum boomerang effect is predicted to occur in a broad class of disordered or pseudo-disordered tightbinding models [15] including the quantum kicked rotor (QKR), a momentum-space realization of a disordered quasi-1D wire [16,17] which provides an ideal platform for the study of the interplay between localization, chaos, interactions, and transport [18][19][20][21][22][23][24][25][26][27][28][29][30]. In any context, the quantum boomerang effect contravenes classical predictions and serves as a sensitive diagnostic of the quantum nature of localization, with the potential, for example, to map mobility edges [13,31].…”