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Coherent multiple forward scattering peak unveiled by Anderson localization

Tomasz Karpiuk, Nicolas Cherroret, K. L. Lee, Benoît Grémaud, Cord Axel Müller, Christian Miniatura

Published Apr 16, 2012• 0 citations
OpenAlex

Abstract

We investigate the dynamics of a coherent matter wave packet launched in a random potential. As predicted by Cherroret et al. [Phys. Rev. A 85 011604(R) (2012)], the coherent backscattering signal in the momentum distribution freezes at the onset of Anderson localization. At the same time, a novel interference peak rises in the forward direction. An explanation in terms of chained maximally crossed diagrams predicts that the forward scattering peak emerges on a time scale $\tau_\text{loc}^* = 2m\xi^2/\hbar$ set by the localization length $\xi$.

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We investigate the dynamics of a coherent matter wave packet launched in a random potential. As predicted by Cherroret et al. [Phys. Rev. A 85 011604(R) (2012)], the coherent backscattering signal in the momentum distribution freezes at the onset of Anderson localization. At the same time, a novel interference peak rises in the forward direction. An explanation in terms of chained maximally crossed diagrams predicts that the forward scattering peak emerges on a time scale τloc∗=2mξ2/ℏ\tau_\text{loc}^* = 2m\xi^2/\hbarτloc∗​=2mξ2/ℏ set by the localization length ξ\xiξ.
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.
This manuscript presents a selection of works on the coherent evolution of atomic matter waves in random potentials. In this context, a number of interference, « mesoscopic » phenomena surviving a disorder average are discussed, in particular in the regime where Anderson localization shows up: coherent backscattering, coherent forward scattering, mesoscopic echo and quantum boomerang effect. The interplay between weak atomic interactions and Anderson localization is also touched upon for spreading wave packets, a scenario frequently considered in experiments. The last chapter, finally, gives an overview of recent works by the author on multiple scattering of light in media of dimension « (2+1) ». These peculiar systems, originally introduced to demonstrate Anderson localization of light in 2D, have sparked a growing interest in the recent years, for light propagation is governed by an effective Schrödinger equation and thus mimics the behavior of a matter wave. We here show that when the vector character of light is properly taken into account, these systems in fact display a physics much richer than the one pertained to this sole analogy.
Signatures of Anderson localization in the momentum distribution of a cold atom cloud after a quantum quench are studied. We consider a quasi-one-dimensional cloud initially prepared in a well-defined momentum state, and expanding for some time in a disorder speckle potential. Quantum interference generates a peak in the forward scattering amplitude which, unlike the common weak localization backscattering peak, is a signature of strong Anderson localization. We present a nonperturbative, and fully time resolved description of the phenomenon, covering the entire diffusion-to-localization crossover. Our results should be observable by present day experiments.
We report on the direct observation of coherent backscattering (CBS) of ultracold atoms in a quasi-two-dimensional configuration. Launching atoms with a well-defined momentum in a laser speckle disordered potential, we follow the progressive build up of the momentum scattering pattern, consisting of a ring associated with multiple elastic scattering, and the CBS peak in the backward direction. Monitoring the depletion of the initial momentum component and the formation of the angular ring profile allows us to determine microscopic transport quantities. We also study the time evolution of the CBS peak and find it in fair agreement with predictions, at long times as well as at short times. The observation of CBS can be considered a direct signature of coherence in quantum transport of particles in disordered media. It is responsible for the so called weak localization phenomenon, which is the precursor of Anderson localization.
We investigate the time- and momentum-resolved dynamics of matter waves undergoing elastic scattering from a disordered potential in the presence of spatially uniform SU(2) gauge fields. We derive the disorder-averaged density matrix as a function of time and momentum within the weak-localization regime. By accurately approximating the frequency dependence of the ladder and maximally crossed diagram series beyond the diffusion approximation, we describe short-time spin-momentum dynamics on timescales comparable to the scattering mean free time, for arbitrary strengths of the SU(2) gauge fields and disorder. We also present a cubic equation that determines the spin isotropization time, which gives accurate asymptotic forms in the limits where the spin-orbit length is much longer (Dyakonov-Perel spin relaxation regime) or much shorter than the scattering mean free path, as well as in the SU(2)-symmetric (persistent spin helix) limit. Comparison with numerical simulations over a broad range of spin-orbit coupling strengths shows quantitative agreement for the predicted spin isotropization time. The same framework also reproduces both the relaxation of the momentum distribution and the transient backscattering peak with a momentum offset coexisting with the robust coherent backscattering dip.