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arXiv:1306.6838 · Physical Review A

Backscattering echo of correlated wave packets

Nicolas Cherroret, Dominique Delande

Published Sep 12, 2013• 2 citations
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Abstract

We present an analytical theory describing a phenomenon of enhanced backscattering corresponding to the spatial refocussing of a spreadout correlated wave packet due to a brief interaction with a disordered potential. Our theory is validated by numerical simulations and explains the physics observed in recent experiments on cold atom transport in disorder.

DOI
10.1103/physreva.88.035602

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We present an analytical theory describing a phenomenon of enhanced backscattering corresponding to the spatial refocussing of a spreadout correlated wave packet due to a brief interaction with a disordered potential. Our theory is validated by numerical simulations and explains the physics observed in recent experiments on cold atom transport in disorder.
We study experimentally and numerically the quasi-bidimensional transport of a 87^{87}87Rb Bose-Einstein condensate launched with a velocity v0v_0v0​ inside a disordered optical potential created by a speckle pattern. A time-of-flight analysis reveals a pronounced enhanced density peak in the backscattering direction −v0-v_0−v0​, a feature reminiscent of coherent backscattering. Detailed numerical simulations indicate however that other effects also contribute to this enhancement, including a "backscattering echo" due to the position-momentum correlations of the initial wave packet.
Summary form only given. A wave propagating in a strongly scattering medium experiences many scattering events which rapidly erase the memory of its initial direction on a typical scale length known as the transport mean free path. It is now known that interference can profoundly alter the wave transport, a spectacular manifestation being weak and strong localisation of waves. We shall briefly review the basics of coherent backscattering (CBS) and the results obtained with classical scatterers. We shall then describe our experiment using cold atoms and discuss the experimental data. The non trivial role of the atomic quantum internal structure in the enhancement reduction will be singled out in a simple situation and results of analytical calculations will be presented.
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.
We analyze the disorder-perturbed transport of quantum states in the absence of backscattering. This comprises, for instance, the propagation of edge-mode wave packets in topological insulators, or the propagation of photons in inhomogeneous media. We quantify the disorder-induced dephasing, which we show to be bound. Moreover, we identify a gap condition to remain in the backscattering-free regime despite disorder-induced momentum broadening. Our analysis comprises the full disorder-averaged quantum state, on the level of both populations and coherences, appreciating states as potential carriers of quantum information. The well-definedness of states is guaranteed by our treatment of the nonequilibrium dynamics with Lindblad master equations.
We analyze the propagation of quantum states in the presence of weak disorder. In particular, we investigate the reliable transmittance of quantum states, as potential carriers of quantum information, through disorder-perturbed waveguides. We quantify wave-packet distortion, backscattering, and disorder-induced dephasing, which all act detrimentally on transport, and identify conditions for reliable transmission. Our analysis relies on the treatment of the nonequilibrium dynamics of ensemble-averaged quantum states in terms of quantum master equations.