We extend the Berezinskii diagrammatic technique to one-dimensional disordered spin systems, in which time-reversal invariance is broken due to a spin–orbit coupling term inducing left–right asymmetric scattering. We then use this formalism to theoretically describe the dynamics of the quantum boomerang effect, a recently discovered manifestation of Anderson localization. The theoretical results are confirmed by exact numerical simulations of wave-packet dynamics in a random potential.
We extend the Berezinskii diagrammatic technique to one-dimensional disordered spin systems, in which time-reversal invariance is broken due to a spin–orbit coupling term inducing left–right asymmetric scattering. We then use this formalism to theoretically describe the dynamics of the quantum boomerang effect, a recently discovered manifestation of Anderson localization. The theoretical results are confirmed by exact numerical simulations of wave-packet dynamics in a random potential.
A particle in an Anderson-localized system, if launched in any direction, should, on average, return to its starting point and stay there.Despite the central role played by Anderson localization in the modern understanding of condensed matter, this "quantum boomerang" effect, an essential feature of the localized state, was only recently theoretically predicted.We report the experimental observation of the quantum boomerang effect.Using a degenerate gas and a phase-shifted pair of optical lattices, we not only confirm the predicted dependence of the boomerang effect on Floquet gauge but also elucidate the crucial role of initial-state symmetries.Highlighting the key role of localization, we observe that as stochastic kicking destroys dynamical localization, the quantum boomerang effect also disappears.Measured dynamics are in agreement with numerical models and with predictions of an analytical theory we present which clarifies the connection between time-reversal symmetry and boomerang dynamics.These results showcase a unique experimental probe of the underlying quantum nature of Anderson localized matter.
The quantum boomerang effect (QBE) is a unique dynamical signature of Anderson localization, characterized by a launched wavepacket that initially drifts but ultimately returns to its initial position due to fundamental quantum interference. In this work, we theoretically establish and quantitatively characterize the QBE in a time-crystalline structure using a periodically driven quantum particle in a one-dimensional potential well. By constructing maximally localized Floquet-Wannier states and introducing temporal disorder, we rigorously map the continuous Floquet dynamics onto a discrete disordered tight-binding lattice. By positioning a detector at a fixed spatial coordinate, we monitor the temporal evolution of the wavepacket, to extract the mean temporal center of mass of the probability density in a time-crystalline structure. This mean temporal center of mass exhibits an initial ballistic expansion, followed by a pronounced U-turn, and ultimately returns to its initial temporal position after long-time evolution. These results confirm the existence of the complete QBE in the time domain. They also demonstrate that non-trivial dynamics can be explored within time-crystalline systems, even though these structures already possess an inherent temporal periodicity.
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.
This thesis theoretically investigates several effects related to Anderson localization, focusing on the context of disordered and chaotic cold-atomic systems. In cold-atomic systems, optical speckle patterns are often used to create the disorder. The resulting potentials felt by the atoms differ from Gaussian random potentials, commonly assumed in the description of condensed-matter systems. In the first part of the thesis, we discuss their specificities, with an emphasis on the spectral properties. Atom-optics experiments offer interesting possibilities, such as the possibility to directly probe the atoms inside the disordered potential. In view of these possibilities, we consider in the second part of the thesis the spreading of matter wave packets initially launched with a non-zero velocity. We find that after an initial ballistic motion, the packet center-of-mass experiences a retroreflection and slowly returns to its initial position, mimicking a boomerang. Atom-atom interactions are then introduced in a third part. We consider dilute condensed bosonic gases, and treat the interactions at the mean-field (Gross-Pitaevskii) level. Various situations are studied numerically, in particular the quantum boomerang scenario, and the dynamical spreading both in momentum and energy of matter waves prepared as plane waves. In the last part, we show that chaotic models offer interesting prospects for the study of Anderson localization. On the one hand, we present strong evidences in favor of a spinless kicked rotor in the sympletic ensemble. On the other hand, a second look at a commonly studied quasi-periodically modulated kicked rotor reveals intriguing results.
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 work is a simple example of the quantum dynamics of a particle in a disordered system in one dimension.In particular, we illustrate numerically the phenomenon of Anderson localisation of a wave packet using a basic model constructed with small random rectangular potential barriers.Also, we study the dynamics of a quantum particle in a disordered potential formed by an harmonic oscillator perturbed by random rectangular barriers.To show the effects of disorder on the dynamics of the system, we compare the time evolution of the wave function of the unperturbed harmonic oscillator with the wave function of the disordered system.We do this by taking the scalar product between the unperturbed and perturbed wave functions at each timestep for different values of the perturbation parameters affecting the disordered wave packet.