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.
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.
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.
When a quantum particle is launched with a finite velocity in a disordered potential, it may surprisingly come back to its initial position at long times and remain there forever. This phenomenon, dubbed ``quantum boomerang effect,'' was introduced in Prat et al. [Prat, Delande, and Cherroret, Quantum boomeranglike effect of wave packets in random media, Phys. Rev. A 99, 023629 (2019)]. Interactions between particles, treated within the mean-field approximation, are shown to partially destroy the boomerang effect: the center of mass of the wave packet makes a U turn, but does not completely come back to its initial position. We show that this phenomenon can be quantitatively interpreted using a single parameter, the average interaction energy.
In this thesis, we theoretically and numerically investigate the quantum boomerang effect - i.e. the return of a wave packet launched with a nonzero velocity to its initial position - in ultra-cold disordered atomic gases. We address three main problems. We study the effect of the time-reversal symmetry breaking on the existence of the quantum boomerang phenomenon. We show that time-reversal symmetry is not a necessary condition for the presence of the quantum boomerang. Next, we investigate the impact of interactions on the quantum boomerang effect, using the mean-field approximation. The interactions lead to partial destruction of the boomerang effect. Within the framework of the Gross-Pitaevskii equation, we identify a universal parameter that describes the observed destruction of the particle's return to the origin. Finally, we numerically study the effect of interactions using a quasi-exact approach. To this end, we study weakly interacting bosons, the Tonks-Girardeau gas, and strongly interacting bosons, which map to weakly interacting fermions. We find that weakly interacting bosons exhibit stronger destruction of the boomerang effect than in the case of the mean-field approach, thus that quantum fluctuations play a major role. Results for the Tonks-Girardeau gas show the existence of the full quantum boomerang phenomenon. Moreover, the results for strongly interacting bosons, where the boomerang is also only partial, provide evidence that the destruction of the quantum boomerang effect does not depend on the details of the interactions between particles.
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 investigate the quantum dynamics of a one-dimensional tight-binding lattice driven by a spatially quadratic and time-periodic potential. Both Hermitian (J1=J2) and non-Hermitian (J1=J2) hopping regimes are analyzed. Within the framework of Floquet theory, the time-dependent Hamiltonian is mapped onto an effective static Floquet Hamiltonian, enabling a detailed study of the quasi-energy spectrum as function of the driving frequency ω. By applying a gauge transformation, we find that critical frequencies ωc emerge, at which nearly equidistant quasi-energy ladders appear, as revealed by a pronounced minimum in the normalized variance Δ(ω) of the level spacings. This spectral regularity leads to robust periodic revivals and Bloch-like oscillations in the time evolution. Numerical simulations confirm that such coherent oscillations persist even in the non-Hermitian regime, where the periodic driving stabilizes an almost real and uniformly spaced quasi-energy ladder.