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arXiv:2403.16923 · Physical Review A

Spin-charge separation in the quantum boomerang effect

P. Capuzzi, L. Tessieri, Z. Akdeniz, Anna Minguzzi, Patrizia Vignolo

Published Jun 10, 2024• 4 citations
arXivHTMLPDF

Abstract

We study the localization dynamics of a SU(2) fermionic wave packet launched in a (pseudo)random potential. We show that, in the limit of strong intercomponent repulsions, the total wave packet exhibits a boomeranglike dynamics, returning to near its initial position as expected for noninteracting particles, while separately each spin-component does not. This spin-charge separation effect occurs both in the infinite repulsive limit and at finite interactions. At infinite interactions, the system is integrable and thermalization cannot occur: the two spin-components push each other during the dynamics and their centers of mass stop further from each other than their initial positions. At finite interactions, integrability is broken, the two spin-components oscillate and mix, with their center-of-mass positions converging very slowly to the center of mass of the whole system. This is a signature that the final localized state is a fully spin-mixed thermalized state.

DOI
10.1103/physreva.109.063315

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We study the localization dynamics of a SU(2) fermionic wave packet launched in a (pseudo)random potential. We show that, in the limit of strong intercomponent repulsions, the total wave packet exhibits a boomeranglike dynamics, returning to near its initial position as expected for noninteracting particles, while separately each spin-component does not. This spin-charge separation effect occurs both in the infinite repulsive limit and at finite interactions. At infinite interactions, the system is integrable and thermalization cannot occur: the two spin-components push each other during the dynamics and their centers of mass stop further from each other than their initial positions. At finite interactions, integrability is broken, the two spin-components oscillate and mix, with their center-of-mass positions converging very slowly to the center of mass of the whole system. This is a signature that the final localized state is a fully spin-mixed thermalized state.
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.
We investigate the dynamics of one-dimensional SU(2) ultracold fermions near the Tonks-Girardeau limit, confined in a box potential. The system is driven out of equilibrium by initially preparing the two spin components in a fully separated configuration, and its evolution is described by the Hamiltonian in the presence of strong repulsive interactions. Building on the results in G. Aupetit-Diallo et al., Phys. Rev. A 107, L061301 (2023), we extend the analysis to out-of-equilibrium dynamics, uncovering the emergence of time-dependent oscillating high-momentum tails in the momentum distribution. These oscillations, due to the finite size of the system, are governed by a nonlocal, high-order spin coherence term, whose amplitude and phase evolve over time. We show that this term initially grows as tN/2{t}^{N/2}tN/2 and subsequently follows the spin-mixing dynamics of the system. Notably, when the spin components are fully mixed, the amplitude of this border-to-border spin coherence reaches its maximum value.
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.
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.
We investigate the component separation in one-dimensional two-component fermion clouds in a spin-dependent external potential. The density distributions and the state diagram are studied by means of spin-dependent density-functional theory. The component separation between spin-up and spin-down atoms is induced by the interplay of the spin-dependent harmonic confinement and the strong repulsive interaction between the intercomponents. We find the existence of a threshold repulsive interaction strength above which the component separation evolves. Different state diagrams are mapped out numerically, from which two regions are distinguished, i.e., the phase-mixed region with both spin-up and spin-down mixtures in the center of the trap and the phase-separated region with only spin-up atoms remaining in the center.