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arXiv:2211.01870 · Physical review. B./Physical review. B

Many-body quantum boomerang effect

Jakub Janarek, Jakub Zakrzewski, Dominique Delande

Published Mar 16, 2023• 6 citations
arXivHTMLPDF

Abstract

We study numerically the impact of many-body interactions on the quantum boomerang effect. We consider various cases: weakly interacting bosons, the Tonks-Girardeau gas, and strongly interacting bosons (which may be mapped onto weakly interacting fermions). Numerical simulations are performed using the time-evolving block decimation algorithm, a quasiexact method based on matrix product states. In the case of weakly interacting bosons, we find a partial destruction of the quantum boomerang effect, in agreement with the earlier mean-field study [J. Janarek et al., Phys. Rev. A 102, 013303 (2020)]. For the Tonks-Girardeau gas, we show the presence of the full quantum boomerang effect. For strongly interacting bosons, we observe a partial boomerang effect. We show that the destruction of the quantum boomerang effect is universal and does not depend on the details of the interaction between particles.

DOI
10.1103/physrevb.107.094204

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We study numerically the impact of many-body interactions on the quantum boomerang effect. We consider various cases: weakly interacting bosons, the Tonks-Girardeau gas, and strongly interacting bosons (which may be mapped onto weakly interacting fermions). Numerical simulations are performed using the time-evolving block decimation algorithm, a quasiexact method based on matrix product states. In the case of weakly interacting bosons, we find a partial destruction of the quantum boomerang effect, in agreement with the earlier mean-field study [J. Janarek et al., Phys. Rev. A 102, 013303 (2020)]. For the Tonks-Girardeau gas, we show the presence of the full quantum boomerang effect. For strongly interacting bosons, we observe a partial boomerang effect. We show that the destruction of the quantum boomerang effect is universal and does not depend on the details of the interaction between particles.
Building on the recent experimental achievements obtained with scanning electron microscopy on ultracold atoms, we study one-dimensional Bose gases in the crossover between the weakly (quasicondensate) and the strongly interacting (Tonks-Girardeau) regime. We measure the temporal two-particle correlation function and compare it with calculations performed using the time-evolving block decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behavior, we highlight that the exact and simple duality between one-dimensional bosons and fermions does not hold when such a dynamical response is probed. The onset of fermionization is also reflected in the density distribution, which we measure in situ to extract the relevant parameters and to identify the different regimes. Our results show agreement between experiment and theory and give insight into the dynamics of strongly correlated many-body systems.
The momentum distribution (MD) dynamics of a Tonks-Girardeau (TG) gas is studied in the context of Bragg reflections of a many-body wave packet. We find strong suppression of a Bragg reflection peak for a large and dense TG wave packet; our observation illustrates the dependence of the MD on the interactions and wave function symmetry. The MD is calculated from the reduced single-particle density matrix (RSPDM). We develop a method for calculating the RSPDM of a TG gas, which is operative for a large number of particles, and does not depend on the external potential and the state of the system. The method is based on a formula expressing the RSPDM via a dynamically evolving single-particle basis.
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.
The wave function of a Tonks-Girardeau (T-G) gas of strongly interacting bosons in one dimension maps onto the absolute value of the wave function of a noninteracting Fermi gas. Although this fermionization makes many aspects of the two gases identical, their equilibrium momentum distributions are quite different. We observed dynamical fermionization, where the momentum distribution of a T-G gas evolves from bosonic to fermionic after its axial confinement is removed. The asymptotic momentum distribution after expansion in one dimension is the distribution of rapidities, which are the conserved quantities associated with many-body integrable systems. Our measurements agree well with T-G gas theory. We also studied momentum evolution after the trap depth is suddenly changed to a new nonzero value, and we observed the theoretically predicted bosonic-fermionic oscillations.
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.
The interaction among fundamental particles in nature leads to many interesting effects in quantum statistical mechanics; examples include superconductivity for charged systems and superfluidity in cold gases. It is a huge challenge for mathematical physics to understand the collective behavior of systems containing a large number of particles, emerging from known microscopic interactions. In this workshop we brought together researchers working on different aspects of many-body quantum mechanics to discuss recent developments, exchange ideas and propose new challenges and research directions.