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arXiv:1603.05611 · Europhysics Letters (EPL)

Diffusion in a system of a few distinguishable fermions in a one-dimensional double-well potential

Tomasz Sowiński, Mariusz Gajda, Kazimierz Rza̧żewski

Published Mar 1, 2016• 17 citations
arXivHTMLPDF

Abstract

Dynamical properties of a few ultra-cold fermions confined in a double-well potential are studied. We show that the dynamics, which is governed by single-particle tunnelings for vanishing interactions, is completely different for strong interactions. Depending on the details of the configuration, for sufficiently strong interactions (repulsions or attractions) the particle flow through the barrier can be accelerated or slowed down. This effect cannot be explained with the single-particle picture. It is clarified with a direct inspection of the spectrum of the few-body Hamiltonian.

DOI
10.1209/0295-5075/113/56003

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Dynamical properties of a few ultra-cold fermions confined in a double-well potential are studied. We show that the dynamics, which is governed by single-particle tunnelings for vanishing interactions, is completely different for strong interactions. Depending on the details of the configuration, for sufficiently strong interactions (repulsions or attractions) the particle flow through the barrier can be accelerated or slowed down. This effect cannot be explained with the single-particle picture. It is clarified with a direct inspection of the spectrum of the few-body Hamiltonian.
This thesis studies the one-dimensional Bose gas in harmonic and double-well traps from a few-body perspective. The main emphasis is on the crossover from weak interactions to the fermionization limit of infinite repulsion, where the system maps to an ideal Fermi gas. To explore the structure as well as the quantum dynamics throughout that crossover, we both develop an exact-diagonalization approach and resort to a multi-configurational time-dependent method (MCTDH). The basic mechanism of the fermionization crossover for the ground state is shown to consist in the formation of a correlation hole in the two-body density, which culminates in a localization of the individual particles for strong repulsion. This is accompanied by a reduction of coherence. We demonstrate how the concrete pathway depends on the trap geometry, on the shape of the interaction, as well as on the atom number. By extension, we also investigate the lowest excitations, whose understanding is a base for studying the impact of the fermionization crossover on the tunneling dynamics in a double well. In symmetric wells, a pathway from single-particle to fragmented-pair tunneling shows up. By energetically offsetting the two wells, tunnel resonances become accessible, which may be used to extract single atoms.
We study the quantum dynamics of strongly interacting few-boson mixtures in one-dimensional traps. If one species is strongly localized compared to the other (e.g., much heavier), it can serve as an effective potential barrier for that mobile component. Near the limit of infinite localization, we map this to a system of identical bosons in a double well. For realistic localization, the backaction of the light species on the ‘barrier’ atoms is explained—to lowest order—in terms of an induced attraction between these. Even in equilibrium, this may outweigh the bare intra-species interaction, leading to unexpected correlated states. Remarkably, the backaction drastically affects the inter-species dynamics, such as the tunnelling of an attractively bound pair of fermionized atoms.
In this thesis, the tunneling dynamics of a few boson system in a double-well is investigated from an ab-initio prospective using the numerically exact Multi-Configuration Time-Dependent Hartree method. We first study a system consisting of single species of bosons with a spatially modulated interaction. The main emphasis is on the role of inhomogeneity and its effect on the tunneling. The dynamics changes from Rabi oscillations in the non-interacting case to a highly suppressed tunneling for intermediate interaction strengths followed by a reappearance of tunneling near the fermionization limit. With extreme interaction inhomogeneity in the regime of strong correlations we observe tunneling between the higher bands. A richer behavior is found for systems with higher particle number. For systems with more than two bosons, the inhomogeneity of the interaction can be tuned to generate tunneling resonances. These observations are explained on the basis of the few-body spectrum and stationary eigenstates. A tilted double-well and its interplay with the interaction asymmetry is discussed next. We demonstrate that the effects of the interaction can be compensated by the tilt leading to tunneling resonances. We then explore tunneling dynamics of binary bosonic mixtures. The focus is on the role of the inter- and intra-species interactions and their interplay. The dynamics is studied for three initial configurations: complete and partial population imbalance and a phase separated state. Increasing the inter-species interaction leads to a strong increase of the tunneling time period analogous to the quantum self-trapping for condensates. The intra-species repulsion can suppress or enhance the tunneling period depending on the strength of the inter-species correlations as well as the initial configuration. Completely correlated tunneling between the two species and within the same species as well as mechanisms of species separation and counterflow are revealed. These effects are explained by studying the many-body energy spectra as well as the properties of the contributing stationary states.
We study few-boson tunneling in a one-dimensional double well. As we pass from weak interactions to the fermionization limit, the Rabi oscillations first give way to highly delayed pair tunneling (for medium coupling), whereas for very strong correlations multiband Rabi oscillations emerge. All this is explained on the basis of the exact few-body spectrum and without recourse to the conventional two-mode approximation. Two-body correlations are found essential to the understanding of the different tunnel mechanisms. The investigation is complemented by discussing the effect of skewing the double well, which offers the possibility to access specific tunnel resonances.
We study few-boson tunneling in a one-dimensional double well with a spatially modulated interaction. The dynamics changes from Rabi oscillations in the noninteracting case to a highly suppressed tunneling for intermediate coupling strengths followed by a reappearance near the fermionization limit. With extreme interaction inhomogeneity in the regime of strong correlations, we observe tunneling between the higher bands. The dynamics is explained on the basis of the few-body spectrum and stationary eigenstates. For a higher number of particles $N\ensuremath{\geqslant}3$, it is shown that the inhomogeneity of the interaction can be tuned to generate tunneling resonances. Finally, a tilted double well and its interplay with the interaction asymmetry are discussed.