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arXiv:0911.5142 · Journal of Physics B Atomic Molecular and Optical Physics

Material-barrier tunnelling in one-dimensional few-boson mixtures

Anika C. Pflanzer, Sascha Zöllner, Peter Schmelcher

Published Nov 18, 2009• 27 citations
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Abstract

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.

DOI
10.1088/0953-4075/42/23/231002

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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.
We study the ground-state properties and quantum dynamics of few-boson mixtures with strong interspecies repulsion in one-dimensional traps. If one species localizes at the center, e.g., due to a very large mass compared to the other component, it represents an effective barrier for the latter, and the system can be mapped onto identical bosons in a double well. For weaker localization, the barrier atoms begin to respond to the light component, leading to an induced attraction between the mobile atoms that may even outweigh their bare intraspecies repulsion. To explain the resulting effects, we derive an effective Hubbard model for the lighter species accounting for the back action of the barrier in correction terms to the lattice parameters. Also the tunneling is drastically affected: by varying the degree of localization of the ``barrier'' atoms, the dynamics of intrinsically noninteracting bosons can change from Rabi oscillations to effective pair tunneling. For identical fermions (or fermionized bosons), this leads to the tunneling of attractively bound pairs.
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 explore the tunneling dynamics of strongly correlated bosonic mixtures in a one-dimensional double well. The roles of the inter- and intraspecies interactions and their interplay are investigated using the numerically exact multiconfiguration time-dependent Hartree (MCTDH) method. The dynamics is studied for three initial configurations: complete and partial population imbalance and a species-separated state. Increasing the interspecies interaction leads to a strong increase of the tunneling time period analogous to the quantum self-trapping for condensates. The intraspecies repulsion can suppress or enhance the tunneling period depending on the strength of the interspecies 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 few-body energy spectra as well as the properties of the contributing stationary states.
We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.
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 investigate the tunneling properties of a two-species few-boson mixture in a one-dimensional triple well and harmonic trap. The mixture is prepared in an initial state with a strong spatial correlation for one species and complete localization of the other species. We observe a correlation-induced tunneling process in the weak interspecies interaction regime. The onset of the interspecies interaction disturbs the spatial correlations of one species and induces a tunneling process between the correlated wells. The corresponding tunneling properties can be controlled by the spatial correlations with an underlying mechanism that is inherently different from the well-known resonant tunneling process. We also observe and analyze the correlated tunneling of both species in the intermediate interspecies interaction regime and the tunneling via higher band states for strong interactions.