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arXiv:cond-mat/0307771 · Physical Review A

Ground-state properties of artificial bosonic atoms, Bose interaction blockade, and the single-atom pipette

Eugene B. Kolomeisky, Joseph P. Straley, Ryan M. Kalas

Published Jun 1, 2004• 13 citations

Abstract

We analyze the ground-state properties of an artificial atom made out of repulsive bosons attracted to a center for the case that all the interactions are short ranged. Such bosonic atoms could be created by optically trapping ultracold particles of alkali-metal vapors; we present the theory describing how their properties depend on experimentally adjustable strength of ``nuclear'' attraction and interparticle repulsion. The binding ability of the short-range potential increases with space dimensionality, only a limited number of particles can be bound in one dimension, while in two and three dimensions the number of bound bosons can be chosen at will. Particularly in three dimensions we find an unusual effect of enhanced resonant binding: for not very strong interparticle repulsion the equilibrium number of bosons bound to a nuclear potential having a sufficiently shallow single-particle state increases without bound as the nuclear potential becomes less attractive. As a consequence of the competing nuclear attraction enhanced by the Bose statistics and interparticle repulsions, the dependence of the ground-state energy of the atom on the number of particles has a minimum whose position is experimentally tunable. This implies a staircase dependence of the equilibrium number of bound bosons on external parameters which may be used to create a single-atom pipette---an arrangement which allows the transport of atoms into and out of a reservoir, one at a time.

DOI: 10.1103/physreva.69.063401

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We establish that the ability of a localized trapping potential to bind weakly interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound state of the trap. Specifically, for repulsive particles and a superthreshold trapping potential the equilibrium number of bound bosons and the size of the ground state diverge upon approaching the single-particle threshold from above. For attractive interactions and a subthreshold trap, a collective bound state always forms for a sufficiently large number of bosons, despite the inability of interparticle attraction alone to form a two-body bound state.

Ultracold atoms offer valuable opportunities where interparticle interactions can be controlled at will. In particular, by extinguishing the two-body interaction, one can realize unique systems governed by the three-body interaction, which is otherwise hidden behind the two-body interaction. Here we study one-dimensional bosons with a weak three-body attraction and show that they form few-body bound states as well as a many-body droplet stabilized by the quantum mechanical effect. Their binding energies relative to that of three bosons are all universal and the ground-state energy of the dilute droplet is found to grow exponentially as ${E}_{N}/{E}_{3}\ensuremath{\rightarrow}exp(8{N}^{2}/\sqrt{3}\ensuremath{\pi})$ with increasing particle number $N\ensuremath{\gg}1$. The realization of our system with coupled two-component bosons in an optical lattice is also discussed.

We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonic trapping potential with a tunable zero-ranged barrier at the trap center. The full characterization of the ground state is done by calculating the reduced single-particle density, the momentum distribution, and the two-particle entanglement. We derive several analytical expressions in the limit of infinite repulsion (Tonks-Girardeau limit) and extend the treatment to finite interparticle interactions by numerical solution. As pair interactions in double wells form a fundamental building block for many-body systems in periodic potentials, our results have implications for a wide range of problems.

The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant, and scattering states are included on an equal footing and we argue that the coupling of all these components is vital for a correct description of the relevant threshold phenomena. In particular, we study the tunneling mechanism for two-body systems in one-dimensional traps and different interaction regimes. We find a strong dominance of sequential tunneling of single particles for repulsive and weakly attractive systems, while there is a signature of correlated pair tunneling in the calculated many-particle flux for strongly attractive interparticle interaction.

Weak potential wells (or traps) in one and two dimensions, and the potential wells slightly deeper than the critical ones in three dimensions, feature shallow bound states with localization length much larger than the well radii. We address a simple fundamental question of how many repulsively interacting bosons can be localized by such traps. We find that under rather generic conditions, for both weakly and strongly repulsive particles, in two and three dimensions---but not in one-dimension---the potential well will trap infinitely many bosons. For example, even hard-core repulsive interactions do not prevent this ``trapping collapse'' phenomenon from taking place. A quantum system acquires the phenomenon along with the universal (asymptotically exact) classical-field behavior at large distances, allowing generic description by the Gross-Pitaevskii equation. We also discuss the possibility of having a transition between the infinite and finite number of trapped particles when strong repulsive interparticle correlations are increased.