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arXiv:0803.0617 · Europhysics Letters (EPL)

Quantum dynamics of one and two bosonic atoms in a combined tight-binding periodic and weak parabolic potential

Manuel Valiente, David Petrosyan

Published Jul 18, 2008• 28 citations
arXivHTMLPDF

Abstract

Strongly interacting bosonic particles in a tight-binding periodic potential superimposed by a weak parabolic trap is a paradigm for many cold atom experiments. Here, after revisiting the single-particle problem, we study interaction-bound dimers of bosonic atoms in the combined lattice and parabolic potential. We consider both repulsively and attractively bound dimers and find pronounced differences in their behaviour. We identify conditions under which attractive and repulsive dimers exhibit analogous dynamics. Our studies reveal that coherent transport and periodic oscillations of appropriately prepared one- and two-atom wave packets can be achieved, which may facilitate information transfer in optical-lattice–based quantum computation schemes.

DOI
10.1209/0295-5075/83/30007

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Strongly interacting bosonic particles in a tight-binding periodic potential superimposed by a weak parabolic trap is a paradigm for many cold atom experiments. Here, after revisiting the single-particle problem, we study interaction-bound dimers of bosonic atoms in the combined lattice and parabolic potential. We consider both repulsively and attractively bound dimers and find pronounced differences in their behaviour. We identify conditions under which attractive and repulsive dimers exhibit analogous dynamics. Our studies reveal that coherent transport and periodic oscillations of appropriately prepared one- and two-atom wave packets can be achieved, which may facilitate information transfer in optical-lattice–based quantum computation schemes.
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We analyze the quantum states of two identical bosons in a combined harmonic oscillator and periodic lattice trap in one spatial dimension. In the case of tight-binding and only nearest-neighbor tunneling, the equations of motion are conveniently represented in the momentum representation. We show that in the case of strong attraction between the particles, the different time scales of relative and center-of-mass motions validate a separation of the problem similar to the Born-Oppenheimer approximation applied in the description of electronic and nuclear motions in molecules.
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We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including an examination of the interaction strengths which induce the formation of a bound dimer of impurities. We also study the dynamics induced after an interaction quench to examine the stability of the bound dimers. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.
Repulsively interacting particles in a periodic potential can form bound composite objects, whose dissociation is suppressed by a band gap. Nearly pure samples of such repulsively bound pairs of cold atoms—“dimers”—have recently been prepared by Winkler et al. [Nature 441, 853 (2006)]. We derive an effective Hamiltonian for a lattice loaded with dimers only, and discuss its implications for many-body dynamics of the system. We show that strong on-site repulsion and nearest-neighbor attraction favor clusters of dimers with minimum surface area and uniform, commensurate filling, representing thus incompressible “droplets” of a lattice liquid.