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arXiv:cond-mat/0608721 · AIP conference proceedings

Repulsively Bound Atom Pairs: Overview, Simulations and Links

Andrew J. Daley, Adrian Kantian, Hans Peter Büchler, P. Zoller, Klaus Winkler, Gregor Thalhammer, Florian J. W. Lang, Rudolf Grimm, Johannes Hecker Denschlag

Published Jan 1, 2006• 2 citations
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Abstract

We review the basic physics of repulsively bound atom pairs in an optical lattice, which were recently observed in the laboratory, including the theory and the experimental implementation. We also briefly discuss related many‐body numerical simulations, in which time‐dependent Density Matrix Renormalisation Group (DMRG) methods are used to model the many‐body physics of a collection of interacting pairs, and give a comparison of the single‐particle quasimomentum distribution measured in the experiment and results from these simulations. We then give a short discussion of how these repulsively bound pairs relate to bound states in some other physical systems.

DOI
10.1063/1.2400651

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Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule.
We theoretically and numerically study the Bose-Hubbard model for two bosons in a one-dimensional optical lattice. We begin with a single-channel model describing two interacting atoms, known as a lattice dimer, and then examine the more nuanced two-channel model. The two-channel model accounts for the presence of an association resonance that facilitates the conversion of an atom pair into a molecule and adds a separate molecular degree of freedom. Lattice dimers in the single-channel case have been extensively investigated, but we resolve the conundrum between these dimers and molecules by employing a two-channel model. The stationary states for the time-independent Schrödinger equation are determined and these states reveal some unusual features, including the existence of the celebrated repulsively bound state. We examine the similarities and differences between the single- and two-channel models and find a peculiar qualitative difference between the two. Whereas the usual atoms-only theory yields one bound state for a molecular dimer for either an attractive or repulsive atom-atom interaction, a two-channel atom-molecule theory may give two bound states that represent attractively and repulsively bound dimers occurring simultaneously. Possible methods for experimentally detecting both the dimers and the simultaneous bound states are discussed and we identify several systems for observing this novel aspect of molecular physics. In addition to our theoretical work, we also present the results and verification of our quantum Monte Carlo simulations of the two-channel model. ^