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arXiv:physics/0703168 · Physical Review A

Effects of nonintegrability on stabilization of Feshbach molecules in atom waveguides

Vladimir Yurovsky

Published Jan 22, 2008• 2 citations
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Abstract

Deactivation of broad quasi-one-dimensional dibosonic molecules is analyzed. Within the integrable Lieb-Liniger-McGuire (LLMG) model an exact expression does not demonstrate suppression of the deactivation at low collision energies. The solution of Faddeev equations demonstrates that when a Feshbach resonance lifts the symmetry of the LLMG model the deactivation becomes suppressed. This effect shows a way for formation of a stable gas of dibosonic Feshbach molecules.

DOI
10.1103/physreva.77.012716

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Deactivation of broad quasi-one-dimensional dibosonic molecules is analyzed. Within the integrable Lieb-Liniger-McGuire (LLMG) model an exact expression does not demonstrate suppression of the deactivation at low collision energies. The solution of Faddeev equations demonstrates that when a Feshbach resonance lifts the symmetry of the LLMG model the deactivation becomes suppressed. This effect shows a way for formation of a stable gas of dibosonic Feshbach molecules.
Three-body collisions of ultracold identical Bose atoms under tight cylindrical confinement are analyzed. A Feshbach resonance in two-body collisions is described by a two-channel zero-range interaction. Elimination of the closed channel in the three-body problem reduces the interaction to a one-channel zero-range one with an energy-dependent strength. The related integrable Lieb-Liniger-McGuire (LLMG) model, with an energy-independent strength, forbids all chemical processes, such as three-atom association and diatom dissociation, as well as reflection in atom-diatom collisions. The resonant case is analyzed by a numerical solution of the Faddeev equations. The results demonstrate that as the internal symmetry of the LLMG model is lifted, reflection and chemical reactions become allowed and may be observed in experiments.
Bound states and collisions of atoms with two-channel two-body interactions in harmonic waveguides are analyzed. The closed-channel contributions to two-atom bound states become dominant in the case of a weak resonance. At low energies and values of the nonresonant scattering length the problem can be approximated by a one-dimensional resonant model. The three-body problem becomes nonintegrable and the properties of triatomic molecules become different from those predicted by the integrable Lieb-Liniger-McGuire model.
Inelastic collisions of ultracold atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of excited states due to inelastic collisions is suppressed. The relation of our results to the Lieb-Liniger model for bosonic atoms is addressed.
Abstract We study a model of two species of 1D linearly dispersing fermions interacting via an s-wave Feshbach resonance at zero temperature. While this model is known to be integrable, it possesses novel features that have not previously been investigated. Here, we present an exact solution based on the coordinate Bethe Ansatz. In the limit of infinite resonance strength, which we term the strongly interacting limit, the two species of fermions behave as free Fermi gases. In the limit of infinitely weak resonance, or the weakly interacting limit, the gases can be in different phases depending on the detuning, the relative velocities of the particles, and the particle densities. When the molecule moves faster or slower than both species of atoms, the atomic velocities get renormalized and the atoms may even become non-chiral. On the other hand, when the molecular velocity is between that of the atoms, the system may behave like a weakly interacting Lieb–Liniger gas.
Ultracold atoms placed in a tight cigar-shaped trap are usually described in terms of the Lieb-Liniger model. We study the extensions of this model which arise when van der Waals interaction between atoms is taken into account. We find that the corrections induced by the finite range of interactions can become especially important in the vicinity of narrow Feshbach resonances and suggest realistic schemes of their experimental detection. The interplay of confinement and interactions can lead to effective transparency where the one-dimensional interactions are weak in a wide range of parameters.