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Bulletin of the American Physical Society

Atom-trimer scattering lengths and four-body bound states for the one-dimensional ``HHHL'' system

Connor Morehead, Nirav P. Mehta

Published Jun 4, 2014• 0 citations
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The energy spectrum, atom-dimer scattering length, and atom-trimer scattering length for systems of three and four ultracold atoms with $\ensuremath{\delta}$-function interactions in one dimension are presented as a function of the relative mass ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat three-body (``HHL'') systems of one light and two heavy atoms, as well as four-body (``HHHL'') systems of one light and three heavy atoms. Zero-range interactions of arbitrary strength are assumed between different atoms, but the heavy atoms are assumed to be noninteracting among themselves. Fermionic and bosonic heavy atoms with both positive and negative parity are considered.

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The phase diagrams for three-body and four-body systems with δ-function interactions are presented. The three-body and four body systems considered are the heavy-heavy-light (HHL) and heavy-heavy-heavy-light (HHHL) systems, respectively. The heavy particles are assumed to be identical. Both systems are treated within the Born-Oppenheimer approximation. The results from [16] are extended to arbitrary values of the heavy-heavy (HH) coupling. The phase diagram presented in [8] is reproduced, and the corresponding HHHL phase-diagram is presented. It was found that in both the three and four body systems the scattering lengths (atom-dimer for HHL and atom-trimer for HHHL) and spectra vary smoothly as the heavy-heavy interaction strength λ is varied from 0 to ∞.

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Tao Yin, Peng Zhang, Wei Zhang

We study few-body problems in mixed dimensions where two or three heavy atoms are trapped individually in parallel one-dimensional tubes or two-dimensional disks and a single light atom travels freely in three dimensions. Using the Born-Oppenheimer approximation, we find three- and four-body bound states for a broad parameter region. Specifically, the existence of trimer and tetramer states persists to the negative scattering length regime, where no two-body bound state is present. As pointed out by Y. Nishida in an earlier work [Phys. Rev. A 82, 011605(R) (2010)], these few-body bound states are stable against three-body recombination due to geometric separation. In addition, we find that the binding energy of the ground trimer and tetramer state reaches its maximum value when the scattering lengths are comparable to the separation between the low-dimensional traps.

arXiv:1104.4352•Physical Review A•Nov 29, 2011•10 citations
The energy spectrum, atom-dimer scattering length, and atom-trimer scattering length for systems of three and four ultracold atoms with $\ensuremath{\delta}$-function interactions in one dimension are presented as a function of the relative mass ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat three-body (``HHL'') systems of one light and two heavy atoms, as well as four-body (``HHHL'') systems of one light and three heavy atoms. Zero-range interactions of arbitrary strength are assumed between different atoms, but the heavy atoms are assumed to be noninteracting among themselves. Fermionic and bosonic heavy atoms with both positive and negative parity are considered.
The phase diagrams for three-body and four-body systems with δ-function interactions are presented. The three-body and four body systems considered are the heavy-heavy-light (HHL) and heavy-heavy-heavy-light (HHHL) systems, respectively. The heavy particles are assumed to be identical. Both systems are treated within the Born-Oppenheimer approximation. The results from [16] are extended to arbitrary values of the heavy-heavy (HH) coupling. The phase diagram presented in [8] is reproduced, and the corresponding HHHL phase-diagram is presented. It was found that in both the three and four body systems the scattering lengths (atom-dimer for HHL and atom-trimer for HHHL) and spectra vary smoothly as the heavy-heavy interaction strength λ is varied from 0 to ∞.
We study few-body problems in mixed dimensions where two or three heavy atoms are trapped individually in parallel one-dimensional tubes or two-dimensional disks and a single light atom travels freely in three dimensions. Using the Born-Oppenheimer approximation, we find three- and four-body bound states for a broad parameter region. Specifically, the existence of trimer and tetramer states persists to the negative scattering length regime, where no two-body bound state is present. As pointed out by Y. Nishida in an earlier work [Phys. Rev. A 82, 011605(R) (2010)], these few-body bound states are stable against three-body recombination due to geometric separation. In addition, we find that the binding energy of the ground trimer and tetramer state reaches its maximum value when the scattering lengths are comparable to the separation between the low-dimensional traps.