In this paper we consider dipolar quantum gases in a quasi-one-dimensional tube with dipole moment perpendicular to the tube direction. We deduce the effective one-dimensional interaction potential and show that this potential is not purely repulsive, but rather has an attractive part due to high-order scattering processes through transverse excited states. The attractive part can induce bound states and cause scattering resonances. This represents the dipole-induced resonance in low dimension. We work out an unconventional behavior of low-energy phase shift for this effective potential and show how it evolves across a resonance. Based on the phase shift, the interaction energy of spinless bosons is obtained using the asymptotic Bethe ansatz. Despite the long-range nature of dipolar interaction, we find that the behavior is similar to a short-range Lieb-Liniger gas emerging at the resonance region.In this paper we consider dipolar quantum gases in a quasi-one-dimensional tube with dipole moment perpendicular to the tube direction. We deduce the effective one-dimensional interaction potential and show that this potential is not purely repulsive, but rather has an attractive part due to high-order scattering processes through transverse excited states. The attractive part can induce bound states and cause scattering resonances. This represents the dipole-induced resonance in low dimension. We work out an unconventional behavior of low-energy phase shift for this effective potential and show how it evolves across a resonance. Based on the phase shift, the interaction energy of spinless bosons is obtained using the asymptotic Bethe ansatz. Despite the long-range nature of dipolar interaction, we find that the behavior is similar to a short-range Lieb-Liniger gas emerging at the resonance region.

arXiv:1307.0899Physical Review AFeb 6, 201412 citations

Bound States in One Dimension

J. D. Kelley, Jacob J. Leventhal

Springer eBooksNov 25, 20160 citations

Boson-Triboson Scattering with Yamaguchi Potential. I: Restriction to s-Wave Contribution from the 3+1-Subamplitude

Yoshiko Matsui

For the investigation of the S-wave boson-triboson phase shift, the Faddeev-Osborn equation is solved numerically by assuming a rank-one separable potential of the Yamaguchi type for the two-particle interaction. The calculation is performed in the exact approach based on rigorous Faddeev theory of the scattering problem. As a first step of the investigation, to gain insight into the origin of a four-body resonance, the contribution from the 3+1-subamplitude is limited to the s-wave only. The calculated phase shift behaves generally like a standard two-body one for a potential that causes one loosely bound state; this phase shift has further characteristic behavior resulting from fine structure consisting of a valley and a peak. The result of the partial cross section indicates the presence of two resonant states in the four-boson system with the Yamaguchi potential.For the investigation of the S-wave boson-triboson phase shift, the Faddeev-Osborn equation is solved numerically by assuming a rank-one separable potential of the Yamaguchi type for the two-particle interaction. The calculation is performed in the exact approach based on rigorous Faddeev theory of the scattering problem. As a first step of the investigation, to gain insight into the origin of a four-body resonance, the contribution from the 3+1-subamplitude is limited to the s-wave only. The calculated phase shift behaves generally like a standard two-body one for a potential that causes one loosely bound state; this phase shift has further characteristic behavior resulting from fine structure consisting of a valley and a peak. The result of the partial cross section indicates the presence of two resonant states in the four-boson system with the Yamaguchi potential.

Progress of Theoretical PhysicsSep 1, 19991 citation

Bound States in One Dimension

S. Brandt, Hans Dieter Dahmen, Tilo Stroh

Springer eBooksNov 26, 20100 citations

Scattering and bound states in two-dimensional anisotropic potentials

Matthias Rosenkranz, Weizhu Bao

We propose a framework for calculating scattering and bound-state properties in anisotropic two-dimensional potentials. Using our method, we derive systematic approximations of partial wave phase shifts and binding energies. Moreover, the method is suitable for efficient numerical computations. We calculate the $s$ -wave phase shift and binding energy of polar molecules in two layers polarized by an external field along an arbitrary direction. We find that scattering depends strongly on their polarization direction and that absolute interlayer binding energies are larger than thermal energies at typical ultracold temperatures.We propose a framework for calculating scattering and bound-state properties in anisotropic two-dimensional potentials. Using our method, we derive systematic approximations of partial wave phase shifts and binding energies. Moreover, the method is suitable for efficient numerical computations. We calculate the $s$-wave phase shift and binding energy of polar molecules in two layers polarized by an external field along an arbitrary direction. We find that scattering depends strongly on their polarization direction and that absolute interlayer binding energies are larger than thermal energies at typical ultracold temperatures.

arXiv:1201.6167Physical Review ANov 22, 201112 citations

One-dimensional problems: bound and unbound states

Mario S. Reis

Elsevier eBooksSep 27, 20250 citations

s

-wave phase shift and binding energy of polar molecules in two layers polarized by an external field along an arbitrary direction. We find that scattering depends strongly on their polarization direction and that absolute interlayer binding energies are larger than thermal energies at typical ultracold temperatures.