### Abstract

We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasimomenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonances appear due to the nonseparability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann-Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.

Original language | English |
---|---|

Article number | 053628 |

Number of pages | 7 |

Journal | Physical Review A |

Volume | 84 |

Issue number | 5 |

DOIs | |

Publication status | Published - 28 Nov 2011 |

### Keywords

- MANY-FERMION SYSTEM
- IMPENETRABLE BOSONS
- ULTRACOLD GASES
- OPTICAL LATTICE
- GROUND-STATE
- QUANTUM
- ATOMS

### Cite this

*Physical Review A*,

*84*(5), [053628]. https://doi.org/10.1103/PhysRevA.84.053628

}

*Physical Review A*, vol. 84, no. 5, 053628. https://doi.org/10.1103/PhysRevA.84.053628

**Quasi-one-dimensional scattering in a discrete model.** / Valiente Cifuentes, Manuel; Molmer, Klaus.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quasi-one-dimensional scattering in a discrete model

AU - Valiente Cifuentes, Manuel

AU - Molmer, Klaus

PY - 2011/11/28

Y1 - 2011/11/28

N2 - We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasimomenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonances appear due to the nonseparability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann-Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.

AB - We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasimomenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonances appear due to the nonseparability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann-Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.

KW - MANY-FERMION SYSTEM

KW - IMPENETRABLE BOSONS

KW - ULTRACOLD GASES

KW - OPTICAL LATTICE

KW - GROUND-STATE

KW - QUANTUM

KW - ATOMS

U2 - 10.1103/PhysRevA.84.053628

DO - 10.1103/PhysRevA.84.053628

M3 - Article

VL - 84

JO - Physical Review A

JF - Physical Review A

SN - 1050-2947

IS - 5

M1 - 053628

ER -