Quasi-one-dimensional scattering in a discrete model

Manuel Valiente Cifuentes, Klaus Molmer

Research output: Contribution to journalArticle

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 languageEnglish
Article number053628
Number of pages7
JournalPhysical Review A
Volume84
Issue number5
DOIs
Publication statusPublished - 28 Nov 2011

Keywords

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

Cite this

Valiente Cifuentes, Manuel ; Molmer, Klaus. / Quasi-one-dimensional scattering in a discrete model. In: Physical Review A. 2011 ; Vol. 84, No. 5.
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Quasi-one-dimensional scattering in a discrete model. / Valiente Cifuentes, Manuel; Molmer, Klaus.

In: Physical Review A, Vol. 84, No. 5, 053628, 28.11.2011.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Molmer, Klaus

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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.

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KW - ULTRACOLD GASES

KW - OPTICAL LATTICE

KW - GROUND-STATE

KW - QUANTUM

KW - ATOMS

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