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2 - Two-Body Interaction

from Part I - Atomic and Few-Body Physics

Published online by Cambridge University Press:  30 January 2021

Hui Zhai
Hui Zhai
Affiliation:
Tsinghua University, Beijing
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Summary

1. Highlight “short-ranged,” “dilute,” and “low-energy” as three main features of interactions between ultracold atoms.

2. Introduce the important concept of the phase shift.

3. Introduce the $s$-wave scattering length as a universal parameter describing the low-energy interaction between ultracold atoms.

4. Discuss the relation between divergent scattering length, low-energy bound state, and jump of phase shift.

5. Discuss the relation between the scattering length and the scattering amplitude.

6. Discuss under what condition a positive scattering length describes repulsive interaction.

7. Discuss the condition when an algebraically decayed potential can be treated as a finite range one.

8. Introduce two types of zero-range single-channel potentials to capture the universal low-energy $s$-wave interaction between ultracold atoms.

9. Introduce the concept of renormalization condition and renormalizable theory.

10. Discuss how the spin rotational symmetry imposes constraints on interaction form for both alkali-metal and alkaline-earth-metal atoms.

11. Introduce Feshbach resonance as an important tool to tune scattering length.

12. Compare the two-channel Feshbach resonance with the single-channel shape resonance and compare the wide and the narrow resonances.

13. Introduce a zero-range two-channel model.

14. Introduce the confinement-induced resonance to tune interaction strength by an external potential.

15. Summarize three key conditions for a Feshbach resonance, and unify the optical Feshbach resonance, the orbital Feshbach resonance, and the confinement-induced resonance all in terms of these three conditions.

16. Introduce the Efimov effect as an important three-body effect at the vicinity of the two-body scattering resonance.

17. Highlight the symmetry aspect of the Efimov effect.

18. Discuss various connections between few-body and many-body physics.

19. Illustrate that few-body calculation can be used to determine properties of many-body systems by using high-temperature expansion as an example.

Keywords

phase shiftscattering lengtheffective rangescattering volumeuniversalityshallow bound statescattering resonancescattering amplitudescattering cross sectionLevinson theoremFermi’s pseudo-potentialrenormalizable contact potentialrenormalizationSchwinger-Dyson equationultraviolet divergenceinfrared divergencespin-exchanging scatteringSU(N) symmetric interactionKondo physicsFeshbach resonanceopen channelclosed channelshape resonancewide resonancenarrow resonancetwo-channel modeloptical Feshbach resonanceorbital Feshbach resonanceconfinement-induced resonanceone-dimensional scattering lengthmixed dimensionEfimov effectcontinuous scaling symmetrydiscrete scaling symmetryEfimovian expansionatom-dimer resonancethree-atom resonancehigh-temperature expansionvirial coefficientupper branchlower branch
Type
Chapter
Information
Ultracold Atomic Physics , pp. 31 - 70
Publisher: Cambridge University Press
Print publication year: 2021

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  • Two-Body Interaction
  • Hui Zhai, Tsinghua University, Beijing
  • Book: Ultracold Atomic Physics
  • Online publication: 30 January 2021
  • Chapter DOI: https://doi.org/10.1017/9781108595216.003
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  • Two-Body Interaction
  • Hui Zhai, Tsinghua University, Beijing
  • Book: Ultracold Atomic Physics
  • Online publication: 30 January 2021
  • Chapter DOI: https://doi.org/10.1017/9781108595216.003
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Two-Body Interaction
  • Hui Zhai, Tsinghua University, Beijing
  • Book: Ultracold Atomic Physics
  • Online publication: 30 January 2021
  • Chapter DOI: https://doi.org/10.1017/9781108595216.003
Available formats
×