Physics of Particles and Nuclei Letters

, Volume 11, Issue 3, pp 238–244 | Cite as

Description of ultracold atoms in a one-dimensional geometry of a harmonic trap with a realistic interaction

  • I. S. Ishmukhamedov
  • D. S. Valiolda
  • S. A. Zhaugasheva
Physics of Elementary Particles and Atomic Nuclei. Theory


We compute the ground-state energy of two atoms in a one-dimensional geometry of a harmonic optical trap. We obtain a dependence of the energy on a one-dimensional scattering length, which corre-sponds to various strengths of the interaction potential V int (x) = V 0 exp {−2cx 2}. The calculation is performed by numerical and analytical methods. For the analytical method we choose the oscillator representation method (OR), which has been successfully applied to computations of bound states of various few-body systems. The main results of this paper are (1) a numerical investigation of the validity range of the previously used pseudopotential method and (2) an investigation of the validity range of the OR for the potential V(x) = V conf (x) + V int (x) = x 2/2 + V 0 exp {−2cx 2}.


Ground State Energy Nucleus Letter Oscillator Representation Validity Range Harmonic Trap 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Chin, R. Grimm, P. S. Julienne, and E. Tiesinga, “Feshbach resonances in ultracold gases,” Rev. Mod. Phys. 82, 1225 (2010).ADSCrossRefGoogle Scholar
  2. 2.
    K. -K. Ni, S. Ospelkaus, D. Wang, G. Quemener, B. Neyenhuis, M. H. G. de Miranda, J. L. Bohn, J. Ye, and D. S. Jin, “Dipolar collisions of polar molecules in the quantum regime,” Nature 464, 1324–1328 (2010).ADSCrossRefGoogle Scholar
  3. 3.
    A. V. Turlapov, “Experimental study of ultracold gas of Fermi atoms,” Abstract of Doctoral Dissertation in Mathematics and Physics (Nizhnii Novgorod, 2012) [in Russian].Google Scholar
  4. 4.
    L. P. Pitaevskii, “Bose-Einstein condensates in the field of laser emission,” Usp. Fiz. Nauk 176(4), 345–364 (2006).CrossRefGoogle Scholar
  5. 5.
    E. Haller, M. J. Mark, R. Hart, J. G. Danzl, L. Reichsoellner, V. Melezhik, P. Schmelcher, and H.-C. Naegerl. “Confinement-induced resonances in low-dimensional quantum systems,” Phys. Rev. Lett. 104, 153203 (2010).ADSCrossRefGoogle Scholar
  6. 6.
    S.-G. Peng, H. Hu, X.-J. Liu, and P. D. Drummond, “Confinement-induced resonances in anharmonic waveguides,” Phys. Rev. A 84, 043619 (2011).ADSCrossRefGoogle Scholar
  7. 7.
    M. Dineykhan, G. V. Efimov, G. Ganbold, and S. N. Nedelko, “Oscillator representation in quantum physics,” Lecture Notes in Physics, vol. 26 (Berlin: Springer, 1995).Google Scholar
  8. 8.
    T. Busch, B.-G. Englert, K. Rzazewski, and M. Wilkens, “Two cold atoms in a harmonic trap,” Found. Phys. 28(4), 549 (1998).CrossRefGoogle Scholar
  9. 9.
    T. Bergeman, M. G. Moore, and M. Olshanii, “Atomatom scattering in the presence of a cylindrical harmonic potential: Numerical results and an extended analytic theory,” Phys. Rev. Lett. 91, 163201 (2003).ADSCrossRefGoogle Scholar
  10. 10.
    S. Saeidian, V. S. Melezhik, and P. Schmelcher, “Mutlichannel atomic scattering and confinement-induced resonances in waveguides,” Phys. Rev. A 77, 042721 (2008).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • I. S. Ishmukhamedov
    • 1
    • 2
  • D. S. Valiolda
    • 1
    • 2
  • S. A. Zhaugasheva
    • 1
    • 2
  1. 1.Joint Institute for Nuclear ResearchDubnaRussia
  2. 2.Al-Farabi Kazakh National UniversityAlmatyKazakhstan

Personalised recommendations