Abstract
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}.
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References
C. Chin, R. Grimm, P. S. Julienne, and E. Tiesinga, “Feshbach resonances in ultracold gases,” Rev. Mod. Phys. 82, 1225 (2010).
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).
A. V. Turlapov, “Experimental study of ultracold gas of Fermi atoms,” Abstract of Doctoral Dissertation in Mathematics and Physics (Nizhnii Novgorod, 2012) [in Russian].
L. P. Pitaevskii, “Bose-Einstein condensates in the field of laser emission,” Usp. Fiz. Nauk 176(4), 345–364 (2006).
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).
S.-G. Peng, H. Hu, X.-J. Liu, and P. D. Drummond, “Confinement-induced resonances in anharmonic waveguides,” Phys. Rev. A 84, 043619 (2011).
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).
T. Busch, B.-G. Englert, K. Rzazewski, and M. Wilkens, “Two cold atoms in a harmonic trap,” Found. Phys. 28(4), 549 (1998).
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).
S. Saeidian, V. S. Melezhik, and P. Schmelcher, “Mutlichannel atomic scattering and confinement-induced resonances in waveguides,” Phys. Rev. A 77, 042721 (2008).
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Original Russian Text © I.S. Ishmukhamedov, D.S. Valiolda, S.A. Zhaugasheva, 2014, published in Pis’ma v Zhurnal Fizika Elementarnykh Chastits i Atomnogo Yadra, 2014.
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Ishmukhamedov, I.S., Valiolda, D.S. & Zhaugasheva, S.A. Description of ultracold atoms in a one-dimensional geometry of a harmonic trap with a realistic interaction. Phys. Part. Nuclei Lett. 11, 238–244 (2014). https://doi.org/10.1134/S1547477114030108
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DOI: https://doi.org/10.1134/S1547477114030108