Document Type : Research

Authors

1 Department of Physics, Yasouj university

2 Department of Physics, yasouj university

Abstract

The present study seeks to scrutinize a two bosonic atoms system in a two-dimensional anharmonic and a short range interatomic potentials. Wave functions and energies are analytically stated, and the effect of anharmonic term on the energy for different strengths of interaction is calculated. The results show that the energy of relative motion and correction energy have different behaviours with the interaction strength. To investigate the dynamics of system, the fidelity for different coupling strengths is also calculated. The results are in agreement to other works.

Keywords

[1] M. Lewenstein, A. Sanpera, V. Ahu_nger, B. Damski, A. Sen and U. Sen, Adv. Phys. 56 (2007) 243.
[2] I. Bloch, J. Dalibard andW. Zwerger, Rev. Mod. Phys. 80 (2008) 885.
[3] V.O. Nesterenko, A.N. Novikov, E. Suraud, Transport of the Repulsive Bose Einstein Condensate in a Double-Well Trap: Interaction Impact and Relation to the Josephson Effect, Laser Phys. 24 (2014) 125501.
[4] C. Chin, R. Grimm, P. S. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82 (2010) 1225
[5] G. Zurn, F. Serwane, T. Lompe, A. N. Wenz, M. G. Ries, J. E. Bohn, and S. Jochim, Fermionization of two distinguishable fermions, Phys. Rev. Lett. 108 (2012) 075303.
[6] E. Haller, M. J. Mark, R. Hart, J. G. Danzl, L. Reichsollner, V. Melezhik, P. Schmelcher, H.C. Nagerl, Confinement induced resonances in low dimensional quantum systems, Phys. Rev. Lett. 104 (2010) 153203.
[7] T. Busch, B.G. Englert, K. Rzazewski, and M. Wilkens, Two cold atoms in a harmonic trap, Found. Phys. 28 (1998) 549
[8] M. Olshanii, Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons, Phys. Rev. Lett. 81 (1998) 938.
[9] J.P. Kestner, L.M. Duan, Anharmonicity-induced resonances for ultracold atoms and their detection, New J. Phys. 12 (2010) 053016.
[10] S. Sala, A. Saenz, Theory of inelastic con_nement-induced resonances due to the coupling of center-of-mass and relative motion, Phys. Rev. A 94 (2016) 022713.
[11] S.-G. Peng, H. Hu, X.-J. Liu, P.D. Drummond, Confinement-induced resonances in anharmonic waveguides, Phys. Rev. A 84 (2011) 043619.
[12] C.F.S. Zephania, T. Sil, Study of autonomous conservative oscillator using an improved perturbation method, J. Vib. Eng. Technol. 9 (2021) 409.
[13] Q. Wang, B. Xiong, Anharmonicity-induced criticality of collective excitation in a trapped Bose Einstein condensate, Internat. J. Modern Phys. B 32 (2018) 1850345.
[14] I. S. Ishmukhamedov, D. T. Aznabayev, and S. A. Zhaugasheva, Two Body Atomic System in a One Dimensional Anharmonic Trap: The Energy Spectrum, Physics of Particles and Nuclei Letters, 12(5) (2015) 680-688.
[15] I.S. Ishmukhamedov, Quench dynamics of two interacting atoms in a onedimensional anharmonic trap, Physica  E 142 (2022) 115228
[16] L. Budewig, S. I. Mistakidis, and P. Schmelcher, Quench dynamics of two one-dimensional harmonically trapped bosons bridging attraction and repulsion, Molecular Physics 117 (2019) 2043-2057.
[17] M. Rontani, G Eriksson, S Åberg and S M Reimann, On the renormalization of contact interactions for the configuration-interaction method in two-dimensions, J. Phys. B: At. Mol. Opt. Phys. 50 (2017) 065301-065311
[18] M. Olshanii, and L. Pricoupenko, Rigorous Approach to the Problem of Ultraviolet Divergencies in Dilute Bose Gases, Phys. Rev. Lett. , 88 (2002) 010402
[19] S. Campbell, M. A. Garcia-March, T. Fogarty and T. Busch, Quenching small quantum gases: Genesis of the orthogonality catastrophe, Phys. Rev. A 90 (2014) 013617.
[20] T. Plaβmann, S. I. Mistakidis, P. Schmelcher, Quench dynamics of finite bosonic ensembles in optical lattices with spatially modulated interactions, J. of Phys. B: Atomic, molecular and optical physics 51 (2018)225001
[21] M. Ebert, A. Volosniev, H. W. Hammer, Two cold atoms in a time dependent harmonic trap in one dimension, Ann. Phys. 1 (2016)12