### Speaker

Prof.
Vladimir Melezhik
(Bogoliubov Laboratory of Theoretical Physics, JINR)

### Description

MATEMATICAL MODELING OF RESONANT PROCESSES IN CONFINED GEOMETRY OF ATOMIC AND ATOM-ION TRAPS
V.S. Melezhik
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna Moscow Region 141980, Russian Federation
E-mail: melezhik@theor.jinr.ru
Mathematical modelling of resonant processes in confined geometry of optical and electromagnetic traps is an actual problem of physics of cold atoms and ions. The conventional theory for free-space resonant scattering is not valid for confined scattering and new approaches, including effects of the confinement, are needed. In our works we have developed a computational methods [1-4] for resonant collisions in tight atomic waveguides and have found several novel effects in its application: the confinement-induced resonances (CIRs) in multimode regimes including effects of transverse excitations and deexcitations [2], the so-called dual CIR yielding a complete suppression of quantum scattering [1], and resonant molecule formation with a transferred energy to center-of-mass excitation while forming molecules [5]. The last effect was recently confirmed in the Heidelberg experiment [6]. Our calculations have also been used for planning and interpretation of the Innsbruck experiment on investigation of CIRs in ultracold Cs gas [7].
Our talk is devoted to computational aspects of the developed theoretical models, based on the nondirect product DVR [4,8,9], for the time-dependent and stationary Schrödinger equations with a few spatial variables..We also plan to discuss resent results obtained with the developed approaches for the confined dipole-dipole [10] and atom-ion scattering [11]. Particularly, we investigate very complicate problem of influence of the ion micromotion in Paul traps [12] on the resonances.
1. V.S.Melezhik, J.I.Kim, and P.Schmelcher, Phys. Rev. A76 (2007) 053611-1-15.
2. S.Saeidian, V.S.Melezhik, and P.Schmelcher, Phys. Rev. A77 (2008) 042721-1-15.
3. V.S.Melezhik, Lecture Notes in Computer Science 7125, Springer (2012) pp. 94-107.
4. V.S.Melezhik, EPJ Web of Conferences 108 (2016) 01008-1-9.
5. V.S.Melezhik and P.Schmelcher, New J. Phys. 11 (2009) 073031-1-10.
6. S. Sala et al. Phys. Rev. Lett. 110 (2013) 203202-1-5
7. E. Haller at al. Phys. Rev. Lett. 104 (2010) 153203-1-4.
8. V.S. Melezhik, ICNAAM 2012, AIP Conf. Proc. 1479 (2012) pp.1200-1203.
9. V.S. Melezhik, Phys. Atom. Nucl. 77 (2014) pp.446-452.
10. P. Giannakeas, V.S. Melezhik, and P. Schmelcher, Phys.Rev.Lett. 111 (2013) 183201-1-5.
11. V.S. Melezhik and A. Negretti, Phys. Rev. A94 (2016) 022704-1-8.
12. D. Leibfried, R.Blatt, C.Monroe, and D.Wineland, Rev. Mod. Phys. 75 (2003)pp.281-324.

### Primary author

Prof.
Vladimir Melezhik
(Bogoliubov Laboratory of Theoretical Physics, JINR)