Renormalization approach to bound state energy computation for two ultracold atoms in an optical lattice

• Main Author: Borzov, Dmitry
• Language: English
• Published: University of British Columbia 2011
• Online Access: http://hdl.handle.net/2429/39749

In experiments with ultra-cold gases, two alkali atoms, that interact with repulsive or attractive potentials and are confined to an optical lattice, can form bound states. In order to compute the energy of such states formed by atoms in the lowest Bloch band, one needs to take into account the intra-band corrections arising from contributions by higher Bloch bands. As it is hard to implement, known calculations tend to neglect them altogether thus setting up a limit for the precision of such computations. To address the problem we apply an approach that uses renormalization-group equations for an effective potential we introduce. It allows for the expression of the bound state energy in terms of the free-space interaction scattering length and parameters of confining potentials. Expressions for bound state energies in 1D, 2D and 3D optical lattices are reported. We show that the method we use can be easily tailored to various cases of atoms confined by external fields of other geometries. A known result for atoms confined to a quasi-2D system is reproduced as an example. Universality of the approach makes it a useful tool for such class of problems.