Coherent tunneling of atoms and dimers in half spaces

Feshbach scattering of fermions in an one-dimensional optical lattice is an intensively investigated subject [1,2]. Scattering theory in free space differs significantly from scattering in a lattice. By breaking the continuous translation symmetry the center-of-mass momentum of the two particles become a new control parameter of Feshbach scattering. We have reported numerical results of this effect in [3]. In the present contribution we study a simple analytic model of this effect by considering the coherent Feshbach scattering of atoms and dimers in half spaces.\newline [1] I.~Bloch, J.~Dalibard, W.~Zwerger, Rev. Mod. Phys. 80, 885 (2008) [2] N.~Nygaard, R.~Piil, K.~M\o lmer, Phys. Rev. A 78, 023617 (2008)\newline [3] M.~Grupp, R.~Walser, W.~Schleich, A.~Muramatsu and M.~Weitz, J. Phys. B: At. Mol. Opt. Phys. 40 (2007) 2703-2718