Exploring the correspondence principle with spinor condensates: from quantum Bloch oscillations to classical Bogoliubov excitations

By tuning the relative strength between single and two-body energies in a spinorial F=1 Bose-Einstein condensate (e.g. $^{87}$Rb), we can effectively control the dynamics of the macroscopic Fock-state [1,2,3]. We will study the static as well as dynamic aspects of this few mode quantum system and illustrate the ``classical'' as well as quantum aspects of this system, which can be realized in deep optical lattices.\\ \noindent [1] M-S. Chang {\em et al.}, Coherent spinor dynamics in a spin-1 Bose-Einstein condensate, Nature Phys., {\bf 1}, 111 (2005). \\ \noindent [2] J. Kronj{\"a}ger {\em et al.}, Evolution of a spinor condensate: coherent dynamics, dephasing and revivals, Phys. Rev. A, {\bf 72}, 063619 (2005).\\ \noindent [3] A. Widera {\em et al.}, Precision measurements of spin-dependent interaction strength for spin-1 and spin-2 $^{87}$Rb atoms, NJP, {\bf 8}, 152, (2006).