CHAPTER 6: NONLINEAR DYNAMICS OF ATOM–MOLECULE CONVERSION

The creation of ultracold molecules has opened up new possibilities for studies on molecular matter waves, strongly interacting superfluids, high-precision molecular spectroscopy and coherent molecular optics. In an atomic Bose–Einstein condensate (BEC) and a degenerate Fermi–Fermi or Fermi–Bose mixture, magnetic Feshbach resonance or optical photoassociation (PA) technique has been used to create not only diatomic molecules but also more complex molecules. In this chapter, we focus on many issues of nonlinear dynamics of atom–molecule systems. In Sec. 1, on the basis of the two-channelmean-field approach, we study the manybody effects on the Landau–Zener(LZ) picture of two-body molecular production through dramatically distorting the energy levels near the Feshbach resonance. In Sec. 2, we investigate the Feshbach resonance with modulation of an oscillating magnetic field. In Sec. 3, we include the nonlinear interparticle collisions and focus on the linear instability induced by the collisions and the adiabatic fidelity of the atom–trimer dark state in a stimulated Raman adiabatic passage (STIRAP). In Sec. 4, we theoretically investigate conversion problem from atom to N-body polyatomic molecule in an ultracold bosonic system by implementing the generalized STIRAP. In the last section, we discuss role of two-body interactions in the Feshbach conversion of fermionic atoms to bosonic molecules.