Ultracold two-level atom in a quadratic potential
  We use a right unitary decomposition to study an ultracold two-level atom interacting with a quantum field. We show that such a right unitary approach simplifies the numerical evolution for arbitrary position-dependent atom-field couplings. In particular, we provide a closed form, analytic time evolution operator for atom-field couplings with quadratic dependence on the position of the atom. 
F. Soto-Eguibar, A. Z\'u\~niga-Segundo, B. M. Rodr\'iguez-Lara, and H.   M. Moya-Cessa
quant-ph