“…1. The order of the Bragg diffraction j 0 describes the number of interactions of the atom with the cavity field and is always an even integer because during one Rabi cycle the momentum imparted to the atom, along the cavity axis, through its interaction with the field is either zero or 2hk [24,25], Thus the momenta acquired by the atom in first-, second-, and third-order Bragg diffraction from the cavity field will be (| Q 0) = l^k ),|G -2) = l-fik)), (|Go) = |2 /lk ),|e _ 4> = \-2 h k )), and (IGo) = |3/ik),|G-6) = |-3fik>), respectively, as a conse quence of the so-called Bragg resonances [27], Such an interaction of a two-level atom with quantized center-of-mass motion is governed by the interaction picture Hamiltonian, written under the dipole and rotating wave approximations as [22,23,25] -Q2 M c H i = ~ + -<r, + hfj. co s{kx)(a cr+ +<5'cr_).…”