Quantum Electronics

Figure 1. Energy-level diagram three-photon Rydberg excitation [77].

### Figure 2.

(a) Geometry of Rydberg excitation via three-photon dipole-dipole-quadrupole transition. (b) Details of vectors and quantities involving in the excitation process [77].

Localized Excitation of Single Atom to a Rydberg State with Structured Laser Beam for Quantum… DOI: http://dx.doi.org/10.5772/intechopen.82319

θ<sup>2</sup> to the z axis. As it is explained in the following section, this special geometry provides the possibility for Doppler and recoil-free excitation.

The Rydberg atom-field interaction considered here corresponds to situations, where firstly the Rydberg atom's size is comparable to the LG-beam waist in the third Rydberg excitation and the Rydberg electron sees the variation of the light intensity. Different parts of the atom can feel different electric fields, and the quadrupole transition, which seems to be negligible in most situations due to a much stronger simultaneous effect of the dipole one, is considerably increased. Secondly, the Rydberg and two intermediate states decay by spontaneous emission, and it is assumed that the lifetime of the Rydberg state is much longer than the other states, and so its decay can be neglected during the time scales relevant to the excitation process. Finally, the dipole-dipole interaction between the Rydberg atoms, which may induce the blockade, is omitted to focus on the single-atom excitation mechanism.
