3. Summary

In this chapter, the Doppler- and recoil-free three-photon GGLG excitation promises to extend a single localized atom to a highly excited Rydberg state, which has application in the control and transformation of high-dimensional quantum states [16]. The adiabatic approximation results in an effective quadrupole Rabi frequency with a rich geometrical dependency. The quadrupole interaction in the last step of the LG excitation transfers a unit of orbital angular momentum to the Rydberg state in addition to the spin angular momentum. The GGLG excitation system allows to greatly reducing the rate of photon scattering and suppresses the loss rate due to collision, while the trapping potential of FORODQT localizes the Rydberg excitation and increases excitation coherency and allows for high detection efficiency and long detection time. A wide range of properties characterizing the excitation configuration can be controlled in real time through changes in geometry, polarization and orbital angular momentum, focal spot size, intensity, and frequency of the laser excitation beams to provide the ability to encode qudit in the internal degree of freedom of Rydberg atom independently to the center-of-mass motion. This aspect is vital to store and manipulate the quantum state of qudits in high-dimensional quantum information processing.

Quantum Electronics
