1.2 Rydberg atoms for quantum information

The optical degrees of freedom of single atoms such as polarization, wavelength, transverse mode, etc., can provide qubits or qudits for quantum information. Thus control and manipulation of single atoms are now of great interest given the potential to create quantum registers with single-atom techniques [21–24]. Furthermore, the observation of entanglement between a single atom and a single photon [25] provides the precondition for quantum communication and computation. Ground atomic states are ideal for preserving quantum coherence [26], but implementation of fast and deterministic quantum operations is challenging due to their weak interactions. Such considerations suggest to employ a quantum superposition of a ground and a Rydberg state to achieve both fast and deterministic quantum operations and long-lived memory [27]. A Rydberg atom is an atom in a highly excited state, typically with a principal quantum number n ≫ 1. The excited valence electron can travel microns from the nucleus, while still remaining bound to it. Because the Rydberg electron is so far from the core of the atom, the Rydberg atom develops exaggerated properties, such as high polarizability. The strong dipolar interactions between Rydberg atoms can potentially be used for fast quantum gates between qubits stored in stable ground states of neutral atoms [28, 29]. The electric dipole strength of highly excited Rydberg atoms results in the Rydberg excitation blockade [28–33] which can be used in combination with electromagnetically induced transparency (EIT) [34, 35] to generate quantum states of light, entanglement of several atoms, and quantum logic gates [36–38]. The mapping of Rydberg interactions onto photons by means of EIT has emerged as a powerful approach to realizing fewphoton optical nonlinearities [39–41] and provides the possibility to control the interaction between photons, which is a key ingredient to the goal of quantum information processing. Due to the nature of Rydberg blockade, the Rydberg nonlinearity is a sufficiently large and long range to build an optical quantum computer. The possibility to coherently control the quantum state of photon via dark-state Rydberg polaritons opens up interesting applications in reversible quantum memories for light waves [42] and shall find a possibility for a fast transformation [43].
