Many-body physics with spin states of trapped Rydberg atoms

Atoms in their highly excited electronic states, referred to as Rydberg atoms, have extraordinary nonlinear optical properties. Such atoms are highly polarizable and interact with each other via the dipole-dipole interactions or the van-der-Waals interactions. At ultra-cold temperatures, Rydberg atoms possess quantum properties that are strongly dependent on their interatomic interactions leading to condensed matter-like collective behavior. Owing to these features, Rydberg atoms became a new platform to study quantum many-body physics. Spin degrees of freedom of trapped Rydberg atoms bring rich new physics including quantum magnetism, new quantum phases, and entanglement, which is a crucial resource in many quantum information and quantum communication tasks. In this talk, I will discuss properties of alkali rubidium atoms trapped in an optical lattice and excited to Rydberg states by laser radiation. I will present a quantum control methodology to create entangled states of two typical classes, the W and the GHZ. I will show that the entangled states of Rydberg atoms can be used to create the multiphoton entangled radiation states in a cavity and in free space. The methodology exploits chirped pulse adiabatic passage.