Rydberg

Rydberg is an adjective most often used in atomic and quantum physics to refer to highly excited electronic states of atoms or to the family of phenomena associated with them. The term derives from the Swedish physicist Johannes Rydberg, whose empirical formula for spectral lines gave rise to the Rydberg constant.

In a Rydberg state, an electron occupies a high principal quantum number n, yielding energies close to the ionization limit and wavefunctions with extended spatial reach. These states have exaggerated properties: large size, strong dipole moments, and strong interactions with other Rydberg atoms, which scale with distance roughly as R^−6 to R^−3 depending on state and regime. Lifetimes increase with n.

The Rydberg formula relates the wavelengths or frequencies of spectral lines to integers n1 and n2 via 1/λ = R∞ (1/n1^2 − 1/n2^2). The Rydberg constant R∞, about 1.097 × 10^7 m−1, is derived from fundamental constants and is widely used in precision spectroscopy. For multi-electron atoms, quantum defects modify the effective principal quantum number n* = n − δℓ, creating Rydberg series with non-hydrogenic energies.

Rydberg atoms are central to several areas of modern quantum science. The strong, tunable interactions enable phenomena such as the Rydberg blockade, where excitation of one atom prevents excitation of nearby atoms within a blockade radius, enabling deterministic entanglement and quantum gates in neutral-atom systems. They are used in quantum simulation, non-linear optics at the single-photon level, and precision electrometry.

Beyond single atoms, Rydberg physics studies ultracold Rydberg gases, Rydberg molecules formed by a ground-state atom bound to a Rydberg electron, and many-body dynamics in driven systems. The field continues to connect atomic spectroscopy with quantum information, metrology, and chemical physics.