Magic Rydberg-Rydberg transitions in electric fields

Rydberg states of atoms and molecules are very sensitive to electric fields. This property makes them ideal electric-field sensors but is detrimental to applications of Rydberg states in quantum optics, quantum-information processing, and quantum simulation because of inhomogeneous Stark broadening and the resulting loss of quantum coherence. We demonstrate, with the example of Rydberg states of K-39, the existence of Rydberg-Rydberg transitions with extremely small differential dc Stark shifts, which we call dc-field-magic Rydberg-Rydberg transitions. These transitions hardly exhibit any Stark broadening, even when the electric-field strength varies by as much as 10 V cm(-1) over the experimental volume. We present a systematic study of dc-field-magic Rydberg-Rydberg transitions combining experiment and calculations and classify them in three main types, which should also be encountered in the other alkali-metal atoms, in alkaline-earth-metal atoms, and even in molecules. The observed insensitivity to dc electric fields does not reduce the interactions between Rydberg atoms, even if they are dominantly electric dipole-dipole in nature. Rydberg states coupled by dc-field-magic Rydberg-Rydberg transitions, therefore, have great potential as qubits.