Optical Radio-Frequency Phase Measurement With an Internal-State Rydberg Atom Interferometer

Abstract

We realize and model an internal-state Rydberg atom interferometer for measurement of phase and intensity of radio-frequency (rf) electromagnetic waves. A phase reference is supplied to the atoms via a modulated laser beam, enabling atomic measurement of the rf wave's phase without a rf reference wave. The rf and optical fields give rise to closed interferometric loops within the atoms' internal Hilbert space. In our experiment, we construct interferometric loops in the state space ${6{P}_{3/2},90{S}_{1/2},91{S}_{1/2},90{P}_{3/2}}$ of cesium and employ them to measure phase and intensity of a 5-GHz rf wave in a room-temperature vapor cell. Electromagnetically induced transparency on the $6{S}_{1/2}$ to $6{P}_{3/2}$ transition serves as an all-optical interferometer probe. The rf phase is measured over a range of $\ensuremath{\pi}$, and a sensitivity of 2 mrad is achieved. Measurements of rf phase and amplitude at submillimeter optical spatial resolution are demonstrated.