Researchers present a simple optical way to measure how the energy of a highly excited “Rydberg” atomic level is shifted by interactions between atoms in a hot vapor. The method looks at a pair of deep dips in the transmission of a weak probe laser. Those two dips come from a split electromagnetically induced absorption (EIA) effect in a four-level ladder of rubidium atoms. By restoring a balance between the two dips with a second laser, the team infers how much the Rydberg level has moved.

The authors analyze a four-level ladder in 87Rb. The ground-to-first-excited transition is driven by a 780 nm probe laser. A 776 nm “dressing” laser connects the first and second excited states. A 1258 nm “coupling” laser links the second excited state to the Rydberg state. They model the atoms with a semi-classical Hamiltonian and include decay and motion. To account for the thermal motion in the vapor, they average the steady-state quantum solution over the Maxwell–Boltzmann velocity distribution.

The measurement idea is qualitative and practical. When the coupling laser is exactly on resonance, the two EIA transmission minima have the same depth. If interactions shift the Rydberg level, that balance is lost and the two dips become unequal. The experimenter then detunes the coupling laser until the two dips are equal again. Because a change in the Rydberg energy acts like an opposite change in the coupling-laser frequency, the amount of detuning needed to rebalance the dips gives the energy shift of the Rydberg level.

This measurement is useful because Rydberg–Rydberg interactions strongly affect the behavior of atomic vapors and of devices that rely on Rydberg atoms, such as radio-frequency sensors. The authors apply the split-EIA balancing method to hot rubidium vapors and compare their measured mean energy shifts with theoretical estimates for two possible mechanisms: Stark shifts caused by stray ions and van der Waals interactions between Rydberg atoms. They report a correspondence with the ion-induced Stark prediction, while the van der Waals prediction shows a different character. They note this conclusion matches previous considerations in the literature.