A conventional radio receiver compares the incoming wave with a reference to extract information from it. Rubidium atoms can do this differently: they themselves act as both antenna and detector. But until now, they required an additional radio signal to set a reference point.

The new scheme does without it. A constant electric field is applied to a glass cell containing rubidium vapor. This field slightly mixes two close energy levels of the atom and opens a path through which laser light can pass only with the participation of the radio wave. A closed loop emerges: the radio wave, the pump light, and the probe light begin to work as a single mechanism.

The key result is a precise rule: if the radio wave has phase Φ, then the n-th harmonic in the probe light carries a factor e^(inΦ). This allows direct measurement of the phase and amplitude of the signal by simply demodulating the desired harmonic. For the amplitude, one needs to invert a simple response function, which is always unambiguous with proper field tuning.

When the field in the cell is inhomogeneous, the picture becomes more complex: different atoms experience different level shifts, and the overall signal gets 'smeared out.' The authors showed how spatial averaging reduces phase accuracy and changes the slope of the amplitude curve. Numerical examples confirm the theory and help choose the mixing angle at which losses in phase and amplitude are balanced.

Such a receiver does not require a bulky reference oscillator and operates on the atomic transition itself, promising high accuracy and miniaturization. In the future, this could lead to compact sensors for communication, navigation, and radio astronomy.