Dispersion readout of micro-wave electric field using double-dark-state Rydberg atoms

A dispersion probe of the electric fields of microwaves (MWs) is proposed using double-dark-state Rydberg atoms with Doppler effects. The MW field splits the atomic absorption spectrum, with normal dispersion at the central frequency. We investigate the sensitivity of the dispersion to the MW field strength. The numerical result reveals a linear relationship between the phase shift induced by the dispersion and the MW field intensity, which can be used to estimate MW electric field strength. Doppler effects can enhance the dispersion and greatly improve the measurement sensitivity. Our simulations show the probe sensitivity increases more than 10 times after Doppler averaging.