  Rydberg atoms have been used for measuring radio-frequency (RF) electric
(E)-fields due to their strong dipole moments over the frequency range of 500
MHz-1 THz. For this, electromagnetically induced transparency (EIT) within the
Autler-Townes (AT) regime is used such that the detected E-field is
proportional to AT splitting. However, for weak E-fields AT peak separation
becomes unresolvable thus limiting the minimum detectable E-field. Here, we
demonstrate using the Rydberg atoms as an RF mixer for weak E-field detection
well below the AT regime with frequency discrimination better than 1 Hz
resolution. Two E-fields incident on a vapor cell filled with cesium atoms are
used. One E-field at 19.626000 GHz drives the 34D_(5/2)->5P_(3/2) Rydberg
transition and acts as a local oscillator (LO) and a second signal E-field
(Sig) of interest is at 19.626090 GHz. In the presence of the LO, the Rydberg
atoms naturally down convert the Sig field to a 90 kHz intermediate frequency
(IF) signal. This IF signal manifests as an oscillation in the probe laser
intensity through the Rydberg vapor and is easily detected with a photodiode
and lock-in amplifier. In the configuration used here, E-field strength down to
? 46 mV/m +/-2 mV/m were detected. Furthermore, neighboring fields 0.1 Hz away
and equal in strength to Sig could be discriminated without any leakage into
the lock-in signal. For signals 1 Hz away and as high as +60 dB above Sig,
leakage into the lock-in signal could be kept below -3 dB.
