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Rydberg atoms have been used for measuring radio-frequency (RF) electric(E)-fields due to their strong dipole moments over the frequency range of 500MHz-1 THz. For this, electromagnetically induced transparency (EIT) within theAutler-Townes (AT) regime is used such that the detected E-field isproportional to AT splitting. However, for weak E-fields AT peak separationbecomes unresolvable thus limiting the minimum detectable E-field. Here, wedemonstrate using the Rydberg atoms as an RF mixer for weak E-field detectionwell below the AT regime with frequency discrimination better than 1 Hzresolution. Two E-fields incident on a vapor cell filled with cesium atoms areused. One E-field at 19.626000 GHz drives the 34D_(5/2)->5P_(3/2) Rydbergtransition 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 Rydbergatoms naturally down convert the Sig field to a 90 kHz intermediate frequency(IF) signal. This IF signal manifests as an oscillation in the probe laserintensity through the Rydberg vapor and is easily detected with a photodiodeand 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 awayand equal in strength to Sig could be discriminated without any leakage intothe 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.

Weak Electric-Field Detection with Sub-1 Hz Resolution at Radio Frequencies Using A Rydberg Atom-Based Mixer