  We investigate the use of a split-ring resonator (SRR) incorporated with an
atomic-vapor cell to improve the sensitivity and the minimal detectable
electric (E) field of Rydberg atom-based sensors. In this approach, a
sub-wavelength SRR is placed around an atomic vapor-cell filled with cesium
atoms for E-field measurements at 1.3~GHz. The SRR provides a factor of 100 in
the enhancement of the E-field measurement sensitivity. Using
electromagnetically induced transparency (EIT) with Aulter-Townes splitting,
E-field measurements down to 5~mV/m are demonstrated with the SRR, while in the
absence of the SRR, the minimal detectable field is 500~mV/m. We demonstrate
that by combining EIT with a heterodyne Rydberg atom-based mixer approach, the
SRR allows for the a sensitivity of 5.5~$\mu$V/m$\sqrt{{\rm Hz}}$, which is
two-orders of magnitude improvement in sensitivity than when the SRR is not
used.
