  Radio frequency antennas based on Rydberg atom vapor cells can in principle
reach sensitivities beyond those of any wire antenna, especially at lower
frequencies where long wires are needed to accommodate a growing wavelength.
They also have other desirable features such as nonmetallic, lower profile,
elements. This paper presents a detailed theoretical investigation of Rydberg
antenna sensitivity, elucidating parameter regimes that could cumulatively lead
to 2--3 orders of magnitude sensitivity increase beyond that of currently
tested configurations. The key insight is to optimally combine the advantages
of two well-studied approaches: (i) three laser ``2D star configuration''
setups that, enhanced also with increased laser power, help compensate for atom
motion-induced Doppler broadening, and (ii) resonant coupling between a pair of
near-degenerate Rydberg levels, tuned via a local oscillator to the incident
signal. The advantage of the star setup is subtle because it only restores
overall sensitivity to the expected Doppler-limited value, compensating for
additional off-resonance reductions where differently moving atom populations
destructively interfere with each other in the net signal. The additional
unique advantage of the local oscillator tuning is that it leads to vastly
narrower line widths, as low as ~10 kHz set by the intrinsic Rydberg state
lifetimes, rather than the typical ~10 MHz set by the core state lifetimes.
Intuitively, with this setup the two Rydberg states may be tuned to act as an
independent high-q cavity, a point of view supported through a study of the
frequency-dependence of the antenna resonant response. There are a number of
practical experimental advances, especially larger ~1 cm laser beam widths,
required to suppress various extrinsic line broadening effects and to fully
exploit this cavity response.
