  In this paper, we present a comprehensive investigation into the sensitivity
of a Rydberg atom electric field sensor, with a specific focus on the minimum
detectable field (MDF) as a key metric. The study utilizes one-mode Floquet
theory to calculate the Stark shift for selected Rydberg states when exposed to
a signal electric field. The results are compared to those obtained using the
rotating wave approximation (RWA). To enhance the sensor's sensitivity when the
frequency of the signal electric field deviates from resonance frequencies
between Rydberg states, we propose incorporating an extra coupling electric
field and using many-mode Floquet theory, a generalization of one-mode Floquet
theory, to theoretically analyze this kind of Rydberg atom electric field
sensor. The Autler-Townes effect resulting from this coupling electric field
causes Rydberg states to split into dressed states, effectively increasing
sensitivity by modulating the frequencies of resonance peaks. Moreover, the
phenomenon of two-photon absorption in the presence of the coupling electric
field is explored. We demonstrate that by appropriately adjusting the coupling
electric field's amplitude or frequency, one can control the occurrence of
two-photon resonances, providing additional sensitivity enhancement for the
Rydberg sensor within the significantly extended off-resonance domain. The
study underscores the significance of coupling fields in enhancing the
sensitivity of Rydberg atom electric field sensors. These insights hold
promising implications for the development of more robust and versatile
electric field sensing devices, applicable in diverse fields such as precision
measurements and quantum information processing.
