Exponential Suppression of the Unruh Effect and Geometric Enhancement in a Fermionic Cavity QED Setup

Abstract: The Unruh effect -- the prediction that an accelerated observer perceives the vacuum as a thermal bath -- remains one of the most profound yet experimentally unverified consequences of quantum field theory. This work analyzes the decay of an excited state within a uniformly accelerated cavity to explain the historical null results and identify an alternative measurable signature. We model a massless Dirac field confined to a uniformly accelerated cavity, coupled to an external massive Dirac field of mass $M$. Our analysis reveals that for fundamental particles with mass $M$, the condition $Mc^2 \gg \hbar a/c$ is satisfied for all achievable accelerations, placing the system in an exponentially suppressed decay regime ($\Gamma_{\text{acc}} \sim e^{-2Mc^2/(\hbar a/c)}$) that holds universally across all cavity sizes, explaining why direct observation of Unruh effects has remained elusive. However, for intermediate-sized cavities ($a l\sim c^2$) with light external fields ($Mc^2 \ll \hbar a/c$), we identify a geometric enhancement of the decay rate, scaling as $\Gamma_{\text{acc}}\sim \Gamma_{\text{in}} \frac{a l/c^2}{\ln(1+a l/c^2)}$ (with $\Gamma_{\text{in}}$ the inertial decay rate), which arises from non-inertial acceleration effects rather than thermal stimulation. This geometric enhancement, reaching up to 26\% for realistic parameters ($a\sim 10^{20}~\text{m/s}^2$, $l\sim 100-500~\mu\text{m}$), provides a measurable signature accessible through quantum simulation platforms. Our results provide a unified theoretical framework that explains historical null results while offering a viable path toward detecting non-inertial quantum effects in accelerated systems.