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

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 a model for the decay of an excited state within a uniformly accelerated cavity to address the historical null results and to identify an alternative, non-thermal signature. In our framework, a massless Dirac field confined to a cavity is coupled to an external massive Dirac field of mass $M$. Our analysis reveals that for fundamental fermions (such as the electron), the condition $Mc^2 \gg \hbar a/c$ is satisfied at all achievable accelerations, placing the system in a regime of exponential suppression, $\Gamma_{\text{acc}}/\Gamma_{\text{in}} \sim \exp(-2 M c^2 / (\hbar a/c))$ (with $\Gamma_{\text{in}}$ the inertial decay rate). This suppression holds universally across all cavity sizes and experimental designs, providing a potential explanation within this model for the non-observation of Unruh effects. Furthermore, for intermediate-sized cavities ($a l \sim c^2$) with light external fields ($Mc^2 \ll \hbar a/c$), the model predicts a geometric enhancement of the decay rate, scaling as $\Gamma_{\text{acc}}/\Gamma_{\text{in}} \sim \frac{a l/c^2}{\ln(1 + a l/c^2)}$, which arises from kinematic constraints rather than thermal stimulation. This enhancement, reaching up to 26% for realistic parameters ($a\sim 10^{20}$ m/s$^2$, $l\sim 500~\mu$m), is presented as a measurable signature accessible through quantum simulation platforms. Our results propose a unified framework that explains past experimental challenges and suggests a viable path forward for detecting non-inertial quantum effects.