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 $M{c}^2\gg \mathrm{\hslash }a\mathrm{/}c$ is satisfied at all achievable accelerations, placing the system in a regime of exponential suppression, ${\mathrm{\Gamma }}_{\text{acc}}\mathrm{/}{\mathrm{\Gamma }}_{\text{in}}\sim \exp (-2M{c}^2\mathrm{/}(\mathrm{\hslash }a\mathrm{/}c))$ (with ${\mathrm{\Gamma }}_{\text{in}}$ 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 ($al\sim c^2$) with light external fields ($M{c}^2\ll \mathrm{\hslash }a\mathrm{/}c$), the model predicts a geometric enhancement of the decay rate, scaling as ${\mathrm{\Gamma }}_{\text{acc}}\mathrm{/}{\mathrm{\Gamma }}_{\text{in}}\sim \frac{al\mathrm{/}{c}^2}{\ln (1+al\mathrm{/}{c}^2)}$, 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.