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

TL;DR

This work analyzes a fermionic cavity QED model to probe non-inertial quantum effects and the Unruh effect. By coupling a massless confined field to an external massive Dirac field in a 1+1D accelerated cavity, it shows that for fundamental particles the condition $Mc^2 \gg \hbar a/c$ induces exponential suppression of the accelerated decay channel, offering a unified explanation for past null results. However, in intermediate cavities with light external fields, a geometric, non-thermal enhancement $\Gamma_{\text{acc}}/\Gamma_{\text{in}} \sim \frac{al/c^2}{\ln(1+al/c^2)}$ emerges, potentially up to 26% for realistic parameters, and is accessible to quantum simulation platforms. The paper develops a rigorous framework using inertial and Rindler quantization, MIT bag and generalized boundary conditions, and long-time resonance analyses to map out regimes defined by $al$ and $M/a$, providing concrete predictions for experiments with superconducting circuits and optomechanical systems. Overall, it offers a unified picture linking acceleration, cavity geometry, and field mass, and identifies a viable non-thermal signature for observing non-inertial quantum effects in engineered quantum systems.

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 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, $Γ_{\text{acc}}/Γ_{\text{in}} \sim \exp(-2 M c^2 / (\hbar a/c))$ (with $Γ_{\text{in}}$ 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 $Γ_{\text{acc}}/Γ_{\text{in}} \sim \frac{a l/c^2}{\ln(1 + a l/c^2)}$, which arises from kinematic constraints rather than thermal stimulation. This enhancement, reaching up to 26% for realistic parameters ($a\sim 10^{20}$ m/s$^2$, $l\sim 500~μ$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.