Transition rates and their applications in accelerated single-qubit for fermionic spinor field coupling

TL;DR

The paper addresses how a uniformly accelerated Unruh–DeWitt detector coherently interacts with fermionic spinor fields, both massless and massive. It develops finite-time transition-rate calculations via perturbation theory with Gaussian switching, including renormalization via normal ordering, and expresses results in dimensionless parameters $ar{a}=a/ Omega$ and $ar{ au}= Omega T$. Applying these rates to a driven two-level system, it reveals that fermionic coupling leads to faster coherence degradation than scalar coupling, while particle mass acts as a protective factor by suppressing absorption when $m$ approaches the detector spacing $ Omega$. The findings have implications for relativistic quantum information processing, suggesting that tuning field mass and coupling structure can mitigate Unruh-induced decoherence in accelerated quantum devices.

Abstract

In this work, we investigate the interaction between a uniformly accelerated single qubit and a fermionic spinor field. Here we consider both the massless and the massive fermionic spinor fields. The qubit-field interaction occurs over a finite time and was evolved via perturbation theory. This approach yields the transition probability rates, from which we subsequently evaluate the quantum coherence of an Unruh-DeWitt (UDW) detector initially prepared in a qubit state. Our findings reveal that the UDW detector responds more when coupled with the fermionic field, and consequently, quantum coherence (for the fermionic case) degrades much more rapidly when compared to the case of the qubit linearly coupled with the scalar field. Moreover, the analysis suggests that particle mass plays a protective role against Unruh-induced decoherence as the rest mass energy becomes comparable to the detector's energy-level spacing, the detector's excitation probability and response decreases, which leads to the mitigation of quantum coherence degradation in accelerated quantum systems.

Figures (8)

• Figure 1: Schematic representation of the measurement of the coherence degradation of an accelerated single-qubit interacting (for a finite time) with a fermionic spinor field.
• Figure 2: Quantum coherence $\mathcal{C}_{\Psi,0}^{l^1}$ as a function of the dimensionless parameter $\overline{a}$ for different values of $\overline{\lambda}_{\Psi}$. We fix the following parameters: $\theta = \pi/2$ and $\sigma = 10$.
• Figure 3: Quantum coherence $\mathcal{C}_{\Psi,0}^{l^1}$ as a function of the dimensionless parameter $\overline{\lambda}_{\Psi}$ for different values of $\overline{a}$. We fix the following parameters: $\theta = \pi/2$ and $\sigma = 10$.
• Figure 4: Comparison between quantum coherence for the case of the fermionic spinor field $\mathcal{C}_{\Psi,0}^{l^1}$ and for the case of the scalar field $\mathcal{C}_{\phi,0}^{l^1}$, both as a function of the dimensionless parameter $\overline{a}$. We fix the following parameters: $\theta = \pi/2$ and $\sigma = 10$.
• Figure 5: Excitation rate $\widetilde{\mathcal{R}}^{-}_{\Psi,\,sm}$ as a function of the parameter $\overline{a}$ for different values of the parameter $\overline{m}$. Where we fix the parameters: $\overline{\lambda}_{\Psi} = 1 \times 10^{-3}$ and $\sigma = 10$. Where $\widetilde{\mathcal{R}}^{\pm}_{\Psi,\,sm} \equiv \lambda_{\Psi}^{2}\overline{\mathcal{R}}^{\pm}_{\Psi,\,sm}$.