Decay of Qubits under arbitrary space-time trajectories: The Zeno & Anti-Zeno Effects

Modeling an arbitrarily accelerating qubit as an open quantum system, we derive an exact solution for the pure-dephasing model ($\sigma_z$ coupling) under arbitrary qubit space-time trajectories, as well as general expressions for the survival probabilities of finite-length qubits interacting with a massless scalar field under $\sigma_x$ coupling (an Unruh-DeWitt detector) to second order. We follow the regularization scheme presented in a previous paper by S. Schlicht, to allow a finite length quantum detector to couple to the massless scalar field. We compute the decay rate of the qubit in different coupling regimes, (pure dephasing, Unruh-DeWitt) and explore the Quantum Zeno (QZE) and Quantum Anti Zeno Effect (QAZE) as the qubit decoheres under it's interaction with the environment. We compute results for four example trajectories: stationary, uniform acceleration, oscillation and circular orbits.