Abstract
We study in detail the dynamics of unstable two-level quantum systems by adopting the Bloch-sphere formalism of qubits. By employing the Bloch-vector representation for such unstable qubit systems, we identify a novel class of critical scenarios in which the so-called energy-level and decay-width vectors, E and Γ, are orthogonal to one another, and the parameter r = | Γ|/(2| E|) is less than 1. Most remarkably, we find that critical unstable qubit systems exhibit atypical behaviours like coherence--decoherence oscillations when analysed in an appropriately defined co-decaying frame of the system. In the same frame, a unit Bloch vector b describing a pure critical qubit will sweep out unequal areas during equal intervals of time, while rotating about the vector E. These phenomena emerge beyond the usual oscillatory pattern due to the energy-level difference of the two-level quantum system. Interestingly enough, we observe that these new features will persist even for quasi-critical scenarios, in which the vectors E and Γ are not perfectly orthogonal to each other. Applications of our results to quantum information and to unstable meson--antimeson and other systems are discussed.