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.Comment: 31 pages, 10 figure