Critical unstable qubits: An application to the B0B¯0 meson system

We extend our previous work on a novel class of unstable qubits which we have identified recently and called them critical unstable qubits (CUQs). The characteristic property of CUQs is that the energy-level and decay-width vectors, E and Γ, are orthogonal to one another, and the key parameter r=|Γ|/|2E| is less than 1. Most remarkably, CUQs exhibit two atypical behaviors: (i) they display coherence-decoherence oscillations in a co-decaying frame of the system described by a unit Bloch vector b, and (ii) the unit Bloch vector b describing a pure CUQ sweeps out unequal areas during equal intervals of time, while rotating about the vector E. The latter phenomenon emerges beyond the usual oscillatory pattern due to the energy-level difference of the two-level quantum system, which governs an ordinary qubit. By making use of a Fourier series decomposition, we define anharmonicity observables that quantify the degree of oscillation of a CUQ. We apply the results of our formalism to the B0B¯0-meson system and derive, for the first time, generic upper limits on these new observables. Published by the American Physical Society 2025