Critical Unstable Qubits: an Application to $B^0\bar{B}^0$-Meson System

TL;DR

This paper introduces Critical Unstable Qubits (CUQs), a new class of unstable qubits with unique coherence-decoherence oscillations and anharmonic behavior, applied to the $B^0ar{B}^0$-meson system to establish upper limits on their properties.

Contribution

The paper extends the concept of unstable qubits by defining CUQs with orthogonal energy and decay vectors, revealing novel anharmonic oscillations and applying this to meson systems.

Findings

CUQs exhibit coherence-decoherence oscillations.

CUQs' Bloch vector sweeps out unequal areas.

Upper limits on anharmonicity observables in meson systems.

Abstract

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, ${\bf E}$ and ${\bf \Gamma}$, are orthogonal to one another, and the key parameter $r = |{\bf \Gamma}|/|2{\bf E}|$ is less than 1. Most remarkably, CUQs exhibit two atypical behaviours: (i) they display coherence-decoherence oscillations in a co-decaying frame of the system described by a unit Bloch vector ${\bf b}$, and (ii) the unit Bloch vector ${\bf b}$ describing a pure CUQ sweeps out unequal areas during equal intervals of time, while rotating about the vector ${\bf E}$. The latter anharmonic 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 non-sinusoidal oscillation of a CUQ. We apply the results of our formalism to the $B^0\bar{B}^0$-meson system and derive, for the first time, generic upper limits on these new observables.