Quantum Coherence of Critical Unstable Two-Level Systems

TL;DR

This paper explores the unique coherence behaviors of critical unstable two-level quantum systems, revealing phenomena like coherence-decoherence oscillations and area sweeping in the Bloch sphere, with implications for quantum information and particle physics.

Contribution

It introduces a novel class of critical unstable qubit systems with orthogonal energy and decay vectors, uncovering atypical coherence phenomena beyond standard oscillations.

Findings

Critical systems show coherence-decoherence oscillations.

Pure critical qubits sweep unequal areas in the Bloch sphere.

Features persist in quasi-critical scenarios.

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, ${\bf E}$ and ${\bf\Gamma}$, are orthogonal to one another, and the parameter $r = |{\bf \Gamma}|/(2|{\bf E}|)$ 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 ${\bf b}$ describing a pure critical qubit will sweep out unequal areas during equal intervals of time, while rotating about the vector ${\bf E}$. 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 ${\bf E}$ and ${\bf\Gamma}$ are not perfectly orthogonal to each other. Applications of our results to quantum information and to unstable meson--antimeson and other systems are discussed.