The interaction between a quantum system and its environments leads to decoherence in the system. Understanding decoherence is crucial for improving our understanding of nature and development of quantum technologies. One such example is telegraph noise where a quantum system decoheres due to interaction with fluctuators which are also a quantum system interacting with its own environment. The reduced dynamics of the quantum system after tracing over the fluctuators and environment in case of strong coupling to the environment is studied as classical telegraph noise [1]. Such dynamics possess a singularity in parametric space due to degeneracy of eigenvalues and eigenvectors [2] (an exceptional point). These exceptional point singularities are candidates for quantum sensing. When the fluctuators are weakly coupled to their environment [1], reduced dynamics can provide a completely different eigenvalue spectrum [3]. We will study the feasibility of observing singularity in parametric space, i.e., exceptional points, for a single qubit evolving under telegraph noise with quantum fluctuator. The work will be mostly analytical supplemented by numerical analysis, if relevant.
[1] H. J. Wold, H. Brox, Y. M. Galperin, and J. Bergli, "Decoherence of a qubit due to either a quantum fluctuator, or classical telegraph noise," Physical Review B 86, 205404 (2012). Based on Master’s thesis 2011. Available at: http://urn.nb.no/URN:NBN:no-28902
[2] V. H. Bakkestuen, "Non-Hermitian Quantum Mechanics: On the role of PT-Symmetry and Exceptional Points." Master's thesis, 2023. Available at: https://www.duo.uio.no/handle/10852/103693
[3] J. D. Lin, P. C. Kuo, N. Lambert, A. Miranowicz, F. Nori, and Y. N. Chen, “Non-Markovian quantum exceptional points”. Nature Communications 16, 1289 (2025).