Telegraph flux noise induced beating Ramsey fringe in transmon qubits

Ramsey oscillations typically exhibit an exponential decay envelope due to environmental noise. However, recent experiments have observed nonmonotonic Ramsey fringes characterized by beating patterns, which deviate from the standard behavior. These beating patterns have primarily been attributed to charge-noise fluctuations. In this paper, we have experimentally observed Ramsey fringe with beating pattern for transmon qubits, and traced the origin is from electric instruments induced flux noise. We develop a random telegraph noise (RTN) model to simulate the impact of telegraph-like flux-noise sources on Ramsey oscillations. Our simulations demonstrate that strong flux-RTN sources can induce beating patterns in the Ramsey fringes, showing excellent agreement with experimental observations in transmon qubits influenced by electronic environment-induced fluxnoise. Our findings provide valuable insights into the role of flux-noise in qubit decoherence and underscore the importance of considering flux-noise RTN when analyzing nonmonotonic Ramsey fringes.