We investigate the validity of exponential models in the analysis of Ramsey coherence measurements and show that finite environmental memory is consistent with a systematic bias in the extracted decoherence rate. Starting from a system–bath Hamiltonian, we derive a finite-memory decoherence function using a second-order cumulant expansion under the assumption of Gaussian noise with finite correlation time. The resulting dynamics exhibit a time-dependent effective decay rate, reducing to exponential behavior only in the long-time limit. We derive an explicit closed-form expression for the decoherence rate extracted by least-squares exponential fitting over a finite time window 0, T, as an explicit function of both T and the environmental correlation time τc. We show that the extracted rate γfit (T) strictly underestimates the intrinsic decoherence rate γ for all finite T > 0, with the deficit decaying as T⁻¹ in the long-window limit, while in the short-window limit the fitted rate scales linearly with T, a regime not directly accessible experimentally due to limited signal contrast at early times. The central implication is that decoherence rates extracted from exponential fits are not intrinsic observables in non-Markovian environments: they encode a protocol-dependent effective average that depends systematically on the chosen fitting window. The conventionally reported coherence time T₂* = 1/γfit is therefore protocol-dependent in non-Markovian environments. Finally, we connect this behavior to experimentally observed non-exponential decay profiles and noise spectra, providing a unified framework for interpreting deviations from exponential coherence decay. These results identify a structural limitation in standard Ramsey analysis and motivate the use of physically grounded models in extracting decoherence parameters.
Mazen Zaino (Sun,) studied this question.