Suppressing Detuning-Induced Bias in Ramsey Magnetometry with Composite Pulses

In quantum sensing, the precision of estimating a physical parameter—such as a magnetic field—is often limited by systematic errors. A common source of error is detuning, where the actual spin frequency of the probe qubit deviates from the nominal frequency used to calibrate control pulses. This study investigates how this detuning biases Ramsey magnetometry and proposes a robust control sequence to suppress this bias.

The authors analyze the dynamics of a single-qubit Ramsey protocol, identifying that while the target magnetic field acts only during the exposure stage, the detuning acts throughout the entire sequence (including preparation and readout pulses). By modeling the system in a rotating frame, they derive the first-order bias introduced by detuning. To mitigate this, they construct a composite-pulse sequence—a series of three pulses with specific durations and phases—designed to cancel the detuning-induced phase accumulation to first order. They then compare the performance of this composite-pulse protocol against a standard single-pulse protocol under depolarizing noise.

The study demonstrates that the single-pulse protocol suffers from a systematic error floor that does not vanish as the number of measurements increases, effectively capping the achievable precision. The proposed composite-pulse protocol successfully removes this first-order bias, resulting in an estimation error that remains flat even as detuning increases. While the composite sequence is more robust against detuning, it also increases the total duration of each experimental trial, which amplifies the effect of depolarizing noise. Consequently, the composite-pulse protocol outperforms the standard approach only when the detuning exceeds a specific threshold, which the authors define analytically.