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arXiv:2607.13422

Suppressing Detuning-Induced Bias in Ramsey Magnetometry with Composite Pulses

Shingo Kukita, Kento Nawata, Yuichiro Matsuzaki

quant-phSubmitted Jul 15, 2026• Announced Jul 16, 2026• 0 citations
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Abstract

Quantum sensing estimates a physical parameter encoded in the state of a probe; with independent spin probes the precision follows the standard quantum limit. Studies of sensing precision often assume that the parameters entering the model, such as the noise, are known. In practice these parameters are not always known, and a mismatch between the assumed and actual values induces a systematic error. Here we study single-qubit Ramsey magnetometry of a DC magnetic field under an unknown detuning between the actual and nominal spin frequencies: A first pulse puts the qubit into a superposition of its two states, the field to be sensed then adds a relative phase during an exposure stage, and a second pulse enables the readout. In our setting, the field acts only during the exposure stage, whereas the detuning acts throughout the whole protocol. We analyze how the detuning biases the estimate, preventing the total estimation error from following the standard quantum limit. We then construct a composite-pulse preparation and readout that exploits the difference in the intervals over which the field and the detuning act to cancel the detuning to first order. We evaluate the performance of this composite-pulse protocol and show that it suppresses the detuning-induced bias.

Comments
9 pages, 3 figures

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Quantum sensing estimates a physical parameter encoded in the state of a probe; with independent spin probes the precision follows the standard quantum limit. Studies of sensing precision often assume that the parameters entering the model, such as the noise, are known. In practice these parameters are not always known, and a mismatch between the assumed and actual values induces a systematic error. Here we study single-qubit Ramsey magnetometry of a DC magnetic field under an unknown detuning between the actual and nominal spin frequencies: A first pulse puts the qubit into a superposition of its two states, the field to be sensed then adds a relative phase during an exposure stage, and a second pulse enables the readout. In our setting, the field acts only during the exposure stage, whereas the detuning acts throughout the whole protocol. We analyze how the detuning biases the estimate, preventing the total estimation error from following the standard quantum limit. We then construct a composite-pulse preparation and readout that exploits the difference in the intervals over which the field and the detuning act to cancel the detuning to first order. We evaluate the performance of this composite-pulse protocol and show that it suppresses the detuning-induced bias.
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Spin systems in solid state materials are promising qubit candidates for quantum information or quantum sensing. A major prerequisite here is the coherence of spin phase oscillations. In this work, we show a control sequence which, by applying RF pulses of variable detuning, allows to increase the spin phase oscillation visibility and to perform DC magnetometry as well. We experimentally demonstrate the scheme on single NV centers in diamond and analytically describe how the NV electron spin phase oscillations behave in the presence of classical noise models. We hereby introduce detuning as the enabling factor that modulates the filter function of the sequence, in order to achieve a visibility of the Ramsey fringes comparable to or longer than the Hahn-echo T2T_2T2​ time and an improved sensitivity to DC magnetic fields in various experimental settings.
The performance of superconducting-qubit magnetometers depends not only on magnetic-field encoding during Ramsey interrogation, but also on how efficiently the encoded information is recovered during readout. Squeezed microwaves provide a promising route to improve information extraction by suppressing readout noise, yet how such readout enhancement translates into accessible information for magnetic-field estimation remains unclear. Here we develop an effective detected-mode framework linking projected quadrature noise, state-assignment error, and the classical Fisher information accessible from binary readout outcomes. A finite mismatch between the squeezed quadrature and the discrimination axis produces an optimal squeezing strength through the competition between squeezed and anti-squeezed fluctuations. We further show that squeezed readout improves the readout-limited magnetic-field sensitivity by recovering information otherwise lost during state assignment, with the enhancement remaining robust against quadrature mismatch, transmission loss, and added noise. These results establish a quantitative connection between squeezed-microwave readout and measurement-stage information recovery in superconducting quantum sensing.
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Ramsey spectroscopy serves as a key tool for frequency measurement. Although entanglement can enhance the measurement precision, the atom-atom interaction required for entanglement generation may lead to a frequency shift. In addition, the spectra also suffer from light shift caused by the interaction between light and atoms. Thus, it is difficult to achieve high precision without inducing additional systematic errors. Here, we propose to realize high-precision entanglement-enhanced Ramsey spectroscopy with composite pulses. First, we utilize spin-squeezed states generated by one-axis twisting (OAT) dynamics to enhance the measurement precision. We find that by applying a suitable pulse after OAT, the resonant frequency can be inferred and the light shift can be reduced by using composite pulses. To increase the signal slope, we use anti-OAT dynamics to perform interaction-based readout after interrogation. By designing suitable composite pulses, it can significantly increase the signal response and further improve the measurement precision. Although both schemes can mitigate the light shift, it cannot be entirely eliminated. Thus, we develop the autobalanced entanglement-enhanced Ramsey spectroscopy. By using combination of different sequences with short and long interrogation times and feedback control, the light shift of both our protocols can be completely suppressed, which increases the measurement accuracy. Besides, we also investigate the effects of background atom-atom interaction and find that it only reduces the measurement precision without introducing additional frequency shift. Our study offers an alternative method for achieving precise frequency measurement, which has the potential to be of significant application in quantum sensors such as atomic clocks.