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arXiv:2610.05907

Robust Diamond Quantum Sensing in Double-Quantum 4-Ramsey Interferometry by Dual-Feedback Scheme

Yuta Araki, Takeharu Sekiguchi, Yuji Hatano, Naota Sekiguchi, Zehan Li, Chikara Shinei, Masashi Miyakawa, Takashi Taniguchi, Tokuyuki Teraji, Hiroshi Abe, Shinobu Onoda, Takeshi Ohshima, Mutsuko Hatano, Takayuki Iwasaki

quant-phSubmitted Oct 5, 2026• Announced Oct 6, 2026• 0 citations
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Abstract

We developed a highly sensitive and long-term stable diamond quantum magnetometer by integrating a dual-feedback system that compensates for common- and differential-mode frequency shifts in double-quantum (DQ) 4-Ramsey interferometry. Detecting extremely weak magnetic-field signals requires extensive signal accumulation to enhance the signal-to-noise ratio. However, deviations from the optimal operating frequencies caused by thermal drift or environmental magnetic noise severely hinder the long-term stability of such a sensing system. To overcome the limitation, we first derived analytical solutions for the signal response to common- and differential-mode detunings based on a detuning-inclusive Hamiltonian to theoretically clarify the robustness limit in DQ 4-Ramsey sensing. Guided by this theoretical model, we introduced synchronized frequency modulation and a dual-feedback scheme to independently track and compensate for these frequency shifts while maintaining an optimal magnetic-field response. The proposed method enabled stable continuous operation against temperature variations of 2.8 K. By maintaining a magnetic field sensitivity of 7.0 pT/Hz^1/2 in the frequency range of 5-100 Hz for a prolonged duration of 4 hours, we achieved an extremely low noise floor of 64 fT/Hz^1/2. During prolonged continuous sensing, the system exhibited the expected 1/T^1/2 scaling with integration time T, and prevented both the underestimation of amplitude and waveform distortion. These results establish a robust approach for long-term DQ 4-Ramsey diamond magnetometry and demonstrate its potential for detecting weak biomagnetic signals.

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We introduce a double quantum (DQ) 4-Ramsey measurement protocol that enables wide-field magnetic imaging using nitrogen-vacancy ($\mathrm{N}$-$V$) centers in diamond, with enhanced homogeneity of the magnetic sensitivity relative to conventional single quantum (SQ) techniques. The DQ 4-Ramsey protocol employs microwave-phase alternation across four consecutive Ramsey (4-Ramsey) measurements to isolate the desired DQ magnetic signal from any residual SQ signal induced by microwave pulse errors. In a demonstration experiment employing a 1-$\ensuremath{\mu}\mathrm{m}$-thick $\mathrm{N}$-$V$ layer in a macroscopic diamond chip, the DQ 4-Ramsey protocol provides a volume-normalized dc magnetic sensitivity of ${\ensuremath{\eta}}^{V}=34\phantom{\rule{0.2em}{0ex}}\mathrm{nT}\phantom{\rule{0.1em}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}\phantom{\rule{0.1em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{3/2}$ across a $125\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}\ifmmode\times\else\texttimes\fi{}125\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}$ field of view, with about $5\ifmmode\times\else\texttimes\fi{}$ less spatial variation in sensitivity across the field of view compared to a SQ measurement. The improved robustness and magnetic sensitivity homogeneity of the DQ 4-Ramsey protocol enables imaging of dynamic broadband magnetic sources such as integrated circuits and electrically active cells.

arXiv:2009.02371•Physical Review Applied•Apr 12, 2021•59 citations
We developed a highly sensitive and long-term stable diamond quantum magnetometer by integrating a dual-feedback system that compensates for common- and differential-mode frequency shifts in double-quantum (DQ) 4-Ramsey interferometry. Detecting extremely weak magnetic-field signals requires extensive signal accumulation to enhance the signal-to-noise ratio. However, deviations from the optimal operating frequencies caused by thermal drift or environmental magnetic noise severely hinder the long-term stability of such a sensing system. To overcome the limitation, we first derived analytical solutions for the signal response to common- and differential-mode detunings based on a detuning-inclusive Hamiltonian to theoretically clarify the robustness limit in DQ 4-Ramsey sensing. Guided by this theoretical model, we introduced synchronized frequency modulation and a dual-feedback scheme to independently track and compensate for these frequency shifts while maintaining an optimal magnetic-field response. The proposed method enabled stable continuous operation against temperature variations of 2.8 K. By maintaining a magnetic field sensitivity of 7.0 pT/Hz^1/2 in the frequency range of 5-100 Hz for a prolonged duration of 4 hours, we achieved an extremely low noise floor of 64 fT/Hz^1/2. During prolonged continuous sensing, the system exhibited the expected 1/T^1/2 scaling with integration time T, and prevented both the underestimation of amplitude and waveform distortion. These results establish a robust approach for long-term DQ 4-Ramsey diamond magnetometry and demonstrate its potential for detecting weak biomagnetic signals.
In this study, we developed a diamond quantum magnetometer based on Ramsey interferometry with a short sensor-to-sample distance. Conventional biomagnetic sensors with ensemble nitrogen-vacancy centers using continuous-wave optically detected magnetic resonance and Ramsey methods typically rely on watt-level lasers to achieve high sensitivity, resulting in thermal issues. In contrast, by employing the light-trapping diamond waveguide technique in a high-pressure and high-temperature diamond sample treated with electron beam irradiation, we obtained a high photon conversion efficiency of 9.5%, enabling us to simultaneously achieve a high sensitivity of 2.93(7) pT/Hz^1/2 in the 100-400 Hz frequency range and a minimal temperature increase of only approximately 13 K at a low laser power of 210 mW. Using a dry phantom designed to mimic magnetoencephalography signals, we measured a weak magnetic field of 77.7(2) pT without signal averaging at a sensor-to-sample distance of 2.5 mm. This short-distance measurement prevents severe spatial signal attenuation, yielding a high signal-to-noise ratio. The development here is crucial for practical biomagnetic applications based on Ramsey interferometry.
Nitrogen-vacancy (NV) centers in diamond offer a promising solid-state platform for rotation sensing, operating across diverse environmental conditions. Our previous work demonstrated a rotation sensor utilizing 14N nuclear spins, detecting rotation via precession rate shifts [1]. This sensor employs direct optical polarization/readout and radio-frequency double-quantum Ramsey interferometry, eliminating microwave pulses. However, magnetic field, temperature, and RF pulse variations limit long-term stability. To enhance robustness, we developed two generalized Ramsey schemes: one utilizing stimulated Raman adiabatic passage (STIRAP) for pulse-area resilience [2], and a dynamical elimination protocol using modulated zero-pulse-area fields to control two-photon transitions and suppress single-photon excitations [3]. Experimental results demonstrate enhanced robustness against pulse parameter variations, yielding improved quantum state generation fidelities and robust Ramsey fringes insensitive to single-photon detuning. Our results pave the way for enhanced long-term stability in diamond-based sensors (clocks, gyroscopes, magnetometers), advancing quantum metrology and spectroscopy. Furthermore, we anticipate that the developed two-photon spectroscopy techniques will find widespread application in atomic, molecular, and spin systems, enabling robust control methods for quantum technology, including high-fidelity quantum gates, Ramsey spectroscopy, atom interferometry, and quantum sensing. [1] A. Jarmola, S. Lourette, V. M. Acosta, A. G. Birdwell, P. Blümler, D. Budker, T. Ivanov, V. S. Malinovsky, Sci. Adv. 7, eabl3840 (2021). [2] S. Lourette, A. Jarmola, J. Chathanathil, S. C. Carrasco, D. Budker, S. A. Malinovskaya, A. G. Birdwell, T. G. Ivanov, and V. S. Malinovsky, arXiv:2407.16057 (2024). [3] S. C. Carrasco, S. Lourette, I. Sola, V. S. Malinovsky, arXiv:2411.05670 (2024).
Diamond quantum sensors utilizing nitrogen-vacancy (NV) centers in diamond can measure a tiny magnetic-field variation at room temperature with a high linearity and high spatial resolution. Because of these advantages, they have been actively studied for application to measure a biomagnetic field. In biomagnetic sensing applications, it is effective to measure at multiple points simultaneously with high sensitivity. In this study, we developed a highly sensitive diamond quantum sensor that can simultaneously measure the magnetic field at two points at the millimeter interval. We used two diamonds that were split from one HPHT-grown diamond and placed them at the 3-mm interval. A laser-induced fluorescence from the two diamonds were detected by a single photodiode. We applied different bias magnetic fields to each diamond, and thus the magnetic resonances at these diamonds had different resonance frequencies. By applying microwave fields whose frequencies were modulated at different modulation frequencies, the magnetic fields at the two diamonds can be obtained independently after demodulation. The noise spectral densities in the magnetic field measurement at the two diamonds’ locations. Since the measurement was performed outside a magnetic shield, a severe low-frequency environmental noise from railways and power line (50 Hz) noise peaks were observed. We evaluated the field sensitivities at the two diamonds to be 22 pT/√Hz in 25-300 Hz range with neglecting the power-line noise peaks and the environment noise peaks. The capability of simultaneously measuring a magnetic field at two points with the such high sensitivities will facilitate the biomagnetic sensing applications.
High-sensitivity magnetometry is of critical importance to the fields of biomagnetism and geomagnetism. However, magnetometry for dc and low-frequency signal detection faces the challenge of sensitivity improvement, resulting from the low-frequency noise induced by multiple types of noise sources. In particular, for the solid-state spin dc quantum magnetometry, the sensitivity has been limited by short dephasing time. Here, we realized the conversion of the magnetic signal from dc to ac by utilizing a flux concentration and modulation (FCM) technique so that the dynamical decoupling method can be applied to prolong the dephasing time. Hence, we have successfully demonstrated a dc magnetometer with a sensitivity of 32 pT/Hz1/2^{{1}/{2}}1/2, which is about two orders of magnitude over that of the Ramsey-type dc magnetometer. Further enhancement of the sensitivity is systematically analyzed, although is challenging but plenty of room is achievable. Our results shed light on the realization of room temperature dc quantum magnetometry with femtotesla-sensitivity in the future.
High-fidelity quantum operation of qubits plays an important role in magnetometry based on nitrogen-vacancy (NV) centers in diamonds. However, the nontrivial spin-spin coupling of the NV center decreases signal contrast and sensitivity. Here, we overcome this limitation by exploiting the amplitude modulation of microwaves, which allows us to perfectly detect magnetic signals at low fields. Compared with the traditional double-quantum sensing protocol, the full contrast of the detection signal was recovered, and the sensitivity was enhanced three times in the experiment. Our method is applicable to a wide range of sensing tasks, such as temperature, strain, and electric field.
We introduce a double quantum (DQ) 4-Ramsey measurement protocol that enables wide-field magnetic imaging using nitrogen-vacancy (N\mathrm{N}N-VVV) centers in diamond, with enhanced homogeneity of the magnetic sensitivity relative to conventional single quantum (SQ) techniques. The DQ 4-Ramsey protocol employs microwave-phase alternation across four consecutive Ramsey (4-Ramsey) measurements to isolate the desired DQ magnetic signal from any residual SQ signal induced by microwave pulse errors. In a demonstration experiment employing a 1-$\ensuremath{\mu}\mathrm{m}$-thick N\mathrm{N}N-VVV layer in a macroscopic diamond chip, the DQ 4-Ramsey protocol provides a volume-normalized dc magnetic sensitivity of ${\ensuremath{\eta}}^{V}=34\phantom{\rule{0.2em}{0ex}}\mathrm{nT}\phantom{\rule{0.1em}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}\phantom{\rule{0.1em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{3/2}$ across a $125\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}\ifmmode\times\else\texttimes\fi{}125\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}$ field of view, with about $5\ifmmode\times\else\texttimes\fi{}$ less spatial variation in sensitivity across the field of view compared to a SQ measurement. The improved robustness and magnetic sensitivity homogeneity of the DQ 4-Ramsey protocol enables imaging of dynamic broadband magnetic sources such as integrated circuits and electrically active cells.