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arXiv:2603.05650

Ramsey correlation spectroscopy with phase cycling using a single quantum sensor

Inbar Zohar, Santiago Oviedo-Casado, Andrej Denisenko, Rainer Stöhr, Amit Finkler

quant-phcond-mat.mes-hallphysics.chem-phSubmitted Mar 5, 2026• Announced Mar 9, 2026• 0 citations
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Abstract

Magnetic spectroscopy at the nanoscale provides unique insights into material properties and dynamics, with quantum sensors like nitrogen-vacancy (NV) centers being ideally suited for these scales. However, detecting low-frequency signals remains a challenge due to finite coherence times ($T_2^*$), as signals oscillating slower than $1/T_2^*$ decay before sufficient phase accumulation occurs. We present RESOLUTE (Ramsey corrElation SpectroscOpy puLse seqUence wiTh phasE cycling), a protocol that overcomes these limitations by combining Ramsey measurements with correlation spectroscopy. By storing accumulated phase as a population imbalance during a correlation period ($T_\mathrm{corr} < T_1$) between two sensing periods, RESOLUTE generates an effective coherence time $T_2^p > T_2^*$. This shifts the frequency-matching condition to the correlation time, enabling detection in the previously inaccessible spectral region between $1/T_1$ and $1/T_2^p$. We experimentally demonstrate an extension of the effective coherence time from $T_2^* = 0.38\,μs$ to $T_2^p = 5.1\,μs$, surpassing Hahn Echo measurements. The technique successfully detects $^{13}$C nuclear spin Larmor precession at fields as low as 49$\,$G ($\sim$50$\,$kHz). We further provide theoretical insight using Fisher information to characterize RESOLUTE's frequency estimation capabilities compared to existing protocols. Finally, by integrating adiabatic pulses and phase cycling, we demonstrate robust spin control and effective DC signal extraction. These advancements provide enhanced sensitivity to weak dipolar interactions, essential for single-molecule imaging and quantum sensing applications.

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arXiv:2209.10466•Journal of Magnetic Resonance•May 7, 2024•4 citations
Magnetic spectroscopy at the nanoscale provides unique insights into material properties and dynamics, with quantum sensors like nitrogen-vacancy (NV) centers being ideally suited for these scales. However, detecting low-frequency signals remains a challenge due to finite coherence times (T2∗T_2^*T2∗​), as signals oscillating slower than 1/T2∗1/T_2^*1/T2∗​ decay before sufficient phase accumulation occurs. We present RESOLUTE (Ramsey corrElation SpectroscOpy puLse seqUence wiTh phasE cycling), a protocol that overcomes these limitations by combining Ramsey measurements with correlation spectroscopy. By storing accumulated phase as a population imbalance during a correlation period (Tcorr<T1T_\mathrm{corr} < T_1Tcorr​<T1​) between two sensing periods, RESOLUTE generates an effective coherence time T2p>T2∗T_2^p > T_2^*T2p​>T2∗​. This shifts the frequency-matching condition to the correlation time, enabling detection in the previously inaccessible spectral region between 1/T11/T_11/T1​ and 1/T2p1/T_2^p1/T2p​. We experimentally demonstrate an extension of the effective coherence time from T2∗=0.38 μsT_2^* = 0.38\,μsT2∗​=0.38μs to T2p=5.1 μsT_2^p = 5.1\,μsT2p​=5.1μs, surpassing Hahn Echo measurements. The technique successfully detects 13^{13}13C nuclear spin Larmor precession at fields as low as 49 \,G (∼\sim∼50 \,kHz). We further provide theoretical insight using Fisher information to characterize RESOLUTE's frequency estimation capabilities compared to existing protocols. Finally, by integrating adiabatic pulses and phase cycling, we demonstrate robust spin control and effective DC signal extraction. These advancements provide enhanced sensitivity to weak dipolar interactions, essential for single-molecule imaging and quantum sensing applications.
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.
Nitrogen vacancy (NV) centers in diamond are widely deployed as local magnetic sensors, using coherent, single qubit control to measure both time-averaged fields and noise with nanoscale spatial resolution. Moving beyond single qubits to multi-qubit control enables new sensing modalities such as measuring nonlocal spatiotemporal correlators, or using entangled states to improve measurement sensitivity. Here, we describe protocols to use optically unresolved NV center pairs and nuclear spins as multi-qubit sensors for measuring correlated noise, enabling covariance magnetometry at nanometer length scales. For NV centers that are optically unresolved but have spectrally resolved spin transitions, we implement a phase-cycling protocol that disambiguates magnetic correlations from variance fluctuations by alternating the relative spin orientations of the two NV centers. For NV centers that are both optically and spectrally unresolved, we leverage the presence of a third qubit, a 13C nucleus that is strongly coupled to one of the NV centers, to effect coherent single-NV spin flips and enable a similar phase-cycling protocol. For length scales around 10 nm, we create maximally entangled Bell states through dipole-dipole coupling between two NV centers, and use these entangled states to directly read out the magnetic field correlation, rather than reconstructing it from independent measurements of unentangled NV centers. Importantly, this changes the scaling of sensitivity with readout noise from quadratic to linear. For conventional off-resonant readout of the NV center spin state (for which the readout noise is roughly 30 times the quantum projection limit), this results in a dramatic sensitivity improvement. Finally, we demonstrate methods for the detection of high spatial- and temporal-resolution correlators with pairs of strongly interacting NV centers.
Spin systems in solid state materials are promising qubit candidates for quantum information in particular as quantum memories or for 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 visibility of spin phase oscillations. 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 T2 time and an improved sensitivity to DC magnetic fields in various experimental settings.
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).
Magnetic sensors are typically much more sensitive to oscillating (AC) magnetic fields than static (DC) fields, due to the presence of more noise at lower frequency, typically scaling with a 1/f1/f1/f dependence. For quantum magnetometers, this characteristic noise is reflected in the ensemble dephasing time T2∗T_2^*T2∗​, the relevant sensing time for a DC field, being much lower than the spin coherence time T2T_2T2​, which determines the sensitivity to AC fields. Here, we demonstrate measurement of DC magnetic fields using a physically rotating ensemble of nitrogen-vacancy centres at a precision limited by the electron spin coherence time, T2T_2T2​. We rotate the host diamond with a period comparable to T2T_2T2​, such that the angle between the NV axis and the magnetic field to be detected changes as a function of time, upconverting the static magnetic field to an oscillating field in the physically rotating frame. Using spin-echo interferometry, we observe an order of magnitude improvement in DC magnetometer response compared to a conventional Ramsey experiments. Enhancements to our scheme could realise DC sensitivities equivalent to demonstrated AC magnetic field sensitivities with NV centres.
The low frequency region of the spectrum is a challenging regime for quantum probes. We support the idea that, in this regime, performing Ramsey measurements carefully controlling the time at which each measurement is initiated is an excellent signal detection strategy. We use the Fisher information to demonstrate a high quality performance in the low frequency regime, compared to more elaborated measurement sequences, and to optimize the correlated Ramsey sequence according to any given experimental parameters, showing that correlated Ramsey rivals with state-of-the-art protocols, and can even outperform commonly employed sequences such as dynamical decoupling in the detection of low frequency signals. Contrary to typical quantum detection protocols for oscillating signals, which require adjusting the time separation between pulses to match the half period of the target signal, and consequently see their scope limited to signals whose period is shorter than the characteristic decoherence time of the probe, or to those protocols whose target is primarily static signals, the time-tagged correlated Ramsey sequence simultaneously tracks the amplitude and the phase information of the target signal, regardless of its frequency, which crucially permits correlating measurements in post-processing, leading to efficient spectral reconstruction.