Two microwave tones sharpen a quantum sensor in boron nitride

How much can a quantum sensor improve without changing its material? A study by Shihao Ru and colleagues explores that question using negatively charged boron vacancies in hexagonal boron nitride, or hBN. Their answer is a different microwave-control scheme that delivers approximately 2.6 times better signal-to-noise in a laboratory magnetic-field measurement.

The work is available as a preprint on arXiv, submitted on November 10, 2026. Its listing reports acceptance in Physical Review Applied. The experiments establish a control and sensing technique, rather than a finished sensor with a fully characterized detection limit.

Using all three spin states

A boron vacancy is a missing boron atom in the crystal. In its negatively charged form, the defect has three ground-state spin levels, labelled 0, +1 and −1. Spin is a quantum property that allows the defect to respond to magnetic fields.

Conventional single-quantum sensing uses the 0 state together with either +1 or −1. Here, the researchers simultaneously applied two resonant microwave tones, addressing both transitions from 0. This enabled double-quantum control involving the +1 and −1 states, whose spin labels differ by two.

The distinction matters because a magnetic field makes the relative quantum phase between these outer states accumulate twice as quickly as in a single-quantum coherence. Disturbances that shift both outer states together can instead cancel from that comparison. This is selective rejection of some disturbances, not immunity to every source of noise.

The room-temperature experiments used an ensemble of defects in an hBN flake several micrometres thick, mounted on a gold microwave structure. Although hBN is a layered material associated with two-dimensional devices, this sample was not a single atomic layer. A green laser initialized the spins, microwave pulses manipulated them, and spin-dependent fluorescence provided the readout. The control instruments shared a common clock to maintain timing and phase relationships.

A clearer magnetic signal

The double-quantum protocol produced approximately twice the optical readout contrast of the single-quantum approach in this ensemble. Contrast describes how clearly the fluorescence distinguishes the manipulated spin populations.

The team then used spin-echo sequences, which reverse phase errors from slowly varying disturbances while retaining sensitivity to suitably timed oscillating fields. Correlation measurements detected an externally applied field at 20 megahertz. A separate feature near 46.3 megahertz appeared even without an external radio-frequency field; the researchers attributed it to coupling between the defects’ electronic spins and neighbouring nuclear spins.

For the principal signal-to-noise comparison, the researchers used quantum heterodyne detection, or Qdyne. Instead of sweeping a delay to reconstruct a spectrum, this method repeatedly samples the signal relative to a stable classical clock.

Under identical experimental conditions, the reported signal-to-noise ratio was 257 for double-quantum sensing and 100 for single-quantum sensing: a factor of 2.57. Another demonstration resolved two applied frequency components separated by 0.8 megahertz.

These results support a comparative improvement for the tested protocol. They do not establish an absolute magnetic-field sensitivity: the comparison did not require absolute calibration of the radio-frequency coil. Clock stability and sampling-related frequency ambiguities also remain relevant to interpreting heterodyne measurements. Longer acquisition can improve spectral resolution, but does not remove those constraints.

Probing what disturbs the spins

The researchers also measured relaxation: how spin populations redistribute after preparation. Comparing single- and double-quantum relaxation provides different sensitivity to environmental disturbances. In the model used here, the double-quantum channel probes transverse electric-field and strain fluctuations, rather than the magnetic fluctuations that drive the single-quantum channels to first order.

Its relaxation rate decreased modestly as the magnetic-field-induced level splitting increased, approaching a largely field-independent background. The team compared models in which disturbances arose throughout the flake or at its surfaces.

Both volume-distributed fluctuations and spatially correlated surface fluctuations could reproduce the observations with moderate model parameters. Short-range, uncorrelated surface models required extremely large local noise scales, making them less plausible within the analysis—not mathematically excluded.

That conclusion is conditional. The depth distribution of defects was not measured, and the numerical comparison assumed a uniform distribution. Only one proton-irradiated sample at one irradiation fluence was studied. The dominant, approximately field-independent background was not microscopically identified either.

Measurements across controlled thicknesses, defect densities, temperatures and surface treatments are therefore needed to locate the disturbances and separate their causes. For now, the strongest result is practical and specific: coordinated control of two transitions improves magnetic-signal readout in this hBN ensemble, while providing an additional way to investigate what limits it.