Micron-sized fiber diamond probe for quantum precision measurement of microwave magnetic field

The precision measurement and metrology of electromagnetic fields (EMF) is crucial for the design of communication systems, development of electronic devices, and understanding of physical phenomena. In order to achieve more accurate measurements and higher resolution, there has been an increasing requirement for probes. Traditional methods use small loop antennas^[1] or PCB-based multi-layer microstrip lines to calculate the magnetic field intensity according to electromagnetic induction, so as to characterize the surface current and EMF of RF devices.^[2] However, the spatial resolution of this method cannot be further optimized due to the size limitation of the probe itself.

Quantum precision measurement is gaining attention for its ability to break the standard quantum limit (SQL) of traditional methods and approach Heisenberg limit. Adaptation to extreme environments further enhances its utility and broadens its application. There are two commonly used quantum precision measurement methods of EMF: Rydberg atoms^[3–5] and alkali atom vapor-cells. Rydberg atoms can measure AC electric fields based on the Autler–Townes (AT) effect, while alkali atom vapor-cells use Rabi oscillation to measure AC magnetic field. However, both methods have drawbacks that cannot be ignored. Rydberg atoms struggle to infer magnetic fields from single electric field data, while the disturbance to EMF by alkali atom vapor-cells cannot be ignored.^[6]

In the measurement of microwave (MW) magnetic fields, an alternative is nitrogen-vacancy (NV) center, which can be excited and read out all-optically, using common equipment like confocal microscopes,^[7] atomic force microscopes,^[8] and CCDs.^[9] Diamond’s non-magnetic nature minimizes MW magnetic field disturbance, enhancing measurement accuracy. Advancements in quantum state control,^[10–12] high-resolution imaging,^[13,14] communication,^[15] and optimization of pulse trains^[16] and magnetic field phases^[17] mark a steady evolution in NV center technology.

In this context, we propose a microwave magnetic field measurement method based on diamond NV center, and prove its disturbance to RF devices and electromagnetic fields. Our methodology unfolds in two key steps:

(i) Use a tapered fiber diamond probe to characterize the microwave magnetic field above the surface of a coplanar waveguide with micron-sized spatial resolution and high accuracy.

(ii) Compare the disturbance of two commonly used diamond structures: fiber diamond probe and bulk diamond on RF devices from two aspects of electromagnetic field and transmission characteristics through simulation.

Through experiments and simulations, our work demonstrates the feasibility and superiority of quantum precision measurement using NV center with fiber diamond probes.

Similar to alkali atom vapor-cells, the NV center measurement of MW magnetic field is also based on Rabi oscillation. In the absence of DC magnetic field, there is a zero-field split D = 2.87 GHz between m_s = 0 and m_s = ±1. When a DC magnetic field is applied, MW magnetic field drives Rabi oscillations between the m_s = 0 and m_s = ±1 states at resonance. The transitions between m_s = 0 and m_s = ±1 are driven by the left and right circular polarization σ_± respectively,^[17] as depicted in Fig. 1(a). The oscillation frequency is linearly proportional to the amplitude of MW magnetic field, as given by the following formula:

where α_NV = 2.802495 MHz/Gs (1 Gs = 10⁻⁴ T) is the gyromagnetic ratio of the electron spin, B_MW denotes the circular polarization component of MW magnetic field projected in the plane perpendicular to the NV axis. On the surface of RF devices, electromagnetic waves usually exist in the form of linear polarization, which can be decomposed into two circularly polarized waves of equal amplitude and opposite rotations. Therefore, the amplitude of the original MW magnetic field can be obtained based on the amplitude calculated by Rabi oscillation.

The coplanar waveguide (CPW) is selected to be measured with a tapered fiber diamond probe (FDP), for its superior transmission properties and uniform EMF distribution. With a signal line width of 150 μm and gap width of 120 μm, the S parameter of CPW is shown in Fig. 1(b). Two commonly used forms of NV center, FDP and bulk diamond, are depicted in Figs. 1(c) and 1(d), with a defined coordinate system for clarity.

The FDP shown in Fig. 1(c) was used in the experiment. A green laser with a wavelength of 532 nm pumps the diamond crystal at the front taper through the fiber, and the red fluorescence is returned along the original path, passing through the dichroic mirror and entering the avalanche photodetector (APD) to output a voltage signal. We characterize the MW magnetic field with the NV axis set vertically,^[18–20] and the Rabi frequency at resonance can reflect the horizontal component of MW magnetic field (composed of the X and Y components). The Zeeman effect splits energy levels under a DC magnetic field, representing four peaks in the optically detected magnetic resonance (ODMR) spectrum.^[21] Typical ODMR spectrum and Rabi oscillation are shown in Figs. 2(a) and 2(b).

The horizontal component of MW magnetic field along the X and Z directions of the CPW is measured and compared against experimental results. The actual output power of the excitation source is confirmed at 23.43 dBm. As shown in Figs. 2(c) and 2(d), there is a close match between the simulation and measurement data, indicating accuracy in the experimental results.

In quantum precision measurements of NV centers, bulk diamonds are widely used for its ability to achieve rapid 2D imaging. The 2D microwave field can be imaged in a short time by using confocal optical path and CCD camera. Such experiments do not require electric displacement tables and point-by-point scanning, which will greatly improve the efficiency, and do not need to consider the impact of environmental changes and other factors. But this requires contact with the RF device, which can affect sensitive electronics and limit 3D scanning in complex circuits. Our previous work introduces a tapered FDP^[22,23] as an alternative, enabling submicron imaging without contact. Although more complex equipment and preparation process are required, as well as point-by-point scanning, which takes more time, it ensures the accuracy of the measurement. This approach offers high-resolution scanning adaptable to various scenarios. To compare the disturbance caused by these methods, we use Ansys HFSS 19.1 to simulate the MW magnetic field and transmission at the frequency of 5 GHz.

Initially, we concentrated on characterizing the MW magnetic field and transmission properties of RF devices disturbed by bulk diamonds. For this, we employ a 150 μm × 150 μm × 20 μm diamond cuboid with ε_r = 5.7 and μ_r = 1. The CPW is placed in the same direction as stated in the previous section, with a feed power of 30 dBm.

The diamond’s bottom aligns with the CPW’s top, centered horizontally. Since CPW has extremely excellent transmission characteristics, it can be regarded as a uniform transmission line. In the direction of the transmission line, the electromagnetic characteristics can be considered to be equal everywhere, so our disturbance analysis focuses on a single reference line. In the simulation, a symmetrical line across the diamond’s center is chosen. The disturbance is quantified by the rate of change (ROC), expressed as a percentage

For the relatively large X component, we calculate the ROC along the specified reference line. As shown in Fig. 3(a), the bulk diamond induces a magnetic field disturbance of about 2%, a value noteworthy and not negligible in our analysis.

Regarding transmission properties, we evaluate the disturbance by monitoring changes of S₂₁. Figure 3(b) shows that at gigahertz frequencies, S₂₁ varies by over 2%, indicating significant impedance mismatch due to the bulk diamond’s direct contact with the CPW. This disturbs RF device’s performance and EMF distribution, conflicting with the objectives of quantum precision measurement.

We proceed with an analysis of the FDP, noting tapered fiber structure’s enhancement of fluorescence collection and efficient pumping.^[22,23] For the simulation, we simplify the model by neglecting the untapered cylindrical section of the fiber and use a round table matching diamond dimensions to represent the tapered part. This approach captures the MW magnetic field disturbance from the fiber’s tapered interface with the diamond. We evaluate the FDP’s disturbance on MW magnetic field and transmission properties using three diamond sizes: 10 μm × 10 μm × 5 μm, 5 μm × 5 μm × 2.5 μm, and 2 μm × 2 μm × 1 μm. A reference line segment at a constant horizontal height of 10 μm from the CPW’s upper surface is chosen. With each reference line’s length double that of the diamond’s horizontal size, we normalize the distance to account for different diamond sizes and plot the H_x distribution trend and ROC on a single graph. It is feasible given that H_x varies little over small dimensions above the CPW.

As shown in Fig. 3(c), H_x varies within 3 A/m. And when converted to ROC, the disturbance of the three FDP on MW magnetic field is less than 0.5%, lower than that of the bulk diamond. Similarly, as depicted in Fig. 3(d), FDPs of these sizes have a minimal impact on the CPW’s S₂₁, less than 0.05%, which is considerably lower than the 2% observed with bulk diamond. This level of impact is negligible in practical applications. Moreover, the smaller the diamond, the lesser the effect on S₂₁. It is reasonable to conclude that submicron or nanoscale diamonds would have an insignificant effect on RF device transmission properties. Therefore, we conclude that FDP is superior to bulk diamond in terms of minimizing MW magnetic field disturbance and preserving transmission properties of RF devices.

In this study, firstly the MW magnetic field of CPW is characterized and a good fit between the experiment and the simulation is obtained. Then we compare the disturbance induced by bulk diamond and tapered FDP on CPW. Our simulations demonstrate that the tapered FDP exerts minimal impact on the CPW’s MW magnetic field (< 0.5%) and S₂₁ parameters (< 0.5%), establishing its suitability for millimeter-wave applications. Notably, we observe that smaller diamond sizes at the fiber’s end further reduce S₂₁ disturbance, suggesting that submicron diamonds enhance spatial resolution and minimize interference with RF devices, resulting in more accurate measurements. Experimental validation corroborates these findings, confirming that these methods remain within acceptable error margins. Consequently, they offer lossless, high-resolution MW field measurement across various frequency bands.