# Optimized Planar Microwave Antenna for Nitrogen Vacancy Center Based Sensing Applications

^{*}

## Abstract

**:**

^{2}while realizing high Rabi frequencies of up to 10 MHz in an ensemble of NV centers.

## 1. Introduction

## 2. Microfabrication Methods

## 3. Numerical Simulation and Optimization

## 4. Experimental Setup and Methods

## 5. Antenna Performance

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) A schematic representation of the $\mathsf{\Omega}$-shaped antenna and its implementation in a confocal microscope utilizing a piezo scanner (coaxial connector design by avitek, coaxial cable design by Steven Minichiello and objective design by thorfynn; source: https://grabcad.com accessed on 7 June 2021). (

**b**) A schematic representation of the geometry of the $\mathsf{\Omega}$-shaped antenna design (note that the scale bar is approximate and the sketch does not give the exact geometry of the simulated antenna but illustrates the design in general). Microwave (MW) modes enter and leave the calculation domain via the waveguide ports indicated in red. Inset: Simulated MW radiation pattern. Here, strong directivity towards the sample is visible.

**Figure 2.**Process flow for Omega antennas. The color key: grey—glass substrate; blue—chromium; yellow—gold; green—adhesion promoter; red—photoresist; black—photomask; violet—UV-illumination.

**Figure 3.**(

**a**) Achievable MW amplitude for different inner radius values ${r}_{w}$. Points from different simulation runs. (

**b**) Calculation of the frequency-dependent ${S}_{11}$ parameter (back reflection coefficient) with a ground plane for the 50 $\mathsf{\mu}$m thick diamond (solid black) and the 300 $\mathsf{\mu}$m thick diamond (solid red) and without the ground plane (dashed lines). (

**c**) MW amplitude and Rabi frequency dependence on the distance to the antenna top surface. Rabi frequencies ${\mathsf{\Omega}}_{\mathrm{R}}$ were determined for a resonantly driven transition of the subset of nitrogen vacancy (NV) centers aligned in $\langle 111\rangle $ crystallographic direction. Input MW power equals 1 W.

**Figure 4.**Field simulation results for a 50 $\mathsf{\mu}$m thick electronic grade diamond (

**a**–

**c**) and for a 300 $\mathsf{\mu}$m thick IIa diamond (

**d**–

**f**). All field data were taken 10 nm below the diamond sample’s top surface and correspond to a MW input power of 1 W. (

**a**,

**b**,

**d**,

**e**) Field distribution of the MW in x and y directions. (

**c**,

**f**) 2D maps of theoretically expected Rabi frequencies ${\mathsf{\Omega}}_{\mathrm{R}}$ for a resonantly driven transition of the subset of nitrogen vacancy (NV) centers aligned in $\langle 111\rangle $ crystallographic direction. The dashed circle marks the circumference of the aperture. Insets: detailed views of the aperture areas.

**Figure 5.**Comparison between sputtered and evaporated layers. The evaporated antennas show better performance in terms of radiated MW amplitude, as shown by the increased optically detected magnetic resonance (ODMR) contrast C ((

**a**), 8% vs. 22%), and Rabi frequency ${\mathsf{\Omega}}_{\mathrm{R}}$ ((

**b**), 800 kHz vs. 2.2 MHz, ${t}_{\pi}$ = $\pi $-pulse duration). Note that the ODMR resonance of the evaporated antenna is strongly power broadened ($\Delta \nu $ = FWHM). Points indicate the experimentally obtained data and solid curve denotes fits used to obtain the mentioned parameters.

**Figure 6.**(

**a**) Continuous ODMR measurements of an NV ensemble with an externally applied magnetic field. For the outermost resonance pair, a splitting of 181 MHz ± 1 MHz with high contrast (4.67% ± 0.06% at −15 dBm source MW power) was obtained. For the corresponding subset of NV centers, we determined a projection of the magnetic field on the NV axis of 6.45 mT ± 0.05 mT. (

**b**,

**c**) Characterization of the homogeneity of the radiated MW field amplitude perpendicular and parallel to the gap. While the amplitude parallel to the gap slightly depended on the distance to the gap, as expected, the amplitude perpendicular to the gap remained unaffected, showing that the full area of the aperture is reliably usable for spin manipulation protocols. (

**d**) Pulsed ODMR of one of the resonances showing the hyperfine transitions due to ${}^{14}\mathrm{N}$ nuclear spin coupling. The black points indicate the experimentally obtained data, solid black lines indicate the error bars and the solid red lines indicate either fits or simulated data.

**Figure 7.**(

**a**) Typical Rabi oscillation measurements, which are primarily used to obtain relevant pulse parameter to be used in multi-pulse sensing schemes. The measurement performed at ${\mathsf{\Omega}}_{\mathrm{R}}\approx $ 6.5 MHz. (

**b**) Spin-echo and Carr Purcell Meiboom Gill (CPMG)-n measurements with the NV ensemble performed with the pulse parameters obtained from (

**a**). The plots have been fit and scaled along the y-axis for comparison. The points show the experimentally obtained data, solid curves denote the fit and the dashed lines indicate the fit envelopes. The spin-echo measurements reveal ${T}_{2}\approx $ 167 $\mathsf{\mu}$s. Applying CPMG-8 pulse sequences leads to almost a fourfold improvement in the decoherence time of the spin state. From the fit, the calculated enhanced decoherence times for the CPMG-2/4/8 protocols were ≈245 $\mathsf{\mu}$s/≈425 $\mathsf{\mu}$s/≈638 $\mathsf{\mu}$s, respectively.

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**MDPI and ACS Style**

Opaluch, O.R.; Oshnik, N.; Nelz, R.; Neu, E.
Optimized Planar Microwave Antenna for Nitrogen Vacancy Center Based Sensing Applications. *Nanomaterials* **2021**, *11*, 2108.
https://doi.org/10.3390/nano11082108

**AMA Style**

Opaluch OR, Oshnik N, Nelz R, Neu E.
Optimized Planar Microwave Antenna for Nitrogen Vacancy Center Based Sensing Applications. *Nanomaterials*. 2021; 11(8):2108.
https://doi.org/10.3390/nano11082108

**Chicago/Turabian Style**

Opaluch, Oliver Roman, Nimba Oshnik, Richard Nelz, and Elke Neu.
2021. "Optimized Planar Microwave Antenna for Nitrogen Vacancy Center Based Sensing Applications" *Nanomaterials* 11, no. 8: 2108.
https://doi.org/10.3390/nano11082108