A cavity-based optical antenna for color centers in diamond

An efficient atom-photon-interface is a key requirement for the integration of solid-state emitters such as color centers in diamond into quantum technology applications. Just like other solid state emitters, however, their emission into free space is severely limited due to the high refractive index of the bulk host crystal. In this work, we present a planar optical antenna based on two silver mirrors coated on a thin single crystal diamond membrane, forming a planar Fabry-P\'erot cavity that improves the photon extraction from single tin vacancy (SnV) centers as well as their coupling to an excitation laser. Upon numerical optimization of the structure, we find theoretical enhancements in the collectible photon rate by a factor of 60 as compared to the bulk case. As a proof-of-principle demonstration, we fabricate single crystal diamond membranes with sub-$\mu$m thickness and create SnV centers by ion implantation. Employing off-resonant excitation, we show a 6-fold enhancement of the collectible photon rate, yielding up to half a million photons per second from a single SnV center. At the same time, we observe a significant reduction of the required excitation power in accordance with theory, demonstrating the functionality of the cavity as an optical antenna. Due to its planar design, the antenna simultaneously provides similar enhancements for a large number of emitters inside the membrane. Furthermore, the monolithic structure provides high mechanical stability and straightforwardly enables operation under cryogenic conditions as required in most spin-photon interface implementations.


I. INTRODUCTION
In the past years, color centers in diamond involving a substitutional atom from group IV of the periodic table and a nearby vacancy (group IV vacancy centers 1 ) gained strong interest for applications in quantum technologies 2 , among them the negatively-charged silicon (SiV − ) 3,4 , germanium (GeV − ) 5,6 , and more recently also tin 7,8 (SnV − ) and lead vacancy center (PbV − ) 8,9 . Their emission into the zero phonon line (ZPL) exceeds the wellstudied negatively-charged nitrogen-vacancy center (NV − ) by one order of magnitude at room temperature 10 . Moreover, group IV vacancy centers possess an optically accessible electron spin 7,11-14 , rendering them well-suited building blocks for spin-photon-interfaces 2 .
However, the high refractive index of diamond at visible wavelengths (n = 2.414 at 620 nm 15 ) induces a severe limitation on the photon extraction efficiency. Total internal reflection, trapping around 98 % of the color center emission inside of bulk diamond, is a well-known problem 16 also in competing systems such as semi-conductor quantum dots, or in classical light sources such as light emitting diodes (LED) 17 , where the refractive index of the host materials is typically even higher. Consequently, there have been many proposals to increase the collectible photon rate from quantum emitters out of high index materials, most of them trying to shape the dielectric environment to circumvent total internal reflection. For color centers in diamond, non-resonant structures such as nanowires [18][19][20] or solid-immersion lenses [21][22][23][24] have been shown to be a feasible solution, yet they enhance the collectible photon rate only by one order of magnitude to around 30 % of the total emission rate, and for only a small fraction of emitters with matching position and orientation. More sophisticated approaches involve resonant cavities, channeling the emission into one spatial and spectral mode and additionally enhancing the emission rate beyond the bulk emission rate via the Purcell effect 25 . This includes fiber-based Fabry-Pérot type cavities [26][27][28][29][30] as well as a plethora of integrated micro-and nanophotonic approaches 16,31 . Generally speaking, interfaces between solid state emitters and freely-propagating photons may be summarized as optical antennas 32 : An optical antenna is defined as a device which is not only enhancing the collectible photon rate from an emitter, but vice versa also enhances the coupling of external light to the emitter. Whereas optical antennas have been realized with a multitude of designs 33 , the simplest structure may consist of a planar stack of dielectric layers as proposed by Lee et al. 34 . This approach has been demonstrated to be a promising option to It is based on two gold mirrors which are directly coated onto the host layer, yielding an intrinsic mechanical stability. The thickness of the host layer as well as of the mirrors is chosen to enhance the beaming of the molecule's emission into a narrow lobe in the far field.
Just recently, an adaption to quantum dots has been reported by Huang et al. 37 , yielding a collection efficiency of around 19 % with an air objective of NA = 0.85. Although there exist theoretical 38,39 as well as first experimental studies 40 to adapt this design also to color centers in diamond, a thorough demonstration is by now missing.
Thus, we start in Section II with a detailed model of a dipole emitting in a planar metallodielectric stack based on a diamond membrane, identifying the design most generally as a monolithic Fabry-Pérot cavity. In contrast to the studies mentioned above, we optimize the design towards a high absolute photon rate from a single SnV − center in the diamond membrane, collectible with an air objective. We show that for certain thicknesses of the involved layers, the cavity enhances the collectible photon rate from single emitters inside the diamond membrane as well as the coupling of an excitation laser to these emitters, satisfying the definition of an optical antenna. The theoretical description is followed by an optimization of the free parameters, revealing the main fabrication challenge: Whereas single molecules and quantum dots can be deposited in a bottom-up-approach, thin diamond membranes are typically fabricated in a top-down-approach involving plasma etching of high quality bulk diamond 41,42 and subsequent doping with color centers. Thus, we continue with briefly describing the fabrication of the diamond membrane as well as of the metallo-dielectric layers (Sec. III). To verify the functionality of the fabricated antenna, we perform a spectroscopic investigation of single SnV − centers prior to and after applying the coatings in Section IV. Yielding a nearly 6-fold enhancement of the single photon emission rates in accordance with theory, together with a severe reduction of the required excitation power, we demonstrate the operation of the fabricated cavity in terms of an optical antenna as defined above. Especially for the implementation of single photon sources or spin-photon interfaces, a monolithic and thus inherently stable optical antenna together with an intrinsically high scalability and low technical overhead paves the way towards the usage of color centers in diamond as versatile building blocks for present and future quantum technologies.

II. THEORETICAL DESCRIPTION
In the following, we focus entirely on the SnV − center with its comparably high photon rate already out of bulk diamond, typically reaching on the order of 10 4 − 10 5 counts per second (cps) at the detectors (compare saturation statistics in Figure 6). The atomic structure of the SnV − center is depicted in Figure 1 (a). Made up of a substitutional tin atom and an adjacent vacancy, the tin atom moves to an interstitial position between the two lattice positions, forming a split-vacancy configuration 1,43 . In contrast to the NV center, this gives rise to an inversion symmetry, yielding a strongly reduced sensitivity of the electronic levels to external perturbations, in particular to electric fields. The photoluminescence (PL) spectrum of the SnV − center consists of the ZPL at 620 nm, followed by a phononic side band (PSB) extending to over 700 nm. In previous work, we have thoroughly studied the temperature-depended Debey-Waller factor, quantifying the branching ratio between ZPL and PSB as 30:70 at room temperature 10 . This exceeds the corresponding value of the NV center by one order of magnitude, rendering the SnV − center a promising candidate for the implementation of efficient room temperature single photon sources. An exemplary spectrum of an SnV − center in bulk diamond at room temperature is shown in Figure 1 In the next section, we want to discuss the emission characteristics of a single SnV − center diamond host layer of thickness t 0 and refractive index n 0 . The dipole spans an angle ϑ with the z-axis and its emission is described by a plane wave expansion approach. The host layer is situated between two layer systems with refractive indices n i and thicknesses t i for the layers above and n i and t i for the layers below, respectively. The whole stack is embedded within semi-infinite layers on both sides with refractive index n + and n -, respectively. We assume the collection optics to be placed in the upper half space with refractive index n + .
situated inside a planar metallo-dielectric stack. From a photonic point of view, the SnV − center can be modelled as an electric point dipole with a dominant dipole axis along one of the high symmetry 111 axes of the diamond lattice 3,10 , depicted as red solid line in Figure   1 (a). An electric dipole radiating inside a planar metallo-dielectric stack is sketched in Figure 1 (c): We assume the dipole to be embedded in a diamond layer of thickness t 0 and refractive index n 0 , enclosed by two arbitrary layer systems. The whole stack is embedded within semi-infinite layers on both sides. We further assume the collection optics to be placed in the half space above the dipole with real refractive index n + , allowing us to collect all emission from the dipole leaving the stack in positive z-direction up to a detection angle θ NA defined by the NA of the collection optics via NA = n + · sin(θ NA ). We call this half space the collection half space.
The dipole emission in such a stack can be treated completely by classical electrody-namics, which has been shown multiple times in literature 44-47 : Starting with a plane wave expansion of the emitted electric field, the corresponding plane waves and evanescent fields are propagated through the layers using generalized Fresnel coefficients for the layer system above and below the diamond layer obtained via a transfer matrix method 48 . In the semiinfinite half spaces, we perform a far field transformation using the method of stationary phase 49 . With this formalism, we can derive expressions for the radiated far fields that can be evaluated numerically.

A. Optical antenna working principle
The optical antenna design is based on a thin (t 0 < 1 µm) diamond membrane with refractive index n 0 = 2.414 at 620 nm 15 , which itself can be modelled as a slab waveguide when surrounded by air (n + = n -= 1.0). Consequently, most of the emission from color centers is trapped inside the membrane due to total internal reflection at the diamond-air interfaces. The corresponding guided modes can be calculated by solving the transcendental eigenvalue equations 50 . Another possibility to reveal the guided modes is to virtually place an electric point dipole inside the slab and look at its emitted power, which is dependent upon the local density of states (LDOS): In a homogeneous medium with refractive index n 0 , the emitted power is given as P hom = n 0 · P 0 with P 0 the emitted power in vacuum.
An arbitrarily shaped inhomogeneous environment such as a slab waveguide gives rise to a modified LDOS and thus a change in the emitted power 51 . This change can be modeled by splitting the total power P tot emitted by the dipole in a sum of the homogeneous power P hom and an additional contribution P inhom . Furthermore, P inhom can be expressed in terms of a plane wave expansion as shown in equation (1).
The integrals in equation (1)  with k = 2π/λ and λ the vacuum wave number and wavelength, respectively. Thus, k is directly related to the polar emission angle θ and we call the function p(k ) the angular power emission spectrum. Defining n eff = n 0 sin(θ), we find the figure n eff , which is wellknown from guided wave optics and is called effective index of the guided modes. As k is a rather unhandy value, we evaluate p(n eff ) instead of p(k ), enabling us to directly extract the effective index of the guided modes. As an example, Figure 2  Using Snell's law, we can calculate the polar angles θ up at which these modes propagate as plane waves in the collection half space. By evaluating Fresnel's equations for plane waves incident on the stack from the collection half space, we can additionally probe the reflectance of the stack.
If the layer above and below the diamond slab is chosen to be air with refractive index n + = n -= 1, the range 1 < n eff < n 0 corresponds to plane waves of the expansion which are trapped in the slab. In this regime, we see peaks corresponding to the guided modes, delivering the same effective indices as the direct approach of solving the transcendent equations for a slab waveguide. By evaluating p(n eff ), however, we can extract to which modes the dipole actually couples, as due to the chosen dipole orientation and position, it does not couple to all existing guided modes.
These considerations also hold, when we introduce silver coatings (n 1 = n 1 = 0.05 + 4.21i at 620 nm 52 ) on both sides of the diamond slab. Instead of having total internal reflection, the diamond-silver interfaces possess a high reflectance independently of the angle of incidence, leading again to modes in the diamond slab which can also be calculated via suitable eigenvalue equations 53 . In the absence of a critical angle, all peaks with n eff < n 0 in p(n eff ) correspond to guided modes of the stack. Reducing the thickness of the top silver layer to values well below 100 nm, the layer becomes transparent enough to let the formerly guided modes leak out of the diamond slab trough the thin silver layer into the collection half space with n + = 1.0. This effectively implies that modes with n eff < n + = 1.0 will be converted to free-propagating radiation at well-defined polar angles in the collection half space beyond the thin silver layer. Consequently, these modes are often named leaky modes.
The resulting angular power emission spectrum for an upper silver mirror with t 1 = 50 nm thickness is shown in Figure 2  The planar design considered here has already been discussed as a cavity in literature and is thus conceptually well understood, especially in the context of enhancing light extraction from LEDs 47,54,55 . We, however, want to point out that some of the underlying theoretical concepts are much more sophisticated than the presented model. As the transmission through the thin silver layer is the major loss source of the cavity, the leaky modes can no longer be taken as confined between the mirrors, which is a major assumption in resonator theory. Instead, they span trough the semi-transparent mirror towards infinity, defining the system as a so-called open cavity. Such open cavities have already been discussed on a fundamental level 56 , identifying Fox-Li quasimodes as the exact solutions. However, as will be shown in the next sections, the model presented above describes the experimental results successfully without the need for specific assumptions on the cavity modes.

B. Optimization
After discussing the basic concept of the design, it becomes obvious that the thickness of the diamond as well as of the thin silver layer can be optimized to enhance the coupling of an SnV − center to the cavity, enabling the functionality as an optical antenna. To quantify the brightness of a single photon emitter driven by an off-resonant continuous wave laser, a well-suited figure of merit is given by the collection factor ξ in equation (2): Γ NA is the far field photon rate into a solid angle defined by the NA of the collection optics, whereas Γ hom is the radiative decay rate of an electric dipole transition inside a homogeneous medium. Thus, we have Γ hom = n 0 Γ 0 with Γ 0 the vacuum emission rate. The collection factor ξ hence defines a handy and comparable value for the absolute collectible photon rate Γ NA under continuous wave excitation. Due to an enhanced LDOS, we may also find ξ > 1, which can be attributed to a lifetime reduction of the emitter (Purcell effect 25 ).
As we calculate classical electromagnetic fields and optical powers, but aim at investigating quantum mechanical emission rates of single quantum emitters, we use the following relation: Equation (3) Table I.  (4).
As an example, for case (I) we find n eff = 0.33 for the s-polarized mode and d pen = 52.1 nm (50.8 nm) for its penetration depth into the upper (lower) stack, summing up to 309.8 nm.
This matches λ/2 = 310 nm very well. The thickness t 2 of the silica layer tends to λ/(4 · n 2 ), working as an anti-reflective coating.
To gain a deeper insight, Figure 3 (a) provides ξ in dependence of t 0 and h for case (I). As expected, high values of ξ, corresponding to the dipole being in resonance with the cavity, occur only for t 0 fulfilling equation (4), and the number of field nodes increases with t 0 . We want to emphasize that in Figure 3 (a), we do neither plot the cavity resonances directly in terms of Purcell factor, nor do we show an actual field distribution. Shown is ξ as a measure of the collectible photon rate. It becomes obvious that an enhanced emission is given only for a good coupling to the cavity, thus ξ maps the field distribution inside the cavity. For thicker diamond layers, additional modes with n eff > 1.0 start to appear.
As mentioned above, modes with n eff > 1.0 are confined in the slab and do not contribute to ξ. Additionally, the coupling to the leaky modes reduces because of a reduced field enhancement for thicker cavities, comparable to an increasing mode volume, leading to a reduction of ξ. implantation, yielding a mean implantation depth for the tin ions of only d = 27.5 nm as we will discuss in the next section. In future implementations, this limitation can be overcome by either implanting at higher energies or by introducing buffer layers with low refractive index such as silica between the diamond and the silver layers 37,38 . This, however, requires a more precise control over the layer deposition and, more challenging, a thinner diamond membrane.
A more severe limitation becomes evident when looking at the width of the cavity resonance for case (I) shown in Figure 3 (c). As designed, ξ peaks around the ZPL at 620 nm.
Although the resonance is comparably broad (23 nm FWHM ), it implies that we have to choose an excitation wavelength inside it, because the cavity will reflect most of the incident light outside. A common experimental situation for off-resonant excitation of many color centers in diamond is using a green laser; in this work we employ a laser emitting at 516 nm. Consequently, for such a situation we have to find a cavity length at which both the green excitation light as well as the ZPL of the SnV − center are resonant. Sweeping t 0 while keeping the other parameters fixed as in case (I), we find t 0 = 609 nm as the smallest thickness at which the cavity is resonant for both wavelengths, defining this thickness as the working point of the cavity as an optical antenna for the off-resonant excitation. We redo the optimization to check whether for this thicker membrane and the limited implantation depth, other thicknesses of the thin silver and silica layer yield a better enhancement. Indeed, as can be seen from case (III) in table I, the optimal silver layer thickness decreases here to t 1 = 24.9 nm, whereas the silica thickness stays nearly the same. With ξ = 0.28, the enhancement is still 12-fold, yet we loose a factor of 5 compared to case (II) with resonant excitation. To demonstrate the functionality, the off-resonant excitation should however provide a measurable change in the collectible photon rate. In future experiments, we may explore resonant excitation to benefit from the full potential of the design. Lastly, it is worth mentioning that in all three cases, the cavity is only resonant for excitation light incident under the correct angle. This can be seen from the reflectance curves in Figure 3 (c), which show a dip in reflectance overlapping with the peak in ξ. Here, the reflectance is calculated assuming an angle of incidence covering the broad emission angle distribution that is inferable from the far field plot in the inset. The white ring in the far field plot indicates the collection angle covered with our experimentally-used NA = 0.8 air objective. As the white ring includes most of the emitted light and the excitation is performed via the same objective, we can vice versa be sure to cover the required angles of incidence in excitation.

A. Fabrication
As starting material, we use commercially-available single crystal diamond, grown by chemical vapor deposition (Element Six, electronic grade). These bulk (

B. Spectroscopic characterization
To characterize the diamond membrane and the SnV − centers inside prior to and after coating, we perform spectroscopy using a home-build confocal laser-scanning PL microscope.

A. Bare diamond membrane
After several etching cycles, we end up with a diamond membrane possessing an average thickness well below 1 µm. In the white light microscopy image in Figure 5  for the emitters we include in the statistics. In the spectrum (a), a clear signature of SnV − center emission is given by the ZPL at 620 nm, which has a linewidth of around 6 nm at room temperature. Recording the detected photon rate I(P ) for increasing excitation power P , we find a saturation behavior as shown in Figure 4 (b). We fit I(P ) with a sum of three contributions 61 : A constant contribution D accounting for the detector dark counts (500 cps in total), a linear contribution c·P accounting for uncorrelated background fluorescence, and a non-linear saturation term modeling the actual PL of the SnV − center yielding equation (5).
For most of the SnV − centers we measure, however, we are not able to satisfactorily fit c = 0 fixed in all fits. We assume that this behavior originates from a complex charge state dynamic at high excitation powers, yet the underlying mechanism is still unclear. The values for P Sat and I Sat are however reliable and suitable for relative comparison of emitters in the bare membrane and in the antenna, as can be seen from the fit (red line) in Figure  powers, we measure a photon autocorrelation with the HBT setup as shown in Figure 4 (c), yielding in this example g (2) (0) = 0.3. The detection time jitter is taken into account in form of a convoluted fitting function. Because of the missing possibility to estimate the background contribution directly from the saturation measurement, we independently estimate the background by integrating a PL spectrum at a position nearby the emitter. For the exemplarily-shown g (2) (τ ) in Figure 4 (c), the residual coincidences from the fit yield a ratio of the emitter PL to the total PL (emitter and background) of 0.87(4), in perfect agreement to a value of 0.88 calculated from an integration of the corresponding spectra.

B. Membrane with applied coatings
Besides the thickness of the diamond membrane, the final performance of the antenna strongly depends on the quality and thus the reflectance of the silver layers. Most probably due to an insufficient calibration of the evaporator, we do not reach the target thicknesses of the layers. We end up with t 1 = 30 nm of silver, followed by t 2 = 128 nm of silica for the upper layers. The thick silver layer on the back side has a thickness of t 1 = 160 nm.

Cavity resonances
Exchanging the fluorescence filters in the detection path of the confocal microscope with a neutral density filter enables us to spatially map the reflectance and thus the cavity resonances for the excitation laser emitting at 516 nm. Figure 5 (b) shows a scan over the whole membrane with applied coatings. It can clearly be seen that the detected photon rate, in this case corresponding to the reflected laser power, drops at sharply defined positions on the membrane, forming fringes of low reflectance. When we perform the same scan again with a 610 nm longpass filter instead of a neutral density filter, we observe the inverted situation in fluorescence, see Figure 5 (c): Whenever the laser hits a resonance, the PL increases. The PL originates from background fluorescence of the diamond membrane that couples to the cavity modes. As we know that the cavity has to be resonant to the laser at these positions, we can directly deduce the membrane thickness at these positions from the plot in Figure 5  Setting the detection bandwidth to 610 -650 nm, we measure a PL map as shown in

Enhancement of color center emission
We search for single SnV − centers at the working point, i.e. close to the bright fringe in   value. Moreover, during the measurement of the antenna we found the coatings to severely degenerate. All of the emitters in the statistics of the optical antenna have been measured before a break in order to examine the first data. After this two months break, the silver layers showed severe color changes, indicating a degradation, although we applied a silica protection coating. As a consequence, no more reliable measurements could be carried out.
Additionally, we tried to recycle the membrane by removing the silica as well as the silver coating via wet chemical processes, which unfortunately led to a destruction of the thin diamond membrane.

V. DISCUSSION & OUTLOOK
Thin free-standing single crystal diamond membranes are a key requirement for the creation of many advanced nanophotonic structures to enhance single photon emission or spinphoton interaction for color centers. We demonstrated the successful fabrication of such a membrane starting with commercially-available high-purity diamond material. Creation of single color centers inside the membrane was shown to be straightforward using ion implantation techniques and subsequent annealing. Transforming the thin diamond membrane into a cavity-based optical antenna requires in principle only established thin-film deposition and analysis technologies. Finally, the investigation of the color centers in the bare membrane and subsequently in the antenna has been carried out thoroughly, in both cases taking great care to unambiguously identify single emitters. As a main result, we found a significant enhancement of single photon emission and reduction of saturation powers of the color centers coupled to the optical antenna compared to the uncoupled case in the bare diamond membrane, yielding count rates up to around half a million photons per second from a single SnV − center. The theoretical framework predicts these enhancements in good agreement to the measured data. Additionally, the occurrence of resonances in PL as well as in reflectance are well explained by the model.
We consider this work as a proof of concept with many options for improvement: Although the emitters proved to be photostable even at high excitation powers, we observe randomly switching background fluorescence from the membrane, severely reducing the signal-to-background ratio of the actual emitter PL. This blinking background is currently the main limitation for the comparably low single photon purity. We observe it independently of the color center PL on all samples that have been plasma etched and subsequently annealed and cleaned as described in this work. We do further not observe it when focusing deep into the diamond, indicating that it originates from the surface. It has been shown that a hydrogen-termination 62 or a disordered oxygen-termination 63 of the diamond surface may act as a source of charge traps, leading to random charge fluctuations upon laser excitation.
Promising options to remove this potential source of the blinking background fluorescence are more sophisticated post-processing techniques, e.g. oxygen annealing 63 or a treatment with a purely inductively coupled oxygen plasma 64,65 . Both methods have been shown to introduce a highly-ordered oxygen termination, severely enhancing the charge state stability and spin coherence of shallow color centers. Moreover, the vanishing linear background contribution in the measured saturation curves gives rise to a different emission dynamic compared to the SiV − center. For more sophisticated applications using SnV − centers, a thorough investigation of this potentially novel photophysic will be mandatory.
As already indicated in the main text, the coating of the diamond membranes appeared to be sufficient for our purposes in the beginning, yet the degradation of the silver layers proved us wrong. A possible explanation for this degradation is the weak chemical bonding between the silver and the silica layer: It is well known that the adhesion between noble metals and oxides such as silica is comparably weak already directly after deposition and degrades over time 66 . Especially thin silver layers are known to be susceptible to dewetting even at room temperature 52 . A commonly used adhesion promotion can be established via a thin titanium or chromium layer between the oxide and the noble metal. In future work, we may thus need to include such an additional layer in our antenna design. As the comparably low reflectance of chromium or titanium may reduce the final performance 37 , one could also think of protecting the upper silver layer with an additional gold layer. Lastly, the thickness gradient in the membrane provides us a varying cavity length, but limits the areas in which the cavity operates as an optical antenna. This raises the question which gradient can be tolerated at most. Our model covers only completely planar stacks and it is obvious that a wedged membrane will at some point severely change the properties of the cavity. Under the assumption that the gradient in first order only shifts the resonance wavelength, we can extract this shift from our model to be 14 nm for a change in thickness of the membrane of per µm gradient we achieve here, we were thus able to show the successful antenna operation.
Anyway, the long-term goal is surely to produce membranes with a well defined thickness and with well defined gradients on areas spanning hundreds of micrometers to fully harness the potential of this planar design. A first step towards dry etching processes that actively planarize diamond membranes has already been shown 67 , demonstrating the feasibility of such approaches.
Besides these technical imperfections just summarized, we have successfully demonstrated a design for an optical antenna based on a planar Fabry-Pérot cavity which is able to boost the emission rate of a single SnV − center center even in the worst scenario (case III in table I) to around half a million photons per seconds at the detectors in saturation. In future work, we want to focus on near-resonant and resonant excitation (case II in table I), which would allow for photon rates on the order of several million counts per second. Additionally, a reduction of the background fluorescence and thus an improvement of the single photon purity should be feasible by employing surface treatments as described above. Already at room temperature, such high photon rates together with a reasonable single photon purity would pave the way towards applications in quantum metrology or quantum sensing. For the implementation of an efficient spin-photon-interface, however, cryogenic temperatures A cavity-based optical antenna for color centers in diamond are unavoidable. Because of the monolithic design and thus the absence of moving parts, the design presented here may also perform well at low temperatures. Operation of the antenna under cryogenic conditions and resonant excitation consequently will fully harness the potential of this comparably simple nanophotonic design.

VI. ACKNOWLEDGEMENTS
We

VII. DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.