Enhanced Spectral Density of a Single Germanium Vacancy Center in a Nanodiamond by Cavity-Integration

Color centers in diamond, among them the negatively-charged germanium vacancy (GeV$^-$), are promising candidates for many applications of quantum optics such as a quantum network. For efficient implementation, the optical transitions need to be coupled to a single optical mode. Here, we demonstrate the transfer of a nanodiamond containing a single ingrown GeV- center with excellent optical properties to an open Fabry-P\'erot microcavity by nanomanipulation utilizing an atomic force microscope. Coupling of the GeV- defect to the cavity mode is achieved, while the optical resonator maintains a high finesse of F = 7,700 and a 48-fold spectral density enhancement is observed. This article demonstrates the integration of a GeV- defect with a Fabry-P\'erot microcavity under ambient conditions with the potential to extend the experiments to cryogenic temperatures towards an efficient spin-photon platform.

The following article has been accepted by Applied Physics Letters.It is found at https://doi.org/10.1063/5.0156787 With increasing advances in quantum technologies and the importance of secure communication, there is great interest in developing a quantum network. 1 In such a network, the communication is based on quantum entanglement, and by using quantum key distribution it provides guaranteed security. 2,3owever, to increase the range of the network on a global scale, 4 nodes are required due to lossy photon channels that limit the range to about 100 km. 5 Essential for the realization of such nodes in a scalable quantum network are a quantum memory capable of storing and processing quantum information, 6 and high rates of coherent photons to establish entanglement in communication schemes.For the interaction between photons and the quantum memory, an efficient interface is necessary.Consequent challenges of overcoming photon losses, maintaining coherence, attaining robustness and enabling scalability can be tackled by using a quantum repeater as a node in the quantum network. 7One approach to realizing such a repeater is to address a single emitter to gain access to a quantum memory via its spin.By placing the emitter inside a high quality optical resonator, 8,9 quantum state writing and reading can be performed efficiently at high rates due to an enhanced spontaneous emission rate. 10romising single emitter candidates for realizing a quantum network are color centers, optically active defect centers in diamond. 11,12In order to couple them to the mode of a microcavity diamond membranes (DMs) 13,14 and nanodiamonds (NDs) 15 are mainly used.Currently, negatively-charged nitrogen vacancies (NV − ) 16 and silicon vacancies (SiV − ) 17 are the most studied color centers.While NV − centers show good a) F.F. and R.B. contributed equally to this work.b) Corresponding author: alexander.kubanek@uni-ulm.despin properties and great strides have been made to entangle them, 18 they show poor optical access, e.g. a low emission in the zero phonon line (ZPL). 19In contrast, group IV defects, with their interstitial doping atom in the diamond lattice, are promising alternative emitters for this concept. 20Among them is the SiV − , which compared to NV − , has superior optical properties with a high Debye-Waller (DW) factor of 0.7. 20 drawback is the technical overhead of mK temperatures, which is required for receiving good spin properties. 21he negatively-charged germanium vacancy (GeV − ) 22,23 is another group IV defect with a heavier impurity atom than the SiV − center.][25] At seven Kelvin, the phonon-induced spin dephasing is exponentially suppressed resulting in good spin properties already below one Kelvin; higher than for the SiV − center. 9,26eside their implementation in diamond waveguides 26,27 the GeV − defect was coupled to photonic resonators 28,29 and to one tunable Fabry-Pérot (FP) cavity. 30With a cavity formed by the end-facet of an optical fiber and a flat mirror with a bonded DM a spectral density enhancement (SDE) of 31 was reported. 30n this work, we demonstrate the transfer of a 200 nm sized ND containing a single GeV − defect with non-blinking and narrow emission to an optical open FP microcavity with a high quality factor by utilizing the pick and place technique with an atomic force microscope (AFM).We realized coupling of the strong ZPL of the GeV − center to the cavity mode, while observing a 48-fold SDE and maintaining a high finesse.In our approach, the ND with the GeV − center is intrinsically aligned with the cavity field, making lateral scanning of the cavity mirror redundant.Therefore, the system is passively very stable with reduced technical overhead.
First, NDs with single GeV − defect centers were grown by high pressure high temperature (HPHT) 31 synthesis under 1,450 • C and 8GPa.In this process, detonation NDs, fluoroadamantane (C 10 H 15 F) and hepta-fluoronaphtalene (C 10 F 8 ) were used as carbon sources.Germanium triphenyl-chloride (GeC 18 H 15 Cl) was added as doping component for germanium.Fig. 1(a) shows a scanning electron microscope (SEM) image of the NDs of varying sizes after the synthesis.Subsequently, the NDs were cleaned by acid boiling and diluted in ultrapure water.After an ultrasonic bath for deagglomeration, the ND solution was drop-casted on a sapphire bulk substrate.The sample was characterized in a confocal microscope (NA = 0.9) at room temperature with an excitation wavelength of 532 nm.NDs with emission from GeV − centers showed a strong ZPL at a median wavelength of (602 ± 2) nm and are presented in fig.1(b).The observed spectral distribution of the ZPL suggests strain in the NDs. 32With a mean FWHM of (1.3 ± 0.3) nm and a distribution between 0.8 -2.2 nm the defects showed narrow linewidths compared to reported values. 23The ND with the identifier GeV-I had good optical properties and was selected for further investigation.Its photoluminescence (PL) is displayed in figures 1(c,d).This color center demonstrated a high and stable emission rate in the ZPL with a high quality factor of  GeV = / = 483 ± 12.
The spectrum shows a small phonon sideband (PSB) with a DW factor above 0.6, which results from different converging evaluations, see supplementary material.At 658 nm and 693 nm emission originated from an unrelated laser and the sapphire bulk, respectively, which was not taken into account for the DW factor.In addition, its saturation curve is illus-trated in fig.1(e) and was fitted with the function The determined values for saturation intensity and saturation power subside the presented data in Ref. 27.To evaluate the properties of the emission signal from the emitter, we performed an autocorrelation measurement under off-resonant excitation.The time resolved correlation without any background correction and with the fitting model can be seen in fig.1(f), for other emitters see supplementary material.A strong anti-bunching of  (2) (0) = 0.11 ± 0.04 was observed.This shows a high rate of emission arising from only a single GeV − center within the ND under green excitation, making this a good candidate for quantum optics experiments and the use as a single photon source.An excited state lifetime of  LT = (2.53 ± 0.20) ns at an excitation power of 60 μW was determined, in agreement with literature. 22ext, the GeV − center containing ND was integrated in the field of the hemispherical FP cavity by placing it in the center of the curved mirror.The concave mirror was fabricated by a CO 2 laser ablation process of a SiO 2 substrate.By creating multiple mirror structures on one substrate, a versatile mirror array could be fabricated.Varying the pulse lengths results Con × ηexc Con )= 2.1 ± 0.4, see supplementary material for complete calculations.This enhancement is attributed to the reflected fluorescence signal of the curved mirror, indicating a beneficial position of the emitter.The 2-fold SDE suggesting efficient emitter coupling indicates that the emitter is located near the electric field maximum, which is estimated to be at a distance of 62 nm from the mirror surface.For characterizing the GeV − center in the cavity, the curved mirror containing the transferred ND and a second plane mirror with the same substrate and coating were assembled and formed the resonator, as illustrated in fig.3(a).After passing a laser clean up filter (600 SP) and the reflection of a dichroic mirror, the excitation laser light (Sirah Matisse 2 DS Dye laser: linewidth below 100 kHz at 600 nm) of a singlemode fiber (IVG Fiber: SM CU600PSC) was coupled into one of the cavity structures with the help of a lens (Asphericon: AHL10-08-P-U-780, f = 8mm, NA = 0.55) mounted to nanopositioners in x, y and z (Attocube ANP series).An additional nanopositioner with z piezo enabled tunability of the cavity length by scanning the plane mirror.The cavity signal and the reflected light passed the lens, the dichroic mirror, a filter (605/15 BP) and were collected by a multimode fiber (Thorlabs: MM FG050LGA) in order to guide it to an APD or spectrometer.The cavity finesse was extracted from the reflection signal by scanning the piezo of the plane mirror, as seen in fig.3(b).
The obtained values were compared to the theoretical possible finesse given by the coating limit in fig.3(c).The cavity maintained a high finesse close to the coating limit.One could receive a maximum finesse of F > 10,300 at 601 nm, while in the measurements a value of F = 7,700 ± 1,800 was achieved.
Comparing the finesse at 648.6 nm before F = 4,100±600 and after F = 4,000 ± 800 placing the ND in the cavity showed no significant losses due to reduced scattering of the small sized nanoparticle.
With an excitation wavelength of 587.8 nm the cavity modulated ZPL signal of the single GeV − center was detected, as shown in fig.3(d).With the signal of the emitter at 599.2 nm and the excitation wavelength at neighboring resonances of the resonator, a cavity length of  = (15.72 ± 0.06) μm was determined.Considering the RoC of (25 ± 5) μm, this resulted in a beam waist on the flat side of  0 = (1.5 ± 0.2) μm and on the curved side of () = (2.5 ± 0.6) μm.From this a mode volume of  =  4  2 0 = (140 ± 40)  3 Las followed and with the finesse of F = 5,000 ± 1,200 at the emitter wavelength the quality factor of the cavity was evaluated to  Cav = 260,000 ± 60,000.Finally, these parameters of the cavity enabled calculating the Purcell-factor with and the refraction index  air = 1, giving the values P flat = 152 ± 56 on the flat side and P curv = 57 ± 29 on the curved side.
However, this enhancement is only achieved for  Cav <  GeV , which was not the case for our room temperature experiments due to thermal broadening of the emitter. 35Therefore, the corrected formula for the Purcell effect is given by yielding the corrected values P * flat = 0.28 ± 0.03 on the flat side and P * curv = 0.12 ± 0.02 on the curved side.In order to determine the SDE experimentally, we extracted the SD (470 ± 120) c/(s GHz mW) of the emitter in the microcavity from fig. 3(d) and compared it to the free space emitter from fig. 1(d).We evaluated the altered excitation efficiency ηexc Cav = 11 ± 4 in relation to the confocal microscope setup, which was caused by the finesse of the cavity, a more efficient excitation wavelength 25 and a wider excitation beam at the emitter.The detection efficiency was corrected by a factor of ηdet Cav = 0.45 ± 0.07 due to different optical components.This resulted in a (48 ± 20)-fold SDE, see supplementary material for complete calculations.Considering that the Purcell effect is limited at room temperature, the enhancement can be attributed to cavity funneling.In conclusion, we demonstrated the assembly of a tunable and versatile cavity system containing a single GeV − inside one ND.The ingrown GeV − defect center showed strong, stable and narrow emission in the ZPL with a small PSB yielding a DW of above 0.6.With a  (2) (0) value of 0.11 ± 0.04 it proved to be a high purity single photon source.The small size of the ND enabled integration into the optical resonator mode without significant scattering losses, maintaining a high quality factor  Cav above 250,000.The nanomanipulation capabilities allowed highly accurate alignment of the precharacterized ND with GeV − center to the cavity field.With this integration into the open, fully tunable FP microcavity photoluminescence measurements could be performed under off-resonant excitation at room temperature, taking advantage of the single emitter emission.We calculated a 48-fold SDE of the emitter and retained a high finesse of F = 7,700 including the nanoparticle.
The passively stable platform, with a mode volume V of (140 ± 40)  3 Las , does not require additional lateral scanning of the cavity mirror, profits from a low thermal expansion due to the main setup material choice of titanium, and allows for remote realignment with the nanopositioners.Altogether this offers robustness even at cryogenic temperatures. 15Cooling this platform to low temperatures, as shown in earlier work with SiV-centers, 15 offers a decreased thermal broadening of the emitter towards the FT limit, which suggests an increased Purcell effect of P > 50.In combination with improved coherence of the emission into the ZPL, this results in a higher spectral enhancement of the signal out of the cavity.In order to receive access to a quantum memory, spin access would be a desirable next goal to establish an efficient spin photon interface.With those advances this hybrid microcavity system is a robust and promising approach for many quantum optic applications such as a quantum repeater node.

SUPPLEMENTARY MATERIAL
For additional information on the DW factor, additional autocorrelation measurements for other NDs, nanomanipulation of the ND, and comprehensive calculations of the spectral density enhancement, please refer to our supplementary material.

II. AUTOCORRELATION MEASUREMENTS
The sample from which ND GeV-I was taken also contained further NDs with single defects e.g.ND GeV-II and ND GeV-III.Their autocorrelation measurements under offresonant excitation are depicted in figure S2  Time delay τ (ns) Time delay τ (ns) g (2) (τ) Off-resonant autocorrelation measurements without background correction.

III. NANOMANIPULATION OF NANODIAMONDS
The employed pick and place technique used here is comparable to earlier works: Fehler et al. 1 transfer of a SiV-ND to a photonic crystal cavity) and Bayer et al. 2 transfer of a SiV-ND to a focused ion beam milled cavity structure).
To scan and identify the NDs before the transfer we used a platinum cantilever (tip: HQ:NSC15/Pt).The selected ND could be picked up using contact mode.Having the ND attached to the cantilever and the upper mirror mount with the CO 2 fabricated cavity structures mounted inside the AFM the structures could be located by scanning in contactless tapping mode.From this imaging the center of the cavity structure could be identified, where the ND was then placed.For a more precise (AFM resolution) positioning of the ND contact nanomanipulation was used to push the ND with a low-adhesion cantilever (tip: 160AC-NA).AFM nanomanipulation of the ND was performed with the help of the JPK nanomanipulation toolbox.
With a ND centered in the cavity mirror we then align our optical cavity on a maximized TEM00 mode in order to overlap the positioned ND with the cavity field.
The presented universal cavity integration can be carried out for other ND and other nanoparticles from different fabrication methods.Advancements in the production methods, such as employing ND growth under lower growth temperatures, 3 or ion implantation 4 could enable small (sub-50 nm) NDs containing single, spectral stable GeV − center in the future.Therewith, the finesse could be increased signifi-arXiv:2307.00916v2[physics.optics]30 Nov 2023 cantly.We analyzed the spectra of ND GeV-I in figures 1(d), 2(f) and 3(d) of the main manuscript, which were acquired in confocal microscope setups I, II and the cavity setup, respectively.The SDs of each spectrum were extracted and the total excitation and detection efficiencies ( exc ,  det ) of each setup were determined, see table S1 For the SD, the FWHM at the confocal configurations were obtained by the Lorentzian fit of the ZPL.The FWHM of the cavity configuration was given by FWHM = FSR / F with FSR = c / 2L and F at the emitter.The total excitation efficiency includes the ratio of the emitter area and the beam area, the relative efficiency of different excitation wavelengths 5 and the effective excitation power by weighting the finesse.The detection efficiency takes the transmission of every optical component of the three different setups into account.

FIG. 2 .
FIG. 2. Assembly of an FP-resonator with a GeV − center containing ND.(a) Microscopic image of the mirror containing the curved structure (circled white) intended for the ND.(b) Confocal scan and AFM images of NDs showing GeV-I.(c) Schematic illustration of the pick and place technique for placing NDs inside a mirror structure using the AFM cantilever.(d) Tilt subtracted AFM image of the spherical mirror containing the transferred ND GeV-I in its center with respective cross sections in x-and y-directions.(e) Confocal scan image of the spherical mirror containing the same ND in its center after transfer.(f) PL of ND GeV-I in the mirror structure with a ZPL at (599.25 ± 0.03) nm and a FWHM of (1.10 ± 0.04) nm using an excitation power of (20 ± 2) μW.

FIG. 3 .
FIG. 3. Characterizing the assembled cavity with a GeV − ND.(a) Schematic illustration of the operated optical microcavity setup.(b) Exemplary finesse measurement showing the reflected laser signal over the z piezo voltage of the flat mirror corresponding to the cavity length.(c) Possible finesse values of the microcavity determined by the transmission of the coating compared to the measurement with the ND inside the cavity.(d) PL of resonance n = 51 of the optical microcavity with an excitation wavelength of 587.78 nm and excitation power of (80 ± 12) μW.The spectrum (spectrometer resolution of 0.03 nm) shows a cavity modulated signal of the GeV − with a peak of emission at (599.20 ± 0.03) nm.

10
Photoncounts (c/s) and show antibunching.It can be concluded that the emission of these NDs is dominated by single GeV − centers with lifetimes ranging between  = 1.3 − 5.8 ns.a) F.F. and R.B. contributed equally to this work.b) Corresponding author: alexander.kubanek@uni-ulm.de

TABLE S1 .
SDE calculations of ND GeV-I including different setup efficiencies.For better comparison the enhancements are calculated in respect to the free space emitter.
. From these values, the SDE with respect to Confocal I is given by