Striving for nanometer-sized solid-state single-photon sources, we investigate atom-like quantum emitters based on single germanium-vacancy (GeV) centers isolated in crystalline nanodiamonds (NDs). Cryogenic characterization indicated symmetry-protected and bright (>106 counts/s with off-resonance excitation) zero-phonon optical transitions with up to 6-fold enhancement in energy splitting of their ground states as compared to that found for GeV centers in bulk diamonds (i.e. up to 870 GHz in highly strained NDs vs. 150 GHz in bulk). Utilizing lithographic alignment techniques, we demonstrate an integrated nanophotonic platform for deterministic interfacing plasmonic waveguides with isolated GeV centers in NDs, which enables 10-fold enhancement of single-photon decay rates along with the emission direction control by judiciously designing and positioning a Bragg reflector. This approach allows one to realize the unidirectional emission from single-photon dipolar sources, thereby opening new perspectives for the realization of quantum optical integrated circuits.
Efficient interfaces between single atoms and single photons are essential ingredients for building quantum optical networks, where atomic nodes (quantum emitters) are linking together via flying photons (qubits) , . The key challenge here is to engineer atom-photon interactions in order to have control over individual quantum emitters on a large scale. Combining isolated atoms with nanophotonic systems is a powerful approach to strongly enhance the atom-photon interaction due to a large cooperativity associated with nanoscale photonic devices, although trapping atoms in tightly focused laser beams (optical tweezers) imposes serious technical challenges , , . Alternatively, an all solid-state approach has been developed, in which naturally trapped “atoms” (e.g. quantum dots) are coupled, created, and multiplexed on a single chip . Despite the progress made for deterministic positioning of quantum dots on a single chip , , , , some challenges remain due to a relatively short coherence time available with quantum dots (in nanosecond range) , resulting in the quantum information being typically lost before reaching distant quantum nodes. Further search for configurations ensuring long coherence times in atomic systems and allowing for scalable implementation in solid-state systems led to the exploration of diamond crystals containing artificial “atoms” (so-called color centers) . Starting with a nitrogen-vacancy (NV) center (i.e. substitutional nitrogen-atom impurity next to a diamond lattice vacant site), remarkable coherence time (in millisecond range)  has been achieved, making it an ideal emitter for spin physics and metrology . However, a lack of symmetry in NV molecular structure severely limits the coherent part of the emission, with the emission to a zero-phonon line (ZPL) being only 4%, and makes the frequency of optical transitions very sensitive to the environment. Replacing nitrogen with larger atoms of group IV in the periodic table (e.g. with a silicon atom that is ~1.5 times larger in size than a carbon atom) enabled circumventing the issues associated with symmetry arguments , , , , ,  (see Figure 1A). The defect atom in group IV (silicon, germanium, tin, or lead) is placed between two diamond lattice vacant sites, resulting in a split-vacancy color center [silicon vacancy (SiV), germanium vacancy (GeV), tin vacancy (SnV), or lead vacancy (PbV)] with spectral stability as a result of its inversion symmetry. This opened a way toward demonstrations of indistinguishable solid-state quantum emitters (without the need for electric field tuning) with spectral stability and large ZPLs . However, the efficiency of photon outcoupling from diamond color centers in bulk crystals is limited (due to a high refractive index of diamond), as mentioned before in Refs. , , , , , , , , .
Progressing toward bright and efficient nanometer-sized solid-state single-photon sources, we here report on the first characterization of individual GeVs in nanodiamonds (NDs) at low temperatures, allowing us to resolve four zero-phonon transitions and actually characterize the ground-level splitting (unlike our previous work at room temperature  and other low-temperature results with GeV in bulk diamonds , , ). Additionally, this is the first demonstration that the dielectric-loaded surface plasmon polariton waveguide (DLSPPW) platform survives cooling to low temperatures, which is not trivial at all because of the different materials in this platform. The usage of gold crystals was also dictated by the necessity to conduct low-temperature experiments taking a much longer time. Cryogenic characterization indicated symmetry-protected and bright (>106 counts/s with off-resonance excitation) zero-phonon optical transitions featuring remarkable energy splitting in their ground states, up to 870 GHz, which is ~6 times larger than that in bulk diamonds. The large energy splitting in the ground state implies a potentially longer spin coherence due to the suppressed phonon-mediated transitions between the lower and upper branches , . This opens new perspectives for deterministic interfacing of isolated atoms with photons along with merging quantum emitters with highly confined surface plasmons in metal-based nanostructures , , , . Utilizing lithographic alignment techniques , , , , we demonstrate an integrated nanophotonic platform for deterministic interfacing plasmonic waveguides with isolated GeV centers in NDs, which enables 10-fold enhancement of single-photon decay rates along with the emission direction control by judiciously designing and positioning a Bragg reflector. This approach allows one to realize the unidirectional emission from single-photon dipolar sources, thereby opening new perspectives for integrated quantum nanophotonics.
2 Results and discussion
Imitating the natural formation of diamonds underneath the earth, diamond crystals were grown at the nanometer scale, under a high-pressure high-temperature (HPHT) condition, and Ge defect atoms were added during the growth in a hydrocarbon metal catalyst-free system based on homogeneous mixtures of naphthalene C10H8 with tetraphenyl germanium C24H20Ge (see details in Supplementary Section 1). Cryogenic characterization shows symmetry-protected optical transitions for the synthesized GeV centers in NDs (see Figure 1A, C), following the reported trend for bulk diamonds , , , . Furthermore, ZPLs indicate a large splitting in the ground state (up to 870 GHz), which is ~17 times larger than SiV  and ~6 times larger than GeV in bulk , , , becoming close to SnV with 850 GHz  (see Figure 1D). It has already been demonstrated that the strain environment can mitigate the effect of thermal phonon bath on a diamond spin qubit and eventually suppress phonon-induced decoherence without lowering the operating temperature . Our results for GeV centers represent the first step in this direction, showing a significant enhancement in the ground-state splitting under the inherently forced tensile strain in NDs. The results can open the way toward further investigation, e.g. use of a nano-electro-mechanical system device , in order to have higher control over the strain conditions and thereby allow for engineering of electron-phonon interaction in GeV centers. Power dependency measurements at low temperatures (shown in Figure 1B) exhibit ultrabright single-photon count rates (~2×106 counts/s, an approximated value at saturation) at ZPLs (i.e. excluding phonon sideband) with clean single-photon emission [strong antibunching dip of g2(0)=0.06, where g2(0) is the autocorrelation function at zero-delay time]. Compared with the brightness of GeV in bulk diamond reported by Iwasaki et al. , a significant (15-fold) enhancement in the brightness is achieved, from 170,000 counts/s in bulk to 2 million counts/s in ND. This increase can be attributed to the circumstances that nanometer-sized NDs would not suffer from the emission loss due to the total internal reflection at diamond-air interfaces and that the Purcell enhancement from GeV emitters coupling to SPPs supported by the air-gold interface further increases their brightness. The measurements performed for another GeV-ND, resulting in 1.3 million counts/s for 1000 μW laser power (see Supplementary Figure 19S), are consistent in the saturation with the measurements shown in Figure 1B. Deterministic loading of dielectric nanostructures on colloidal gold crystals enabled trapping a preselected ND at a plasmonic hot spot for realizing a sustainable nanoplasmonic platform for integrated quantum photonics. This introduces a powerful approach, alternative to the current deterministic techniques – atomic force microscope (AFM) manipulation , site-controlled and strain-induced excitation , in situ cathodoluminescence lithography , and optical trapping ,  – to improve the level of control on coupling and, at the same time, to facilitate scalable fabrication (see Figure 2).
In the experiment, colloidal gold crystals were grown on a silicon substrate using a thermolysis synthesis technique  (see details in Supplementary Section 2). Lithographic alignment markers were made on top of (and nearby) the gold crystals, and NDs were deposited on the substrate afterwards. The sample was then loaded on the cold finger of a continuous-flow helium cryostat, which was cooled to 4.7 K for confocal microscopy measurements (see Section 4.2). A fluorescence image was taken from a crystalline gold flake on which NDs containing single GeV centers were deposited (see Supplementary Figure 4S for the corresponding confocal image). A single GeV emitter was selected based on fluorescence spectrum measurements, and its location was determined with respect to the markers. Utilizing lithographic alignment techniques , , , , we fabricated a waveguide-mirror configuration with reflecting Bragg gratings (RBGs), where the preselected ND is embedded in the waveguide. Realization of the unidirectional coupler requires implementing the waveguide-emitter coupling exactly at the specific constructive interference point (at the distance of the second constructive point of the RBG mirror, i.e. d=3λn/4, where λn is the wavelength of the plasmonic mode ), as shown in Figure 2A and B. This means that a higher degree of accuracy is needed for the deterministic realization of the device. Without such determination, the emitter may be placed at the destructive interference points (d=iλ/2ne, i=1, 2, …, n) for which the emission rate is becoming suppressed by a factor of (1−R)2, instead of being empowered by (1+R)2, where R represents the reflectance of the RBG mirror (see Supplementary Figure 18S).
A scanning electron microscopy (SEM) image of the fabricated device is shown in Figure 3A. Excited with the green laser (λ=532 nm), the fluorescence light was collected from the excitation point (GeV-ND) and away of it within several micrometers using a galvanometric scanning mirror. The result is illustrated in Figure 3B, showing two spots, one from the excited GeV emitter and the other from the grating output at the end (outcoupler). This indicated coupling of GeV emission to the waveguide mode (DLSPPW mode) of the unidirectional SPP device. Plasmonic decay (Γpl/Γ0) of GeV emission to the fundamental transverse magnetic (TM) mode of the DLSPPW is maximized for the emission transition dipole moment oriented perpendicular to the gold plane (z-axis), as shown in the simulation results in Supplementary Figure 16S. The results indicate that ~85% of the plasmonic decay is due to the coupling of this transverse out-of-plane dipole to the DLSPPW mode [Figure 16S(b)-left]. There is also an ~14% contribution from the longitudinal dipole oriented along the waveguide axis, i.e. along the x-axis [Supplementary Figure 16S(c)-left], while there is almost no contribution from the transverse in-plane, i.e. along the y-axis, dipole [Supplementary Figure 16S(d)-left]. These differences are dictated by the DLSPPW mode polarization content , , so that the main DLSPPW mode power contribution originates from the emission dipole component, which is perpendicular to the sample surface (i.e. the projection of the dipole source on the z-axis). To compare with the experimental observations, we implemented the far-field projection to simulate the far-field images observed by a microscope with 0.95 numerical aperture (NA) (as discussed in Section 4.4). The results indicate that the electric dipole source that is oriented along the z-axis [see Supplementary Figure 16S(b)-right], i.e. the transverse out-of-plane dipole, is the one that is the strongest coupled to the fundamental DLSPPW mode (because the transverse out-of-plane electric field component of the fundamental DLSPPW mode is the strongest one), producing a visible spot at the outcoupling grating, while the contributions of other two dipoles are negligible [no outcoupled spots are seen in Supplementary Figure 16S(c,d)-right]. In the simulations, for each dipole source with a specific polarization component, we plot all polarization components of the generated far-field distributions.
Fluorescence spectra taken from the embedded GeV-ND at the center and from the output grating at the waveguide end are shown in Figure 4A and B, respectively. For this ND, all four ZPLs have been merged together and appeared as a single line at 605 nm. The merging of the ZPLs observed in this experiment (Figure 4) is not really understood; however, the stability of the line for elevated temperatures (shown in Supplementary Figure 7S) and the room-temperature measurements (with no bleaching or blinking) confirm that the observed emission line should indeed be ascribed to an individual GeV center in this particular ND. The ZPL shift, from 602 to 605 nm, in this sample can be explained by the occurrence of the isotopic substitution of the impurity atom and specific isotopic compression of the carbon lattice, as discussed in Ref. . These isotopic shifts of the ZPLs have also been reported for SiV centers (see, e.g. Ref. ). Lifetime measurements before and after structure fabrication indicate a 5-fold lifetime shortening from 11.2 ns (Figure 4C, ND on gold flake) to 2.3 ns (Figure 4D, ND embedded in device). The lifetime data were analyzed by a single exponential fit with a fast decay within the first few nanoseconds of the data being excluded in the fitting, as these are related to background fluorescence. Considering an additional 2-fold lifetime reduction due to the metal layer  (see Supplementary Section 11), we estimated a 10-fold enhancement in the total decay rate of the GeV emitter, a remarkable record due to the interaction with the unidirectional SPP coupler (see Supplementary Figure 5S–11S for further details and additional experiments). Furthermore, we demonstrated another experiment with a single NV center for which the periodicity of the RBG was tuned for NV ZPL (637nm), and we see a 6-fold lifetime shortening (from 26.3 to 4.3) for the coupled NV, as shown in Supplementary Figure 8S(i), indicating a 12-fold decay rate enhancement in total (due to the additional 2-fold reduction for the metal layer).
In order to verify the properties of the unidirectional SPP coupler, we performed scanning near-field optical microscopy (SNOM) measurements with a titanium sapphire laser source (wavelength 775–1000 nm). To experimentally evaluate the reflectance of the RBGs, the periodicity of the Bragg grating was scaled up from 240 nm (designed for the GeV ZPL) to 380 nm (designed for λ=850 nm) in order to increase the central Bragg wavelength to those available in our SNOM setup. Because our SNOM is operating in a transmission configuration with sample illuminated from below, a grating was fabricated in the gold layer for efficient excitation of plasmonic mode (see schematic in Figure 5A and details in Section 4). An SEM image of the fabricated device and an AFM image of the excitation point are shown in Figure 5B and C, respectively. The RBG mirror period was modified to produce strong back-reflection at the central operating wavelength (Figure 5D, λ=850 nm), while no reflection was observed outside the TM bandgap (Figure 5E, λ=1000 nm). Mode parameters (effective mode index, propagation length, and reflection coefficient) were extracted from near-field maps, obtained for different laser wavelengths, using a simple fitting procedure , ,  (see Supplementary Figures 13S and 14S). The resulting SNOM measurements indicate ~80% reflectance from the RBG mirror (Figure 5G).
Adding a Bragg reflector to the end of the waveguide has a great potential to enhance the Purcell factor further up to (1+R)2 times (in addition to the enhancement associated with the plasmonic waveguide itself), where R denotes the reflectivity. For the Bragg reflector with 80% reflectivity (as measured in our near-field setup) and the emitter located at the constructive interference node, one can estimate an ~3.25 times Purcell enhancement in addition to the enhancement achieved due to the plasmonic waveguide system (see Supplementary Figure 18S). As mentioned already in the article, the main advantage of GeV centers (and in general group IV color centers) is their structural symmetries leading to indistinguishability of photons emitted from different emitters. Our cryogenic measurements clearly show that the zero-phonon optical transitions for the synthesized GeV centers in NDs are indeed protected by inversion symmetry (see four-line fine structure in Figure 1A) and therefore have a great potential to create indistinguishable or “coherent” photons. Furthermore, our achievement in Purcell enhancement by using a deterministic emitter-waveguide interface at plasmonic hot spots (constructive nodes) of the Bragg reflector is one of the important steps needed for realizing the plasmonic speed-up strategy for overcoming quantum decoherence. The plasmonic speed-up approach is a new technology trend aiming to enhance the light-matter interaction and thereby shorten the spontaneous emission time in quantum emitters, so that it would eventually outpace fast quantum decoherence rates in matter and beat the dephasing time (see, e.g. the recent perspective paper by Bogdanov et al. published in Science ).
GeV centers in diamond nanocrystals have been investigated at low temperatures, indicating symmetry-protected and ultrabright (2×106 counts/s, an approximated value at saturation) zero-phonon optical emission. A large energy splitting of 870 GHz in the ground state has been determined for the GeV centers in highly strained ND samples, which is ~6 times larger than that in bulk diamonds. An integrated crystalline gold-based nanophotonic platform has been realized, on which optical centers in NDs interface with highly confined SPP modes in a unidirectional manner, resulting in remarkable Purcell enhancements (10-fold enhancement for GeV-ND and 12-fold for NV-ND). The unidirectional interaction enables efficient guiding control of the emitted single photons, revealing the potential of our approach for realizing on-chip quantum optical network.
4.1 Device fabrication
Direct e-beam writing was performed using a negative-tone electron-beam resist composed of 6% solution of hydrogen silsesquioxane (HSQ) diluted in methyl isobutyl ketone solvent [XR-1541-006 (6%), Dow Corning, MI, USA]. Using a standard spin-on coating equipment, HSQ was deposited on the substrate at a speed of 1200 rpm (1 min), and subsequently the solvent was boiled off during a hotplate bake process (170oC, 2 min). This resulted in a 180-nm film on gold crystal flakes. Using a single exposure tool with 30-keV beam energy and area doses from 400 to 700 μC/cm2, the HSQ film was patterned, with capability to define features as small as 6 nm, and nanoridge waveguides were defined and accurately positioned onto preselected NDs, whose locations were determined with respect to the specifically designed and prefabricated alignment markers. Then, the HSQ film was developed in tetramethylammonium hydroxide (25 wt.% solution in water, Sigma-Aldrich, MO, USA), a standard aqueous base developer (see further details in Supplementary Figure 5S). After the development, HSQ turned to silicon dioxide (SiO2).
4.2 Cryogenic measurements
The sample was mounted on the cold finger of a continuous-flow helium cryostat, which was cooled to 4.7 K for imaging with a home-built confocal microscope (see details in Supplementary Figure 3S). Experimental control was provided by the Qudi software suite . The GeV centers were off-resonantly excited by linearly polarized 532-nm green laser to map the fluorescence of GeV ZPL. A band-pass filter (599/13 nm) was placed in front of the avalanche photodiode. Spectra were measured after a 560-nm long-pass filter (Supplementary Figure 3S).
Near-field investigation was performed using commercial AFM-based scattering-type SNOM (NeaSpec, Munich, Germany). In this setup, used in transmission mode, the sample was illuminated normally from below (focused by a bottom parabolic mirror with NA ~0.3) using a tunable continuous-wave Ti:sapphire laser (wavelength 775–1000 nm, Spectra Physics, MA, USA). The illumination was coupled into the waveguiding SPP mode by means of a grating in the gold layer. The sample was scanned in a non-contact mode by a commercial Pt-coated AFM tip (Arrow-NCPt from NanoWorld, Neuchâtel, Switzerland), which acts as a scatterer of the near field. The tapping amplitude and frequency were ~60 nm and Ω ~250 kHz, correspondingly. The tip’s scattered light was collected by a top parabolic mirror (NA ~0.7) and forwarded toward a photodetector. In order to resolve both amplitude and phase, a Mach-Zehnder interferometer was integrated into our setup, in which the optical path difference was modulated by an oscillating mirror in the reference arm (frequency f ~300 Hz). The detected signal was then demodulated using a pseudo-heterodyne detection method  (see further details in Supplementary Figure 12S–14S).
4.4 Numerical simulations
Finite-difference time-domain (FDTD) simulations were performed using a commercial software (FDTD Solutions v8.11.318, Lumerical, Vancouver, BC, Canada). Perfectly matched layers were applied to enclose the computational domain of 8.5 μm×3 μm×2 μm in all calculations. The finest mesh grid size of 5nm was used in the simulations. The optical constants of the gold were taken from the experimental data reported by Johnson and Christy . To mimic the experimental conditions, we utilized an electric dipole oriented along different directions to excite the propagating mode in the waveguide. The distance between the dipole and the RBG mirror was set as d=3λn/4 for an efficient unidirectional excitation while the height of the dipole was set to 30 nm. To compare with the experimental observations, we implemented far-field projection to simulate the far-field images observed by a microscope with NA 0.95  (see Supplementary Figure 16S). We added further simulations in order to mimic the experimental conditions at cryogenic temperatures. Cooling to cryogenic temperatures allows one to suppress the SPP propagation losses due to the reduction in the collision frequency of free electrons, as discussed in Supplementary Section 14.
This work was supported by the European Research Council (ERC), Advanced Grant 341054, Funder Id: http://dx.doi.org/10.13039/100010663 (PLAQNAP). FJ acknowledges support of the DFG, BMBF, VW Stiftung, and EU (ERC, DIADEMS). VAZ, SB, and NAM acknowledges support of VILLUM FONDEN (grant no. 16498). VAD and LFK thank the Russian Foundation for Basic Research (grant no. 18-03-00936) for financial support. AK acknowledges support of the DFG, the Carl-Zeiss Foundation, IQST, and the Wissenschater-Ruckkehrprogramm GSO/GZS.
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© 2020 Hamidreza Siampour et al., published by De Gruyter, Berlin/Boston
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