Low charge-noise nitrogen-vacancy centers in diamond created using laser writing with a solid-immersion lens
Viktoria Yurgens, Josh A. Zuber, Sigurd Flågan, Marta De Luca, Brendan J. Shields, Ilaria Zardo, Patrick Maletinsky, Richard J. Warburton, Tomasz Jakubczyk
LLow charge-noise nitrogen-vacancy centers in diamond created using laser writingwith a solid-immersion lens
V. Yurgens, J. A. Zuber, S. Fl˚agan, M. De Luca, B. J. Shields, I. Zardo, P. Maletinsky, R. J. Warburton, and T. Jakubczyk
1, 2, ∗ Department of Physics, University of Basel, CH-4056 Basel, Switzerland Faculty of Physics, University of Warsaw, 02-093 Warsaw, Poland
We report on pulsed-laser induced generation of nitrogen-vacancy (NV) centers in diamond facil-itated by a solid-immersion lens (SIL). The SIL enables laser writing at energies as low as 5.8 nJper pulse and allows vacancies to be formed close to a diamond surface without inducing surfacegraphitization. We operate in the previously unexplored regime where lattice vacancies are createdfollowing tunneling breakdown rather than multiphoton ionization. We present three samples inwhich NV-center arrays were laser-written at distances between ∼ µ m and 40 µ m from a diamondsurface, all presenting narrow distributions of optical linewidths with means between 61.0 MHz and78.3 MHz. The linewidths include the effect of long-term spectral diffusion induced by a 532 nmrepump laser for charge-state stabilization, thereby emphasizing the particularly low charge-noiseenvironment of the created color centers. Such high-quality NV centers are excellent candidatesfor practical applications employing two-photon quantum interference with separate NV centers.Finally, we propose a model for disentangling power broadening from inhomogeneous broadening inthe NV center optical linewidth. I. INTRODUCTION
The negatively charged nitrogen-vacancy (NV) centerin diamond is among the most promising solid-state sys-tems implementations of a quantum bit [1, 2]. Its appli-cations include sensing [3, 4] and quantum communica-tion, with progress demonstrated in spin-photon [5] andlong-distance spin-spin entanglement [6]. However, in-terconnecting many NV centers for large-scale quantumnetworks suffers from the low generation rate of indistin-guishable photons from individual NV centers [6].Fabrication of any diamond-based photonic device re-quires structuring of the diamond on a sub-micron scale.An example is the open Fabry-Perot microcavity – a plat-form enabling easy optical access, mode-matching and insitu tuning of the cavity resonance to an emitter [7–10].In this case, bulk diamond is thinned down to a few-micron-thick membrane, a minimally invasive fabrication[11–16]. The technique is a promising route to enhanceradically the generation rate of indistinguishable photonsfrom individual NV centers. However, even such minimalprocessing has so far resulted in degradation of the NVcenters’ optical quality, manifested in a large spectral dif-fusion [13, 17]. The random spectral fluctuations in thezero-phonon line (ZPL) frequency are caused by chargenoise present in the structured crystal: NV centers ex-hibit a large change in the static dipole moment betweenthe ground- and excited state [18], making the ZPL emis-sion frequency strongly dependent on the local electricfield [19]. The electric field in turn depends on the spatialconfiguration and occupation of the surrounding chargetraps in the form of defects and impurities. Methods ofNV center creation that do not result in the formation of ∗ [email protected] parasitic defects and impurities are therefore desired.The creation of an NV center typically involves displac-ing a carbon atom from its lattice site to create a vacancy.This occurs above a threshold energy of 35 eV [20]. Whileproximity to the surface is required for photonic appli-cations, it is at the same time desirable to form the NVcenters at a depth of at least tens of nanometers from thediamond surface in order to minimize the impact of thesurface charge- and magnetic-noise on the NV centers’spin- and optical coherence. The challenge is thereforeto provide this energy inside the crystal lattice. Elec-trons or ions with kinetic energies far above keVs readilyprovide such an energy to depths from a few nanometersto tens of micrometers and above in the case of electrons[21]. However, most of this energy is released via colli-sions on the particle’s trajectory, leaving extended dam-age and presumably hard-to-anneal vacancy complexes.A widely employed technique to create NV centers atprecisely controlled depths consists of nitrogen-ion im-plantation followed by high-temperature annealing [22].The technique is well suited for creating NV centers forsensing applications [23, 24], but has recently been shownto create NV populations where approximately half ofthe NV centers show spectral diffusion above a few GHz[25, 26]. In addition, the NV centers formed from theimplanted nitrogen ions have on average much pooreroptical quality than their counterparts formed from thenative nitrogen [25, 26], suggesting that vicinity to thefabrication-related damage plays a crucial role for thespectral diffusion.Typically, the inhomogeneously-broadened linewidthdistribution in unprocessed bulk samples irradiated byions or electrons is characterized by linewidths on theorder of 100 MHz [17, 25, 26], disregarding half of thepopulation with above-GHz linewidths for the nitrogen-implanted samples. After thinning the samples down toless than a micron by reactive ion etching, most of the a r X i v : . [ phy s i c s . op ti c s ] F e b observed NVs are characterized by > ∼
13 MHz [29], far below typical inhomogeneouslinewidths. However, in a resonant microcavity, the Pur-cell effect strongly reduces the lifetime, thereby increas-ing the lifetime limit. Nevertheless, in current devices,the inhomogeneous broadening is still higher than thePurcell-enhanced homogeneous linewidth [13]. Radicalprogress in improving the emitter properties or micro-cavity properties, ideally both, is therefore required.A recent study demonstrated progress in obtainingNV centers with linewidths of approximately 200 MHz in3 . µ m-thick diamond membranes [17]. In even thinnerstructures, linewidths down to 250 MHz were reportedwith a new approach based on implanting nitrogen af-ter micro-structuring [26] and also in samples structuredwith a slow etching procedure [30]. To the best of ourknowledge, narrower linewidths than these have neverbeen reported in micron-thick diamond. The origin ofthe decrease in the NV centers’ optical quality is poten-tially related to the damage caused to the crystal latticeduring implantation and etching, but the microscopicsare not well understood. The lack of optically coherentNV centers in structured diamond clearly points to theneed for improved NV creation methods.Laser writing has emerged as a promising techniquefor creating deterministically positioned NV centers indiamond [32] and other color centers in various wide-bandgap materials [33–37]. NV centers created throughlaser writing in ultrapure diamond are characterized bylong spin coherence times, low spectral noise and highcharge stability [32]. Crucially, their fabrication inducesminimum damage to the diamond lattice, potentially re-ducing the charge noise in thin diamond membranes.These NV centers are formed from native nitrogen atomsand implantation is avoided completely, meaning that thelattice is damaged only locally in the laser focus.Initial studies demonstrated laser writing of NV cen-ters using an oil-immersion lens in combination withwavefront correction [32, 38]. Here, we report on a differ-ent approach employing a standard air objective togetherwith a solid-immersion lens (SIL), giving a high numeri-cal aperture (NA) together with minimized aberrations,yielding a diffraction-limited laser focal volume inside di-amond. This technique not only enables creation of NVcenters with low pulse energies, but also makes it possibleto laser-write in close proximity to the diamond surfaceowing to the decreased laser intensity at the diamond-airinterface. We demonstrate the high quality of the NVcenters created with this method, with a record-low noisemeasured in the presence of a charge-state reinitializationpulse, and determine separately the inhomogeneous andpower-broadening contributions to the ZPL linewidths. a bc dn=1 n=2.42 n=1 n=2.42n=2.14 ∆ x ∆ z d FIG. 1. Geometrical optics simulation of the spread of rayson focusing through an air-diamond interface. (a) Sphericalaberration for rays passing from air (left) to diamond (right)without corrective optics. ∆ x is the in-plane focal spread and∆ z is the focal spread along the optical axis; d is the dis-tance from the point of minimum ∆ x to the diamond surface.(b) Spherical aberration for rays passing from air to diamondthrough a truncated hemispherical solid-immersion lens (t-SIL). (a,b) were calculated using the tool from Ref. 31. (c)Calculated focal spread in plane (solid lines) and along the op-tical axis (dashed lines) for the cases without a SIL and witha t-SIL on passing through an air-diamond interface, as afunction of the focusing depth d . (d) Calculated focal volumeversus d without and with a t-SIL. (c) and (d) take a t-SILtruncation of 30 µ m and an NA of 0.6. In (d), the diffractionlimit is estimated as (∆ x ) ∆ z with ∆ x = 1 . λ/ ( n NA) and∆ z = 2 . λ/ ( n NA ), with n = 2 . II. LASER WRITING OF NV CENTERS
Laser writing of NV centers is based on irradiation ofa diamond sample with single high-energy femtosecondpulses. The laser pulses create vacancies; NV centersform in a subsequent thermal annealing step in whichthe mobile vacancies combine with nitrogen impuritiesin the diamond. Photo-induced damage in a transparentwide-bandgap material such as diamond requires the gen-eration of excited free electrons through nonlinear mecha-nisms. This optical breakdown can result from tunnelingor multi-photon absorption followed by avalanche ioniza-tion in the volume of the tightly focused laser beam [39–41]. These processes displace single atoms locally and cancreate vacancies. In diamond, vacancy creation can beidentified by the vacancy’s spectral signature GR1 [42].The dominant mechanism for the creation of the ener-getic seed electrons responsible for the optical breakdowncan be determined using the Keldysh parameter [43] γ = ωe (cid:114) m eff cn(cid:15) E g I (1)where ω is the angular frequency of the laser, I the laserintensity per unit area, m eff the electron effective mass, c the speed of light in vacuum, n the linear refractive in-dex of the material, (cid:15) the vacuum permittivity, and E g the direct bandgap of the material. For γ <
1, tunnelingbreakdown is the primary process behind the creation ofseed electrons, while for γ >
1, multi-photon ionizationdominates. In the multi-photon ionization regime, owingto the strong nonlinearity of the process [32], the vol-ume in which the atom displacement takes place can bemuch smaller than size of the focal spot. However, duringthe annealing step, the created vacancies diffuse and thisprocess limits the NV placement accuracy, offering a pre-cision down to hundreds of nanometers in initial reports[32, 38]. The laser-written NV centers exhibit a robustcharge state with little need for charge-state repump [32].However, the question remains if the good optical qualityis maintained after processing of the diamond.To minimize the impact of the laser writing process onthe crystal quality, the volume of the laser focus needsto be reduced by maximizing the NA of the focusing op-tics. However, spherical aberration induced at the air-diamond interface (with a refractive index of n = 1 and n = 2 .
42, respectively) also increases with increasing NA.We resolve this dilemma by using a truncated hemispher-ical cubic zirconia SIL (t-SIL) with a refractive index of n = 2 .
14, which both maximizes the NA and reduces thespherical aberrations (Fig. 1(a),(b)).An absolutely crucial problem is that the energy ofthe ultra-short laser pulses required to create vacanciesin bulk diamond typically exceeds the threshold at whichthe diamond surface is degraded [32, 44, 45]. Creatingvacancies in bulk diamond with laser writing is thereforeonly possible if the laser focus is spread over a significantarea at the surface. To investigate this, we consider thecase of imaging a laser with wavelength 800 nm with anobjective lens of NA=0.6 in Fig. 1. In air, the extent ofthe focal spot along the optical axis, ∆ z , is in the bestcase limited by diffraction to a value of approximately3 . µ m. This extent will be preserved approximately onfocusing a few microns below the diamond surface. Thelarge ∆ z is problematic: the intensity at the surface islarge, and as a result, surface graphitization will occurbefore vacancy creation within the diamond. Focusing ata larger depth does not solve this problem. Geometricaloptics shows that the spherical aberrations cause ∆ z toincrease with depth d (Fig. 1(c)) – the focal spot becomesso elongated along z that surface graphitization is likelyto remain a problem. This corresponds to our experience– without a t-SIL, surface graphitization occurred beforevacancy creation. In the limit that the t-SIL is made ofdiamond, spherical-aberration-free imaging is achieved ata depth d which matches the truncation t . Furthermore,the diffraction limit reduces simply because the relevantwavelength is the wavelength in the diamond, λ/n . ForNA= 0 .
64, ∆ z reduces to 1 . µ m. These considerationssuggest that vacancy creation is possible at depths start-ing at about 2 µ m from the diamond surface and it mo-tivates the use of the t-SIL. In practice, the t-SIL has aslightly lower refractive index than diamond (such that a
10 µm c bd 8.45.57.6 E pu l s e ( n J ) Sample B (
10 µm
640 740
Wavelength (nm) C oun t s / s E pu l s e ( n J ) E pu l s e ( n J ) NV - GR1
10 µm
10 µm
10 µm
10 µm kcps30 kcps20kcps1205 00a 7.67.06.65.85.3 E pu l s e ( n J ) Sample A (2.0 μm)
10 µm
10 µm
FIG. 2. (a,b) Confocal scans of samples A and B (indicatingtheir respective NV creation depths and pulse energies) show-ing GR1 photoluminescence (inset in b) at room temperaturebefore annealing. The scans were performed through a t-SIL.(c,d) Confocal scans of samples A and B, showing NV − photo-luminescence (inset in d) at room temperature after annealingto 1100 ◦ C. spherical aberration is introduced at the t-SIL–diamondinterface) and it is impractical to use a different t-SIL foreach depth. We find however that a single t-SIL givesgood imaging out to a depth up to 50 µ m (Fig. 1(c),(d)).The main improvement over imaging without the t-SIL isthe reduction in ∆ z , crucial in order to keep the intensityat the surface small.An additional advantage is that the t-SIL improves thephoton collection efficiency and thereby the sensitivity tothe weak signals emitted by the created vacancies by re-ducing the number of photons lost due to total internalreflection at the diamond-air interface [46–48]. Moreover,the implementation of a t-SIL is both cost-effective andeasily implemented. A limitation is perhaps the writingarea – excellent imaging is achieved only close to the cen-ter of the t-SIL. However, a writing area of approximately25-by-25 µ m is available for a t-SIL with a diameter of0.5 mm, sufficiently large for many purposes.We perform laser writing in a room temperature home-built confocal microscope with a separate injection pathfor the femtosecond pulsed laser. A 532 nm Nd:YAG laseris used for non-resonant excitation of the NV centers.Photoluminescence (PL) is filtered by a longpass filter(Semrock, 594 nm RazorEdge) and collected by an APD(Excelitas, SPCM-AQRH-15-FC) or a liquid nitrogen-cooled CCD camera coupled to a grating spectrome-ter (Princeton Instruments). We use a Spectra PhysicsSpirit 1030-70 femtosecond ytterbium-doped fiber lasertogether with a Spirit-NOPA-2H non-collinear opticalparametric amplifier, which together create pulses at awavelength of 800 nm with a duration of approximately35 fs. A half-wave plate and a Brewster-angle polar-izer are used for tuning the pulse energies. The flatside of a t-SIL (radius 500 µ m, truncation between 0 and50 µ m) is polished using a polishing suspension contain-ing 50 nm-sized alumina particles. The t-SILs are thenplaced on the diamond samples together with an opticalcoupling gel in an attempt to reduce aberrations resultingfrom interface imperfections. In order to achieve resultsclose to what was simulated for NA= 0 . ± . λ √ for the confocalconfiguration (taking NA= 0 . µ m thick, [N] < ◦ C to create NV centers. Surface mark-ers for locating the laser-written arrays after annealingare made through graphitization of the diamond surfaceby increasing the pulsing frequency of the femtosecondlaser to 100 kHz, removing the t-SIL, and increasing theenergy to a value above the graphitization threshold ofthe surface (typically around 10 nJ).Results on two diamond samples are shown in Fig. 2,with arrays of vacancies (a,b) and NV centers (c,d), re-spectively, created with increasing pulse energies fromthe bottom of the arrays. The scans were recorded atroom temperature. The arrays were made at a depthof 2 . µ m and 7 . µ m below the diamond surface, re-spectively, where we note that the former demonstratesthat our method can be used to create NV centers inclose proximity to the diamond surface without induc-ing graphitization. Vacancy creation at shallower depthswas not possible without damaging the diamond surface.This observation aligns with the analysis of the dimen-sions of the focal spot. For sample A, pulse energies of be-tween 4.8 nJ and 7.6 nJ were used, with visible GR1 pho-toluminescence (inset Fig. 2(b), 100 s integration time)appearing for 5.8 nJ per pulse; for sample B, pulse en-ergies between 3.8 nJ and 8.4 nJ were used, with visibleGR1 photoluminescence appearing for 6.1 nJ per pulse.All pulse energies refer to values at the output of themicroscope objective. Both samples were annealed invacuum for three hours at 1100 ◦ C, after which the spec-tral signatures of negatively charged NV centers (insetFig. 2(d), 100 s integration time) were observed.Calculation of the Keldysh parameter γ for thesevacancy-creation threshold energies, with the specifiedpulse duration and focal volume, gives γ (cid:28)
1, mean-ing that we operate in a regime where tunneling break-down is dominant over multi-photon ionization, in con-trast to previous work [32]. Tuning of the vacancy cre- ac xzy xyz z y x E pulse = E d z xyx Sample C (15-30 μm) E pu l s e ( n J ) b 35.8±1.0 E pu l s e ( n J )
10 µm kcps
10 µm
10 µm 10 µm E FIG. 3. (a) Confocal scan of NV centers in sample C, laser-written in an inverse geometry where laser pulses were focusedclose to the bottom surface of the diamond. The colorbarapplies to a-c. (b) Cross-section in the plane indicated bythe red dashed-line in (a). The white dashed-line indicatesthe bottom diamond surface, determined by the position atmaximum intensity of the reflected excitation laser. (c) Cross-section in the plane indicated by the green dashed-line in (a),for a pulse energy E = 25 . ± . ation regime could be carried out by changing the laserwriting wavelength and increasing the pulse length, butwith the latter shrinking the window for NV center cre-ation due to a decrease of the graphitization threshold[49].Sample B shows a clear array-like NV pattern afterannealing, where the main array points contain multipleNV centers, as demonstrated by the photon count in theconfocal scans and by the existence of more than twolines in subsequent photoluminescence excitation (PLE)measurements. The diffusion of vacancies during anneal-ing is also clearly visible – single NV centers form upto several hundreds of nanometers from the array spots,similar to the results of previous experiments [32, 50, 51].Lower pulse energies and a larger spatial separation be-tween the focal spots were therefore used for sample A inorder to obtain predominantly spots with single- ratherthan multiple NV centers.Vacancy photoluminescence after laser writing was ob-served both with the t-SIL and after displacing the t-SILfrom the laser-processed area. If no t-SIL was used duringthe laser-writing process, neither graphitization nor GR1photoluminescence could be detected in the bulk of thesample up to a pulse energy of 52 nJ (highest available inour experimental configuration) and a continuous expo-sure with a pulse repetition rate of 1 MHz with durationsup to tens of seconds. Similar observations were made af-ter exposures performed with an t-SIL but without usingthe index-matching gel. Also after annealing there was noNV photoluminescence in areas exposed without a t-SIL.These observations indicate that the use of a t-SIL dra-matically reduces the threshold for vacancy-generationand can act as the key element enabling laser-inducedNV formation using fs laser sources.A third sample, sample C, was patterned in a way tocreate NV centers as close to the diamond surface as pos-sible without inducing visible damage [52]. PL images ofthe resulting array of NV centers are shown in Fig. 3(a-c).The increased energy density on the top diamond surfaceupon focusing the laser less than ∼ µ m from it typicallyresulted in graphitization of the diamond surface or dam-age of the t-SIL. For this reason, an inverse geometry waschosen. In this geometry, the laser pulses were appliedthrough the t-SIL and diamond, but focused close to thediamond back surface, the one further from the t-SIL.Several NV arrays were patterned at different depths inthe diamond in this configuration. An objective lens withNA=0.85 and correction ring was used for this study tofurther minimize the spherical aberration; the correctionring was set to maximize the laser focus intensity at thebottom surface of the sample.NV centers could be created in the full range of pulseenergy in Fig. 3(a), from 7 . ± . . ± . . µ m. This re-sulted in NV centers covering distances from ∼ µ m upto 15 µ m from the bottom diamond surface, correspond-ing to laser writing depths of between 25 µ m and ∼ µ mfrom the top surface. Fig. 3(b),(c) show cross sectionsthrough the diamond to illustrate the resulting slightlytilted layers. In Fig. 3(b) it is apparent that a lower pulseenergy was needed to create the NV centers closest to thesurface, as compared to writing NV centers further insidethe bulk. Fig. 3(d) illustrates the cross sections and thegeneral t-SIL-on-diamond geometry. III. LINEWIDTH CHARACTERIZATION
We characterize the ZPL linewidths through PLEscans in a liquid helium bath cryostat. The NV centersare resonantly excited using a tunable narrow-linewidthexternal cavity diode laser (New Focus Velocity TLB-6704) and the linewidths are determined by sweepingthe excitation frequency over the ZPL resonance whilerecording the photons emitted into the phonon sideband.Between the periods of excitation and readout, a neg-ative charge-state repump is carried out with a 532 nmNd:YAG-laser with a power of 0.6 mW. The full cycle = 0.05 ac bd Detuning (GHz) P o w e r ( µ W ) -0.1 0.0 0.1 0.2 0.4 I n i t i a li z a t i on E xc i t a t i on / µ s µ s A v e r aged c oun t s / s P (µW) Γ ( M H z ) r eadou t FIG. 4. (a) Optical linewidth measured on an NV in sam-ple A. Zero detuning corresponds to a ZPL frequency of470.494 THz. The inset shows the measurement sequencefor the photoluminescence excitation measurement. (b)Linewidth measured on an NV center in sample B. Zero de-tuning corresponds to a ZPL frequency of 470.509 THz. (c)Dependence of the linewidths in the two samples on the fslaser pulse energy used in the laser writing process. Eachdata point corresponds to a separate NV center, except for afew cases where two lines were measured for one NV center.The dotted line is a linear fit with a Pearson’s ρ = 0 .
05 in-dicating little to no correlation between linewidth and pulseenergy. (d) Resonant power dependence of the ZPL of an NVin sample A, fitted according to equation (3). The inset showsthe dependence of the extracted FWHM linewidth on power,fitted following equation (4) and demonstrating clear powerbroadening. of repump followed by resonant excitation and readout isrepeated at a frequency of 100 kHz, with a 21-to-68 green-to-red laser duty cycle. The inset in Fig. 4(a) shows thePLE measurement sequence.Two PLE scans are presented in Fig. 4(a),(b), show-ing ZPL resonances with Lorentzian lineshapes withFWHM linewidths of 35 . ± . . ± . . ± . x -and E y transitions of the same color center.) In gen-eral, the three laser-written samples demonstrate severaldoublets with exceptionally low peak splittings down to81 MHz, but a more systematic study is required in or-der to obtain a definite conclusion on the strain levelsof laser-written NV centers and to exclude the possibil-ity that the two lines originate from separate NVs (how-ever, such coincidence in spatial location, linewidth andZPL energy between different NVs is highly unlikely).Fitting the lines measured at low power (where inhomo-geneous broadening dominates) with Gaussian functionsrather than Lorenztians yielded an average difference inFWHMs of only 2.0% for the three samples, justifying theuse of a Lorentzian function to describe the inhomoge-neous broadening. Fig. 4(c) shows the dependence of thelinewidths on the femtosecond laser pulse energy, wherethe dotted line is a linear fit to the data. A Pearson’s ρ = 0 .
05 for the fit indicates no significant correlationbetween ZPL linewidth and pulse energy, in contrast toRef. 32.To disentangle inhomogeneous broadening of thelinewidths (Γ in ) from power broadening characterized bythe Rabi coupling Ω, we perform a systematic study ofthe linewidth as a function of resonant power. To sim-plify the analysis we assume a Lorentzian spectral diffu-sion shape characterized by FWHM Γ in : the probabilityof the emitter frequency being equal to f is given by the(normalized) Lorentzian function L ( f − f , Γ in ) where f is the average emitter frequency. The occupation of theexcited level of a driven two-level system with radiativedecay rate γ is given by [53] ρ = 14 π (cid:0) Ω (cid:1) ( f − f ) + (cid:0) γ (cid:1) + Ω (2)where Ω = √ c · P , with P the excitation power and c aneffective coupling strength which depends on the laser’sfocal volume, laser incoupling efficiency and the NV cen-ter’s dipole moment and orientation. The experimentallymeasured line shapes can be described by a convolutionof L with ρ , yielding an expression for the counts as afunction of frequency in a PLE measurement: C ( f ) = A π Ω (cid:112) γ + 2Ω Γ( f − f ) + (cid:0) Γ (cid:1) (3)where A depends on the setup’s collection efficiency andthe average NV photon emission rate, the ”dead” timeduring the repump pulse and the time spent in the NV charge state, as well as the time spent in spin states thatare not cycled with the resonant laser [54]. The FWHMlinewidth is Γ = Γ in + (cid:112) γ + 2Ω π (4)where we assume γ = 13 MHz.Fig. 4(d) shows a PLE measurement as a function ofthe resonant excitation power and the data can be fit-ted well with Eq. (3). Power broadening is clearly visi-ble. The inset shows the extracted FWHM linewidth as afunction of power, fitted with the linewidth described by Sample A (2.0 μm)
Sample B (7.0 μm) a Sample C(15-30 μm) b cd e f Linewidth (MHz) O cc u r en c e s Linewidth (MHz) O cc u r en c e s Linewidth (MHz) O cc u r en c e s m = 61.0 MHz ECDF(100 MHz) = 0.929SD = 22.8 MHzSE = 4.3 MHz m = 62.1 MHz
ECDF(100 MHz) = 0.909SD = 24.6 MHzSE = 4.3 MHz m = 78.3 MHz
ECDF(100 MHz) = 0.794SD = 53.3 MHzSE = 9.1 MHz
FIG. 5. Linewidth statistics of sample A (a,d), B (b,e),and C (c,f), with empirical cumulative distribution functions(ECDF, a-c) with 95% confidence intervals and linewidth his-tograms with log-normal fits (d-f). The values of the ECDFsfor 100 MHz as well as the means (m), standard deviations(SD) and the standard errors (SE) of the mean are specified.
Eq. (4), giving a value of c = (1 . ± . · MHz / µ Wfor the effective coupling strength and a value of Γ =25 . ± . IV. CONCLUSION
In conclusion, we have demonstrated that a t-SIL en-ables laser-induced vacancy creation within bulk dia-mond with pulse energies as low as 5.8 nJ. There is alarge window in pulse energy before the pulse createsirreversible damage. We interpret this wide range ofuseful pulse energies as a consequence of working in thetunneling breakdown regime for vacancy creation. Thevacancies can be created across the full depth of 40 µ mbulk diamond samples. An estimated 92.9% of the cre-ated NV centers have an inhomogeneously broadenedlinewidth below 100 MHz, illustrating that laser writ-ing yields an exceptionally high probability of generatingnarrow-linewidth NV centers as compared to standardimplantation and annealing [22, 25, 26]. This metric iscrucial for applications based on spin-photon entangle-ment as it is greatly beneficial to perform experimentswith minimal pre-selection of NV centers. Importantly,the linewidths presented contain the full inhomogeneousbroadening. To the best of our knowledge, this is the low-est charge noise measured to date including the full ef-fects of the off-resonant charge-state repump [17, 22, 32].The narrow linewidths suggest reduced damage in thevicinity of the NV centers compared to other NV creationmethods. The t-SIL lowers significantly the thresholdpulse energy for vacancy generation. This result pointsto the feasibility of using a standard Ti:sapphire ultra-fast laser without the need for a regenerative amplifier for vacancy creation in diamond.The main goal of the current work is implementationof the laser-written NV centers into a diamond-cavitysystem, which in the first stage requires etching of thediamond down to a few micrometers. On account of thestrongly reduced lattice damage and improved linewidthstatistics compared to other methods, the hope is thatafter etching the charge noise will remain low. If the lowcharge-noise is maintained, it should be a key step towardgenerating spin-spin entanglements at higher rates thanwhat has been achieved so far. In a broader context,the high-optical-quality NV centers created through laserwriting present a major advancement not only for cavityapplications but also in any application requiring a lowcharge-noise environment and charge-state-stable colorcenters. ACKNOWLEDGEMENT
We acknowledge financial support from the NationalCentre of Competence in Research (NCCR) QuantumScience and Technology (QSIT), a competence centerfunded by the Swiss National Science Foundation (SNF),as well as from the EU FET-OPEN Flagship ProjectASTERIQS (grant No. 820394), the SNF project grantNo. 188521, and the SNF R’Equip grant No. 170741. TJacknowledges support from the European Unions Hori-zon 2020 Research and Innovation Programme underthe Marie Sk(cid:32)lodowska-Curie grant agreement No. 792853(Hi-FrED) and support from the Polish National Agencyfor Academic Exchange under Polish Returns 2019 pro-gramme (agreement PPN/PPO/2019/1/00045/U/0001).SF acknowledges support from the Initial Training Net-work (ITN) SpinNANO. We thank Lucas Thiel for skillfulcoding assistance and Yannik Fontana for reviewing themanuscript. [1] F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber,and J. 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