We report on the coherent internal-state control of single-crystalline nanodiamonds, containing on average 1200 nitrogen-vacancy (NV) centers, embedded in three-dimensional direct-laser-written waveguides. We excite the NV centers by light propagating through the waveguide, and we show that emitted fluorescence can be efficiently coupled to the waveguide modes. We find an average coupling efficiency of 21.6% into all guided modes. Moreover, we investigate optically detected magnetic-resonance spectra as well as Rabi oscillations recorded through the waveguide-coupled signal. Our work shows that the system is well suited for magnetometry and remote readout of spin coherence in a freely configurable waveguide network, overcoming the need for direct optical access of NV centers in nanodiamonds. These waveguide-integrated sensors might open up new applications, such as determining magnetic field distributions inside opaque or scattering media, or photosensitive samples, such as biological tissue.

Over the past decades, a variety of magnetic field sensors have been developed based on SQUIDs,1–3 the Hall effect,3,4 the magnetostrictive effect,5,6 atomic vapor and cold gases,7–11 magnetic force microscopy,3,12,13 and color centers.14 In this context, nitrogen-vacancy (NV) centers in diamonds have advanced to a highly promising nanoscale probe. A prominent feature of the NV center is optical initialization and readout of its spin degree of freedom.15 Because of relatively long coherence times, for example, up to T2 = 3 ms at room temperature,16 and its high sensitivity to external fields, it is widely used to detect dc and ac magnetic fields,17–21 to sense temperature distributions in biological samples,22 and even to show a loophole-free test of the Bell inequality.23 

Most such applications require a direct line of sight to the location of the NV center investigated for excitation and fluorescent light detection, i.e., direct optical access, usually granted by microscopes with high numerical apertures. An alternative way is to guide the NV center’s signal to detector harnessed waveguides. Such waveguides, directly fabricated from a diamond membrane24–27 or micrometer long, free-standing polymer waveguides,28,29 guiding the NV fluorescence signal have been reported elsewhere. Moreover, it has been shown that waveguides, as well as NV centers, can be deterministically defined inside bulk diamond using a direct laser writing technique.30 

Here, we show the integration of individual single-crystalline nanodiamonds containing an ensemble of NV centers into flexible, three-dimensional waveguide networks that can be on millimeter length scales and connected to more complex optical networks with high integration density. Our motivation to choose polymer waveguides is threefold. First, we position the nanodiamond inside the waveguide, where the intensity of the guided modes is much higher than that in the evanescent field outside the waveguide. This allows for remote excitation as well as detection of the NV centers’ fluorescence and thus ensures constant and optimal coupling of light to and from the NV centers independent of external conditions. Second, polymer waveguides feature 3D capability, which enables simultaneous addressing of NV center ensembles lying in different focal planes, while keeping one side of the sample accessible for additional manipulation. These 3D capabilities will also allow for integration into micro-optics or microfluidics on a chip.31 Third, such polymer waveguide structures can even be fabricated on the tip of an optical fiber.32 

The waveguides can be configured to feature extended planar networks lying on the substrate with three-dimensional features, e.g., for perpendicular coupling. We harness the optical waveguide both to address and to bidirectionally detect the NV center ensemble. For addressing, a green laser beam for optical initialization and readout of the spin ensemble is guided through the waveguide to the nanodiamond. For detection, the fraction of total fluorescence, which is coupled to the waveguide, is guided to the microscope’s focal plane, where input and output ports of the waveguide are imaged simultaneously.33 

Such integrated NV-center ensembles, embedded in polymer waveguides, might be used to sense magnetic field gradients and distributions in real-time. Furthermore, the integration of NV centers into a waveguide might enhance the applicability of these color centers as probes in biological tissue, which in general gets heated, gets photodamaged, and autofluoresces when illuminated with focused green laser light.34 Since the waveguide, made from a biocompatible material,35 guides the excitation light and separates it spatially from the biological sample, the photodamage is strongly reduced in contrast to that when using confocal microscopy, where the excitation light is focused through the sample volume.

We present the integration of strong fluorescent nanodiamonds into a photoresist and the direct laser writing of three-dimensional waveguides with micrometer-scale cross section from this functionalized photoresist. These devices are characterized with respect to coupling efficiency from nanodiamonds to guided waveguide modes, their use as a waveguide coupled magnetometer, and influence of waveguide integration on the NV centers’ coherence properties.

The NV center is a paramagnetic point defect in the diamond lattice, see Figs. 1(a) and 1(b). Its structure, shown in the inset of Fig. 1(b), is composed of a substitutional nitrogen atom (N) and an adjacent vacant lattice site (V). We use the negatively charged state, which binds an additional electron from nearby N donors.39 Its ground state is a spin-triplet with D ∼ 2.87 GHz zero-field splitting between the ms = 0 and degenerate ms = ±1 spin states, quantized along the NV-axis. This degeneracy is lifted in the presence of an external magnetic field. Ground-state splitting and Zeeman shift, caused by the magnetic field component along the NV-axis, can be described by the Hamiltonian39 

(1)

where ggs=ggs=g is the g-factor.40 Due to the system’s higher probability to undergo an intersystem crossing and subsequent decay from the excited 3E ms = ±1 states to a long-lived singlet state 1E, the system is optically pumped into the ms = 0 ground state under optical excitation. This causes a higher fluorescence rate of the ms = 0 state, harnessed in the optical spin-state read-out.

FIG. 1.

(a) Level structure of the NV center.36–38 (b) Fluorescence spectrum of the negatively charged NV center in the used nanodiamonds; inset: lattice structure of the NV center, with the substitutional nitrogen atom in blue, the NV-axis in red, and the vacancy in silver. (c) Sketch of the experimental setup. A green laser beam is coupled into the waveguide, containing a fluorescent nanodiamond. The fraction of the fluorescence guided in the waveguide is detected at the waveguide couplers, the unguided fraction is detected at the nanodiamond’s position, while green excitation light is blocked using a long-pass filter in the detection beam path. This is shown in the EMCCD image in (d) for a single integrated fluorescent diamond, where the detected fluorescence is shown in false colors and the measured count rate in the white areas is given. In (e), the reflected light microscope image is shown in gray scale, overlaid with the detected red fluorescent light from the nanodiamond. Scale bar: 20 µm. For comparison, a tilted SEM image of such a waveguide is shown in (f).

FIG. 1.

(a) Level structure of the NV center.36–38 (b) Fluorescence spectrum of the negatively charged NV center in the used nanodiamonds; inset: lattice structure of the NV center, with the substitutional nitrogen atom in blue, the NV-axis in red, and the vacancy in silver. (c) Sketch of the experimental setup. A green laser beam is coupled into the waveguide, containing a fluorescent nanodiamond. The fraction of the fluorescence guided in the waveguide is detected at the waveguide couplers, the unguided fraction is detected at the nanodiamond’s position, while green excitation light is blocked using a long-pass filter in the detection beam path. This is shown in the EMCCD image in (d) for a single integrated fluorescent diamond, where the detected fluorescence is shown in false colors and the measured count rate in the white areas is given. In (e), the reflected light microscope image is shown in gray scale, overlaid with the detected red fluorescent light from the nanodiamond. Scale bar: 20 µm. For comparison, a tilted SEM image of such a waveguide is shown in (f).

Close modal

In order to immerse nanodiamonds into the waveguides, we follow a probabilistic approach. The waveguides used are fabricated via direct laser writing in a polymer photoresist, using a commercial system (Nanoscribe Photonic Professional GT41). The nanodiamonds (120 nm size on average and more than 1200 NV centers per diamond, Sigma-Aldrich-798088) were used as received and have been dispersed within the resist EpoClad 50 (micro resist technology). For technical details on the integration, see  Appendix A.

Since the resist film is solid, the nanodiamonds are not mobile and the resist is exposed to laser lithography from the side of the substrate in order to produce waveguides on the substrate, including nanodiamonds. These waveguides written have been characterized in detail elsewhere.33 In short, they feature bend radii down to 40 µm, insertion losses (i.e., the total loss of the device, including coupling loss on both sides, propagation loss, and bend loss) on the order of 10 dB, and loss coefficients smaller than 0.81 dB/mm. To insert and extract light to and from the waveguide, we use three-dimensional out-of-plane couplers with a bend radius of 7 µm. This small coupler radius is chosen as a compromise between insertion loss, small footprint, and stability. The number of nanodiamonds integrated into individual waveguides follows a Poisson distribution.42 We select waveguides containing exactly one nanodiamond in the planar waveguide section for the following investigations. Such waveguides are produced with a yield of 29%, based on statistics of 100 devices produced. In Figs. 1(c) and 1(f), a sketch of the waveguide and its working principle are shown, as well as a light microscope image of a waveguide containing one single nanodiamond and a scanning electron microscope (SEM) image of a fabricated structure.

In order to excite integrated NV centers, a green laser beam (λ = 532 nm) is focused on the incoupling port of the waveguide. We use a high numerical aperture objective (Nikon CFI Plan Apochromat Lambda 60XC, NA = 0.95), but this can be replaced by other means of coupling to the waveguide, for example, an optical fiber. For fluorescence readout, an EMCCD-camera (Andor iXon 885) or a fiber-coupled single-photon counting module (Laser Components Count 100C-FC) is used.

As can be seen from Fig. 1(d), if a nanodiamond is excited by green light through the waveguide, it will emit light both into free space and into the waveguide. An important question regards the coupling efficiency β of fluorescent light into the waveguide. We define the minimum coupling efficiency as

(2)

where Icoupler (IND) is the fluorescence count of the nanodiamond guided by the waveguide (emitted into free space) and simultaneously detected by an EMCCD camera; α = 2.85 corrects for the independently measured coupling loss of the waveguide coupler,33 and γ = 9 corrects for the limited numerical aperture (NA) of 0.95 of the imaging system collecting the free-space fluorescence of the nanodiamond. This correction factor does not apply to the couplers since the waveguide couplers have NA < 0.95. This yields a lower bound for β, neglecting the propagation loss of the waveguide and anisotropic emission of the nanodiamond. Details on the measurement of the coupling efficiency are given in  Appendix B.

We have verified that the fluorescent light originates from the nanodiamond rather than waveguide autofluorescence by modulating the fluorescence rate of the NV center via applying a microwave at the electronic spin resonance (ESR) of 2.865 GHz without an external magnetic field. This allows for an estimate of the total coupling efficiency taking the fluorescence signal of all NV axes into account simultaneously. We find a noise level of a waveguide on the glass substrate being on the order of the fluorescence of one to two NV centers in a nanodiamond on the same substrate, see  Appendix B and Fig. 6(a). However, in the case of smaller ensembles and single NV centers, distinction between the NV center’s fluorescence and the waveguide’s autofluorescence is feasible taking their different lifetimes into account, see  Appendix B and Fig. 6(b). Evaluating the single-side coupling efficiency for both couplers of 50 nanodiamond-containing waveguides separately, we find a distribution of coupling efficiencies (see Fig. 2) with a median of βmin=10.8+15.15.6% in each propagation direction, where the errors denote the standard deviation evaluated separately for values below and above the mean, corresponding to a total coupling efficiency of βmin,total=21.6+21.47.9%.

FIG. 2.

Distribution of corrected single-sided coupling efficiencies of the total emission to one propagation direction. The excitation laser is coupled into one of the waveguide ports, and the fluorescence counts in the camera image are integrated over a small area surrounding the respective coupler or nanodiamond (“ND”). The median is marked in blue, and negative values were neglected. The device shown in the inset yields strongly different coupling to the respective couplers. This is due to an increased loss at coupler 2. Devices produced in batches of 1000 are therefore subject to fluctuations in the DLW and production process.

FIG. 2.

Distribution of corrected single-sided coupling efficiencies of the total emission to one propagation direction. The excitation laser is coupled into one of the waveguide ports, and the fluorescence counts in the camera image are integrated over a small area surrounding the respective coupler or nanodiamond (“ND”). The median is marked in blue, and negative values were neglected. The device shown in the inset yields strongly different coupling to the respective couplers. This is due to an increased loss at coupler 2. Devices produced in batches of 1000 are therefore subject to fluctuations in the DLW and production process.

Close modal

Additionally, simulations in Comsol Wave Optics43 have been performed for different positions of the nanodiamond within the waveguide cross section, see  Appendix B. From the simulations, the maximum coupling efficiency of the integrated emitters to the waveguide mode, i.e., the β-factor, is around 15% for one propagation direction, which corresponds to βmax, total around 30% in total. This value, however, does not include any experimental imperfections, such as finite solid detection angle or coupling and propagation losses of the waveguides. Furthermore, it is highly dependent on the nanodiamond’s position relative to the mode structure inside the waveguide. For comparison, from a planar diamond membrane, only approximately 8% of the emitted photons would be collected by a standard microscope objective with NA = 1.3. To increase this extraction efficiency from bulk diamond, elaborate nanostructuring schemes are necessary, also requiring excellent alignment to the investigated color center. For example, for a solid immersion lens, up to 29.8% coupling efficiency was reported,44 and for parabolic reflector structures, up to 41% coupling efficiency was reported.45 

From the comparison of fluorescence into free-space and fluorescence guided by the waveguide, we also find that the ESR fluorescence contrast is only little affected by the waveguide, and hence, the contribution of waveguide fluorescence is negligible for the NV center concentration used.

A possible limitation for the application of NV centers as magnetometers is the need for direct optical access to the NV centers under investigation, when probing, for instance, strongly scattering, opaque media, or samples being sensitive to the excitation or fluorescent light. We show that our waveguides mediate this access to individual integrated nanodiamonds for excitation light and readout, such that these nanodiamonds can be used for vector magnetometry of a target magnetic field B in a known external field Bext, according to Ref. 46. Another possibility to extract the magnetic field components in a Cartesian basis is to modulate magnetic offset fields in the respective directions with incommensurable frequencies, see Ref. 47.

The position uncertainty of the waveguide-coupled magnetometer is on the order of 1 µm in the waveguide’s transversal direction, defined by the waveguide’s cross section, and on the order of 0.5 µm along the waveguide axis, determined by the resolution of the microscope used for initial characterization. In fact, high-resolution microscopy is only necessary for initial characterization, and all other measurements rely on the use of photon counting devices and the signal extracted from the waveguide couplers, only.

To acquire fast ODMR spectra with high SNR, the microscope is operated in confocal configuration, detecting the fluorescence power with a single photon counting module (SPCM). The high resolution of the microscope is not used to detect the nanodiamond’s position, but to collect emitted fluorescence photons with high efficiency. In the current setup, this is only possible for one spot under investigation at a given time. Such an ODMR spectrum measured via the waveguide is shown in Fig. 3(a).

FIG. 3.

(a) ODMR measurement on a nanodiamond detected via the waveguide. The inset shows the magnetic field orientation B in gray, relative to the four NV center directions, retrieved from the fit data (a sum of eight Lorentzians) shown as a solid line. The resonances are highlighted in the color of the corresponding NV axis. The magnetic field amplitude is measured to be 16.1 mT from the ESR positions. (b) Systematical investigation of the dependence of the magnetometer sensitivity on laser and microwave powers. Cuts through the minimum for constant laser power (red) and microwave power (blue) are shown projected on the faces of the encapsulating box of the plot. (c) Calculated cw sensitivity of the NV centers used, depending on the applied MW-power. The solid curve is a fit to the data according to the formula given in the text with fit parameters a = 0.1721, b = 0.032 32 Hz2, and C=46.3×105 T/Hz.

FIG. 3.

(a) ODMR measurement on a nanodiamond detected via the waveguide. The inset shows the magnetic field orientation B in gray, relative to the four NV center directions, retrieved from the fit data (a sum of eight Lorentzians) shown as a solid line. The resonances are highlighted in the color of the corresponding NV axis. The magnetic field amplitude is measured to be 16.1 mT from the ESR positions. (b) Systematical investigation of the dependence of the magnetometer sensitivity on laser and microwave powers. Cuts through the minimum for constant laser power (red) and microwave power (blue) are shown projected on the faces of the encapsulating box of the plot. (c) Calculated cw sensitivity of the NV centers used, depending on the applied MW-power. The solid curve is a fit to the data according to the formula given in the text with fit parameters a = 0.1721, b = 0.032 32 Hz2, and C=46.3×105 T/Hz.

Close modal

In this spectrum, the four pairs of resonances show different amplitudes and linewidths, depending on the polarization of optical and microwave driving fields with respect to each NV-axis orientation.48–50 The resonances’ amplitudes also differ between the detection of nonguided and guided waveguide modes. A comparison of ODMR-spectra for guided and nonguided modes is shown and further discussed in  Appendix B. Observation of such an ODMR spectrum at the waveguide coupler confirms the presence of an individual single-crystalline nanodiamond inside the waveguide because a second nanodiamond would contribute additional resonances due to deviations of its crystal orientation. Furthermore, the magnetic field orientation with respect to the diamond lattice is determined from this spectrum, see the inset in Fig. 3(a), and the magnetic field amplitude is determined to be 16.1 mT.

The figure of merit for a magnetometer is its sensitivity. For cw-ODMR measurements, the photon shot noise limited sensitivity for dc magnetic fields is given by51 

(3)

where P0.77 for a Lorentzian resonance shape, Δν is the FWHM of the dip, C is the dip depth, and R is the detected count rate. The dependence of the sensitivity on the laser and microwave power for one waveguide coupled nanodiamond is systematically investigated in Fig. 3(b). Over a broad range of laser and microwave powers, the sensitivity varies only slowly and shows a maximum for low microwave and moderate laser powers. It decreases dramatically for very low microwave and laser powers. Maximum sensitivity is found for a different nanodiamond, as shown in Fig. 3(c). Here, we determine the sensitivity of the waveguide-coupled magnetometer for a fixed laser power by measuring the width and depth of the dip at the lowest frequency while varying the microwave power, see Fig. 3. We fit the sensitivity with a function of the form ηB=Ca+Pb/(PP+ab), which is a simplified form of the theoretical description in Ref. 51 for constant excitation laser power. Typical values are C 0.014–0.027, R800000, and Δν ≈ 7 MHz–20 MHz. The maximum sensitivity is (1.53±0.12)×105 T/Hz at a microwave power of 0.316 W applied to the wire loop antenna. The microwave power cannot easily be compared for both devices shown since the coupling strength of microwaves to nanodiamonds is highly dependent on the position of the antenna. For higher microwave powers, the sensitivity decreases, since the width of the resonance is dominated by power broadening of the microwave, while for lower microwave powers, the decrease in the sensitivity is possibly dominated by laser power broadening of the resonance due to optical polarization of the spin state, shot noise, or spin projection noise.

To circumvent power broadening, a pulsed measurement scheme, temporarily separating microwave and laser pulses could be used.51 For the nanodiamonds in our case, however, the sensitivity is inherently limited by the diamonds’ quality. In fact, the improved sensitivity of sensors made of ultrapure bulk samples is due to a reduced abundance of 13C-atoms and a lower amount of nitrogen (P1-center or Ns0) and other impurities, acting as spin bath and reducing NV-center’s coherence times.52,53

A remarkable property of the NV center is its relatively long room-temperature spin-coherence time, which can reach T2 = 3 ms16, depending on the diamond’s quality. It is known that, for high NV concentrations, the NV density and other impurities are the dominant sources of decoherence as in the nanodiamonds investigated here. A minor influence might originate from the surface of the nanodiamonds. We verify that integration into the photoresist and the connected environmental change at the surface do not alter the NV centers’ coherence time. We show the remote detection of Rabi oscillations of an ensemble of NV centers through an optical waveguide, see Fig. 4, where the coherence time is compatible with the coherence time of uncoupled nanodiamonds, limited by the impurities in the volume and on the surface of the nanocrystals. Without waveguide, we measure typical coherence times of T2 ≈ 1.5 µs and T2* 78 ns, and for a waveguide integrated nanodiamond, we measure for one specific device coherence times of T2 ≈ 1.4 µs and T2* 74 ns. The coherence times depend strongly on the nanodiamonds’ quality and hence vary from nanodiamond to nanodiamond. For details on the measurement of Rabi oscillations, Hahn-echo, and Ramsey fringes, see  Appendix C.

FIG. 4.

(a) Experimental sequence to measure Rabi oscillations; (b) Rabi oscillations of NV centers in a single nanodiamond, detected via the waveguide, for 2 W MW power at the antenna. The solid line is a fit to a damped sine, yielding a damping time of T = (0.9 ± 0.1) µs. Each sequence is repeated 500 000 times. Error bars are estimated by the standard deviation of relative fluorescence intensity in 50 000 repetitions.

FIG. 4.

(a) Experimental sequence to measure Rabi oscillations; (b) Rabi oscillations of NV centers in a single nanodiamond, detected via the waveguide, for 2 W MW power at the antenna. The solid line is a fit to a damped sine, yielding a damping time of T = (0.9 ± 0.1) µs. Each sequence is repeated 500 000 times. Error bars are estimated by the standard deviation of relative fluorescence intensity in 50 000 repetitions.

Close modal

The Rabi oscillations detected show a coherence time of 0.9 µs, which is comparable to coherence times measured in bare nanodiamonds. We expect that reducing the number of surface impurities and lowering the N-concentration of the nanodiamonds embedded into the waveguides will enhance coherence times.54,55 This will reduce brightness but increase sensitivity applying a detection method that harnesses the different fluorescence lifetimes of the photoresist and NV centers, as shown in  Appendix B.

We have shown the integration of single-crystalline nanodiamonds containing an ensemble of NV centers into direct-laser-written waveguides, which enables the creation of extended three-dimensional waveguide networks on a chip. These NV centers can be used as integrated sensors for magnetic fields, which are initialized and read out via the waveguides they are embedded in. The ODMR signal of the NV ensemble is not affected by the fluorescence of the waveguide material. However, for small ensembles or even single NV centers, the fluorescence contributions of different origins might be separated by harnessing the strongly different lifetimes of 33.6 ns (5.28 ns) for NV centers (photoresist), see  Appendix B. Furthermore, we have shown the detection of Rabi oscillations via the waveguide housing the nanodiamond, allowing for coherent control over an ensemble of remote quantum emitters. The T2* time of the waveguide embedded NV ensembles is relatively short (T2* 80 ns), probably limited by a large number of impurities in and on the surface of our nanodiamonds. While this limits their use for magnetometry using the Ramsey scheme, further enhancement can be achieved by employing nanodiamonds with improved coherence properties. Therefore, our waveguides pave the way to optical networks, hosting three-dimensional arrays of spin sensors. In the future, it will be interesting to explore the prospects of detecting magnetic fields as well as gradients in a small volume by direct-laser-written three-dimensional photonic structures with multiple nanodiamonds embedded. Another option is to directly connect the waveguide to an optical fiber, where no confocal microscope is needed anymore.

These sensors are also useful for opaque, scattering, or sensitive biological samples under investigation, since the laser light used to excite NV centers, as well as their fluorescent light, is guided within the waveguide, reducing the amount of optical power deposited at the sample by orders of magnitude and simultaneously keeping the whole sample optically accessible. At the same time, the processed photoresist is stable against watery solutions and might thus be compatible with sensing applications in life science.

We thank Henning Fouckhardt and his group Integrierte Optoelektronik und Mikrooptik (Technische Universität Kaiserslautern) for access to their wet chemistry lab, and we also acknowledge the technical support by the Nano Structuring Center (Technische Universität Kaiserslautern). Furthermore, we thank Stefan Dix for help with the experimental setup.

Since the nanodiamonds are received suspended in de-ionized water (concentration: 1 mg/ml), the de-ionized water is exchanged with gamma-butyrolactone (GBL), the solvent of EpoClad. This is achieved by, first, centrifuging the suspension for 15 min at 6000 rpm and, second, exchanging the water with the same amount of GBL. To suspend the new mixture, it is vortexed and exposed to an ultrasonic bath for 5 min to disperse agglomerates into single-crystalline nanodiamonds. This procedure is repeated two times to ensure a low residual water concentration. For the integration of nanodiamonds into a photoresist, equal mass ratios of the suspension and EpoClad 50 are mixed for 30 min at 200 rpm, using a magnetic stir bar. The photoresist with immersed nanodiamonds is processed for direct laser writing, as described in detail in Ref. 33. In brief, the mixture of EpoClad and therein suspended nanodiamonds is drop cast to an initially cleaned glass coverslip and baked for 10 h at 120 °C on a contact hotplate to remove a majority of the solvent by evaporation. Thereafter, three-dimensional waveguides are defined by DLW in four subsequent writing passes. Finally, samples are developed in mr-Dev 600 (micro resist), rinsed with isopropanol, and blow-dried with nitrogen. The samples are stored at ambient conditions and show no degrading of the devices after one year. However, we find that strongly increased exposure of 10 mW green laser light leads to permanent higher autofluorescence and subsequent degrading of individual waveguides.

In order to compare the ODMR signal collected directly from the nanodiamond, on the one hand, and via the waveguide, on the other hand, an ODMR measurement is taken. Using the microscope’s EMCCD camera, both the waveguide port and the nanodiamond’s free-space fluorescence are imaged simultaneously. The resulting spectra are shown in Fig. 5, showing the spin-resonances, as expected, for the same frequencies. However, the contrast of specific dips differs for guided and nonguided modes detected via the coupler and at the nanodiamond’s position, respectively. We attribute this to a different overlap of the two transition dipole orbitals48,56,57 of each NV-orientation to the guided modes.

FIG. 5.

(a) SEM image of a series of direct-laser-written waveguides with nanodiamonds indicated by a square. (b) Comparison of ODMR signals excited via the waveguide and detected via the waveguide (orange), free space (black).

FIG. 5.

(a) SEM image of a series of direct-laser-written waveguides with nanodiamonds indicated by a square. (b) Comparison of ODMR signals excited via the waveguide and detected via the waveguide (orange), free space (black).

Close modal

In the case presented here, on the order of 103, NV centers contribute to the signal. Neglecting the influence of the polymer waveguide might thus not be valid for weaker signals of few or single NV centers. This is shown in Fig. 6(a) for a comparison of detected count rates of the components of the material system used in dependence of excitation laser power, which shows that a different substrate might improve SNR for a lower concentration of NV centers. In this case, the contribution of NV fluorescence vs waveguide fluorescence may still be separated by exploiting markedly different time scales of fluorescence lifetimes in a pulsed measurement, as shown in Fig. 6(b).

FIG. 6.

(a) Detected fluorescence count rates for a bare nanodiamond on glass, an individual integrated nanodiamond, a waveguide on glass, and a glass coverslip; (b) fluorescence lifetimes of the photoresist measured by exciting a waveguide in comparison with the lifetime of NV centers in nanodiamonds and the laser switching characteristics. The fluorescence signal of the resist is much noisier due to the low count rate (ratio of initial count rates is approximately 102), and the fluorescence intensity of each data set is independently normalized to 1 at the beginning. The error bars are statistical (1σ) errors.

FIG. 6.

(a) Detected fluorescence count rates for a bare nanodiamond on glass, an individual integrated nanodiamond, a waveguide on glass, and a glass coverslip; (b) fluorescence lifetimes of the photoresist measured by exciting a waveguide in comparison with the lifetime of NV centers in nanodiamonds and the laser switching characteristics. The fluorescence signal of the resist is much noisier due to the low count rate (ratio of initial count rates is approximately 102), and the fluorescence intensity of each data set is independently normalized to 1 at the beginning. The error bars are statistical (1σ) errors.

Close modal

We prepare and measure 50 nanodiamonds, each embedded in another waveguide structure. In order to verify that the fluorescent light originates from the nanodiamond rather than waveguide autofluorescence, we modulate the fluorescence rate of the NV center by applying a microwave at the electronic spin resonance (ESR) of 2.865 GHz (vertical line in the inset of Fig. 7) without an external magnetic field. The distribution of ratios between both contrasts is shown in Fig. 7, and it is well centered around unity (a median of 0.978). We conclude that, for our concentration of NV centers in the nanodiamond, the fluorescence contrast is only little affected by the waveguide, which shows that the contribution of waveguide fluorescence is negligible for the NV center concentration used.

FIG. 7.

Distribution of ratio of ESR contrasts Ci at 2.865 GHz, detected at the couplers i = 1, 2, relative to the contrast CND, detected at the nanodiamond. The median is marked in blue. The contrast Ci is defined as Ci=1IiIi, where Ii (Ii) is the detected count rate at the position i with (without) microwave applied. Insets: free space ODMR spectrum in the absence of an external magnetic field (the microwave frequency used is marked in red) and the microscope image of a waveguide under investigation with marked positions for evaluation.

FIG. 7.

Distribution of ratio of ESR contrasts Ci at 2.865 GHz, detected at the couplers i = 1, 2, relative to the contrast CND, detected at the nanodiamond. The median is marked in blue. The contrast Ci is defined as Ci=1IiIi, where Ii (Ii) is the detected count rate at the position i with (without) microwave applied. Insets: free space ODMR spectrum in the absence of an external magnetic field (the microwave frequency used is marked in red) and the microscope image of a waveguide under investigation with marked positions for evaluation.

Close modal

Experimentally, we determine the quantities in Eq. (2) to extract the minimum coupling efficiency βmin. Evaluating camera images, we can simultaneously determine the fluorescence of the nanodiamond emitted into free space Icoupler and the guided fluorescence at the waveguide output couplers IND.

Comparing the ODMR-signal counts at the waveguide couplers with those detected from free space, corrected by γ, we get a median bare ratio of the counts of Icoupler/(γIND)=3.8+5.32.0% for the coupling efficiency of total emission to the waveguide modes propagating in one direction, with error given by the standard deviation evaluated separately for values below and above the mean, see Fig. 2. If we take the correction factor α into account, we get a corrected median coupling efficiency of βmin=10.8+15.15.6%. This spread is caused by a strong dependence of the coupling efficiency on the position of the nanodiamond in the waveguide.

Additionally, we performed simulations in Comsol Wave Optics to estimate the maximum coupling efficiency and coupling to the waveguide modes. Simulations show a strong dependence of the lateral nanodiamond position inside the waveguide on the amount of guided light. In Fig. 8, the intensity distribution of the emitted light from a fluorescent nanodiamond is shown at multiple propagation distances for one of those simulations.

FIG. 8.

Simulated propagating light field in the waveguide, emitted by a nanodiamond positioned at the center of the fundamental mode. From the ratio of guided energy to total irradiated energy, the coupling factor can be deduced.

FIG. 8.

Simulated propagating light field in the waveguide, emitted by a nanodiamond positioned at the center of the fundamental mode. From the ratio of guided energy to total irradiated energy, the coupling factor can be deduced.

Close modal

In order to address only one single spin transition of one NV orientation of the ensemble, an external magnetic field is applied and an ODMR spectrum is recorded. A well separated ESR with a dip depth of around 3% is chosen for the microwave frequency. The Rabi measurement sequence consists of three pulses. First, the spin ensemble is initialized in the ms = |0⟩ state via a green laser pulse of 50 µs duration, coupled to the waveguide. Second, the microwave pulse of varied length is applied to transfer the addressed ensemble spins into the state ms = |−1⟩ or |+1⟩. Subsequently, a green laser pulse for state readout is coupled to the waveguide, similar to initialization. The fluorescent light emitted during the first 1.5 µs of the readout pulse of 3 µs duration is guided to an SPCM via the waveguide and the confocal microscope. The detected number of photons is normalized to the number of photons detected without the microwave field applied, and it shows oscillation between the two spin states. The excitation pulses are chosen relatively long compared to single emitters to protect the SPCM from too intense illumination due to the large NV ensembles investigated. In order to remove effects from drifts, or fluctuations, e.g., of surface charges and charge states of crystal defects, this sequence is followed by the same sequence without microwave pulse, which is used as a reference for normalization. The relative fluorescence intensity is determined in 10 independent runs of 50 000 repetitions leading to a total number of 500 000 measurements. We calculate the standard deviation of the relative fluorescence intensities measured in each repetition of 50 000 sequences estimating the error.

From the Rabi oscillations, the duration for π/2 and π pulses is determined and used to determine T2* and T2 times from Hahn-echo and Ramsey measurements, see Figs. 9 and 10, respectively. These measurements are quite similar to the measurement of Rabi oscillations, besides the fixed length of the applied microwave pulses and varying precession time between the microwave pulses.

FIG. 9.

(a) Experimental sequence for Ramsey measurements. (b) Comparison of Ramsey measurements for a nanodiamond inside a waveguide and bare nanodiamond on the glass coverslip. The coherence time T2* was extracted from an exponential decay fit to T2*=(74±15) ns [T2*=(78±13) ns] for the nanodiamond in the waveguide (bare nanodiamond). The length of the π/2 pulses is 30 ns. Each sequence is repeated 500 000 times. Error bars are estimated by the standard deviation of relative fluorescence intensity in 50 000 repetitions.

FIG. 9.

(a) Experimental sequence for Ramsey measurements. (b) Comparison of Ramsey measurements for a nanodiamond inside a waveguide and bare nanodiamond on the glass coverslip. The coherence time T2* was extracted from an exponential decay fit to T2*=(74±15) ns [T2*=(78±13) ns] for the nanodiamond in the waveguide (bare nanodiamond). The length of the π/2 pulses is 30 ns. Each sequence is repeated 500 000 times. Error bars are estimated by the standard deviation of relative fluorescence intensity in 50 000 repetitions.

Close modal
FIG. 10.

(a) Experimental sequence for Hahn-echo measurements. (b) Hahn-echo signal for a nanodiamond inside a waveguide and bare nanodiamond on the glass coverslip. The coherence time T2 was extracted from an exponential decay fit to T2 = (1.4 ± 0.1) µs [T2 = (1.5 ± 0.2) µs] for the nanodiamond in the waveguide (bare nanodiamond). In the case of the waveguide embedded nanodiamond, π/2 (π) pulses of 30 ns (60 ns) duration were used. Each sequence is repeated 500 000 times. Error bars are estimated by the standard deviation of relative fluorescence intensity in 50 000 repetitions.

FIG. 10.

(a) Experimental sequence for Hahn-echo measurements. (b) Hahn-echo signal for a nanodiamond inside a waveguide and bare nanodiamond on the glass coverslip. The coherence time T2 was extracted from an exponential decay fit to T2 = (1.4 ± 0.1) µs [T2 = (1.5 ± 0.2) µs] for the nanodiamond in the waveguide (bare nanodiamond). In the case of the waveguide embedded nanodiamond, π/2 (π) pulses of 30 ns (60 ns) duration were used. Each sequence is repeated 500 000 times. Error bars are estimated by the standard deviation of relative fluorescence intensity in 50 000 repetitions.

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