1. Introduction

Many suggested applications in the area of quantum information demand a reliable source of single photons—an optical source with essentially zero probability of simultaneous emission of two photons [1]. An ideal single photon source (SPS) is bright (high emission rate) with high collection efficiency, deterministic or triggerable (emit photons on demand), and able to produce indistinguishable photons (occupying a single spatial mode and transform-limited in time and frequency). The lack of reliable sources possessing even several of these qualities is a significant impediment to progress in applied quantum information science. For quantum key distribution (QKD) indistinguishability is not required, and a strongly attenuated laser pulse currently offers the best available transmission rates [2]. By comparison, quantum entanglement and linear optical quantum gates do require indistinguishable photons [3], for which the best available source is parametric down-conversion in nonlinear crystals which unfortunately suffer from low emission rates. Single atoms can be used to provide a high quality SPS [4, 5], although these often require optical traps. Research has progressed over the last few years and other promising systems, including quantum dots and diamond color centers, are gaining momentum.

Quantum dots have some excellent qualities for a SPS. They have a high quantum efficiency and narrow linewidths at low temperatures, and can also cover a broad spectral range through the choice of different material systems [6]. Quantum dots also have some unwanted qualities in that they have short coherence times and a tendency to blink/bleach at room temperature [7]. In this work, we focus on another candidate—the nitrogen-vacancy (NV) center in diamond. Single NV centers, composed of a substitutional nitrogen and an adjacent vacancy, occur naturally in bulk diamond and diamond nanocrystals, and can also be induced by nitrogen implantation [8]. NV centers have recently emerged as viable room temperature single photon sources [9] for several reasons: the NV center is photostable and exhibits an optical transition between a ³A ground state and ³E excited state which has near-unity quantum efficiency. The zero phonon line of this transition is at 637 nm, which is homogeneously broadened to around 750 GHz (or 1 nm) at room temperature [10] (far beyond the transform-limited bandwidth). Furthermore, phonon side bands broaden the overall emission to around 100 nm (the relative integral intensity of the zero phonon line to the entire spectrum, the Debye-Waller factor [11], is 0.04).

Despite quantum dots and NV centers having attractive properties as a SPS there has been a push to modify the properties of these emitters by altering the environment in which they emit. Microsphere resonators have been used to extract energy from NV centers preferentially into high-Q whispering gallery modes at room temperature [12], and also to attain strong coupling with low temperature NV centers [13]. Recent measurements of a NV center emitting in close proximity to a pair of gold nanospheres revealed an increase in the emission rate of almost one order of magnitude thanks to coupling to plasmonic resonances [14].

Periodic structures in the form of photonic crystals (PCs) provide an excellent means of modifying the local density of states (LDOS) seen by an emitter, which determines the optical channels into which a photon can be emitted. The incorporation of quantum dots into micropillar (1D PC) cavities resulted in a five-fold increase in the single photon spontaneous emission rate (SER) [15], while a cavitiy in a 2D PC slab offered an improvement on this, with an eight-fold increase in the measured single photon SER [16]. Recently, a chiral one-dimensional liquid-crystal PC was used to create a SPS with a circularly polarized output from embedded quantum dots [17].

While these approaches offer some control over the emission properties of the single photon source, ultimately it may be 3D PCs that offer the most effective modification. These 3D periodic dielectric structures exhibit a vanishing LDOS within the gap [18], and enhanced LDOS near the band edges [19] and thus offer strong control over emission. Fabrication of 3D PCs remains challenging, and for emission control experiments, self-assembly of colloidal microspheres into thin films has proved a popular approach. The resulting crystal is often referred to as ‘opal’ due to its similarities to the naturally occurring gemstone. Self-assembled PCs may be used as templates for inverse opals, which have been shown both theoretically [20] and experimentally [21] to possess a complete photonic band gap. Self-assembly can produce PCs with short periods, and so permit a complete bandgap for embedded emitters operating close to the visible spectrum. For these reasons, there has been promising progress in emission control in self-assembled PCs, mostly using dyes [22, 23] as emitters, with some work on rare-earth ions [24, 25] and quantum dots [24, 26]. A complete bandgap requires high quality crystals and a large dielectric contrast, so many of these initial studies have investigated emission in a particular direction, exploiting a photonic partial bandgap or stopband.

We present the first measurements of a single NV center in a 3D PC. We demonstrate an effective and controlled method of incorporating diamond nanocrystals into a 3D PC, with measurements of the modified NV fluorescence spectrum and correlation of this to the photonic stopband. Photon antibunching measurements are presented, showing that single NV centers can be measured from inside the crystal. Time-resolved fluorescence measurements showed an increase in the lifetime of the source, indicating that the photonic crystal has modified a fundamental property of the emitter. The embedding of single NV centers into a 3D PC is an important first step in being able to completely control the emission properties of a SPS.

2. Materials and Methods

One of the difficulties with placing defects such as emitters in 3D PCs is controlling their location. This is especially true in self-assembled crystals due to the lack of control over the placement of each period in the structure. To address this problem, we have employed a three step growth process whereby the diamond nanocrystals are ‘sandwiched’ between two thin opal films. The resulting sample has a random distribution of nanocrystals in the plane parallel to the substrate, but at a common and well defined depth in the film. The experimental details of the fabrication process are as follows. Microscope slides (Menzel) were cut in half along the long sides and used as substrates. The substrates along with scintillation vials (18 mL, Samco) were soaked in a piranha solution (H₂SO₄:H₂O₂, 3:1) for 20 minutes. They were then rinsed with ultra-pure water directly from a Milli-Q water system (18.2 MΩ cm^-1), and then rinsed with ethanol before being dried in a stream of nitrogen. Opal films were grown using a controlled evaporation method [27]. A microscope slide was placed into a scintillation vial containing a 10 mL solution of polystyrene microspheres (0.320±0.016 µm diameter, Bangs Laboratories) diluted by ultra-pure water. The refractive index of the microspheres was specified to be 1.59. Dilutions of 0.1% weight of polystyrene were used. The vial was placed in a temperature-controlled oven, set to 40°C. The increased temperature was used to speed up the evaporation process, as well as to give the microspheres enough thermal energy to prevent sedimentation. The experiment was left for approximately 24 hours to let the solution evaporate. Diamond-doped opal samples were created by spreading an aliquot of diamond nanocrystals over the top of the opal film and allowing it to dry. For the experiments detailed here, a 100 µL ethanol solution of diamond nanocrystals (containing 0.035 ± 0.002 g diamond nanocrystals per millilitre) was spread over the initial opal film. Finally, a second opal layer was grown over the top of the diamond layer. The resulting structure was made up of diamond nanocrystals ‘sandwiched’ between two thin opal films.

The diamond nanocrystals used in these experiments were high-pressure high-temperature type 1b diamond. A detailed analysis of these diamond nanocrystals was recently carried out [28], and the size of the nanocrystals containing NV centers was found to be 54±25 nm. Without any processing, the crystals were found to include naturally occurring NV centers, and were thus used untreated. A scanning electron microscope (JEOL JSM- 6480 LA) was used to characterize the microscopic structure of the opal films. Transmission spectra of the opal films were measured with a dual-beam spectrophotometer (Cary 5E UV-Vis-NIR), while reflection spectra were measured using a spectrophotometer (USB2000+ Miniature Fiber Optic Spectrometer) and a tungsten halogen light source. A 100mW continuous wave laser (only 300 µW incident on the sample) operating at 532 nm (Coherent Compass 315M-100) was used to generate fluorescence from the NV centers. The laser was focused into the sample using a 100× objective with a numerical aperture of 0.9 and fluorescence was collected confocally through a 50 µm pinhole. The diamond was excited at normal incidence to the 〈111〉 plane of the opal, which naturally grows parallel to the substrate. A spectrometer was used to characterize the fluorescence spectrum and a Hanbury Brown and Twiss interferometer including two single photon counting modules (Perkin Elmer SPCM-AQR-14) was used to measure the photon statistics. Single photon counting and second-order correlation were carried out using a time correlated single photon counting (TCSPC) module (PicoHarp 300, PicoQuant GmbH). This arrangement is shown Fig. 1(a). Lifetime of the NV centers embedded in the opal films was measured by replacing the CW excitation laser with a 1 kHz pulsed laser operating at 532 nm. The pulse duration of this laser was approximately 1 ns. A photodiode was placed behind the first turning mirror shown in Fig. 1(a) and this signal was used as the trigger (or start pulse). One of the single photon counting modules in the Hanbury Brown and Twiss setup was used to detect the NV fluorescence and acted as the stop signal. The TCSPC module was used to collect the lifetime data.

 

Fig. 1. (a) Schematic of confocal fluorescence detection system, including Hanbury-Brown Twiss interferometer for measurement of photon antibunching from single photon sources. (b) SEM of top surface of opal film prior to second opal growth. Isolated diamond nanocrystals are seen as well as nanocrystal clusters.

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3. Results and Discussion

Figure 1(b) shows a scanning electron microscope (SEM) image of the initial opal film after the diamond nanocrystals were spread across the surface. The image displays the 〈111〉 plane of the opal and shows excellent periodicity. The period of the opal is 0.305±0.015 µm, indicating some shrinkage of the spheres during the growth process. This shrinkage is consistently around 5%, and so can be accounted for in the initial design of the crystal. The thickness of the entire sandwiched structure was approximately 20 µm, or 75 layers of microspheres. Subsequent fluorescence measurements confirmed that the diamond nanocrystals were located approximately halfway through the sample. The quality of the structure was also characterized by reflection and transmission spectroscopy (Fig. 2(a)) taken at normal incidence to this surface. The spectra show that the opal has a strong rejection for wavelengths close to 710 nm, the signature of the photonic stopband for the 〈111〉 direction. The reflection and transmission spectra were taken using low irradiance broadband light sources so that no diamond fluorescence was excited. The stopband matches well to that predicted from the band structure of a close-packed face-centered cubic structure, calculated by the plane wave method, and is indicated by the shaded region in Fig. 2(a).

A typical fluorescence spectrum of a NV center (emitting into free-space) can be seen in Fig. 2(b). The noise that is evident in the data arises from the low light levels being detected from the single color centers. The spectrum has a FWHM of ~100 nm, with the peak of the emission occurring at around 700 nm. Comparison of this fluorescence spectrum to the stop-band associated with the opal in Fig. 2(a) shows that the two are spectrally aligned. Figure 2(b) also shows the emission spectrum of an NV center from approximately ten micrometers within the opal sample. There are two significant differences in the spectra shown in Fig. 2(b). Firstly, the emission from within the opal displays two closely spaced peaks at 630 nm and 636 nm. We attribute these peaks to two closely spaced Raman shifts associated with polystyrene around 2904 cm^-1 and 3054 cm^-1 measured elsewhere [29, 30]. Secondly, it displays lower emission levels in the central region of the fluorescence. This is attributed to the light in this region being blocked by the stopband of the opal. Since there is a stopband blocking wavelengths around 710 nm (in the direction of detection), the spectrum of the NV center shows lower emission at these wavelengths. On closer comparison to the position of the measured stopband (Fig. 2(a)) the wavelength region for which the NV center emission is depleted seems slightly blue-shifted. This can be attributed to the angular variation of the stopband near the 〈111〉 direction, coupled with the high numerical aperture (NA) of our collection objective.

 

Fig. 2. (a) Normal incidence reflection and transmission spectra for the opal film. The grey shaded region indicates the modeled position of the photonic stopband. (b) free-space emission spectrum of an NV center (in red) and emission spectrum of NV center encapsulated in an opal (in black). The wavelength region indicated by the arrow corresponds to the broadened stopband that arises from using a high NA lens for light collection.

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In the Bragg scattering picture, the wavelength of maximum reflectance λ, for an opal depends on the diameter of the microspheres d, the averaged refractive index of the opal n _eff, the angle of incidence with respect to the 〈111〉 plane θ, and the packing factor q. The relationship can be written as [31]:

where

and f is the volume fraction occupied by the spheres. For the case where the spheres are packed in a face-centered cubic arrangement, f=0.74 and $q=\sqrt{2⁄3}$.

It is obvious from Eqn (1) that the Bragg wavelength decreases as the angle from normal incidence is increased. The confocal detection apparatus that was used to measure the NV emission has an objective with a NA of 0.9 (the high NA objective is used for its high spatial resolution and collection efficiency, both critical for detecting single NV centers). This means the measurement is taken over a range of Δθ ~64° which broadens the Bragg peak to Δλ ~200 nm. This leaves us with a broad, weak stopband in contrast to the strong and relatively narrow stopband illustrated in Fig. 2(a). To minimise this effect an iris was used (shown in Fig. 1(a)) to reduce the measured angular range to Δθ ~20°. From Eqn (1), this causes the effective Bragg peak to broaden (and hence the range for which the NV spectrum was blocked to also broaden) to Δλ ~80 nm. This reduction in angular range proved to be sufficient to obtain a strong and narrow stopband that could be seen in the NV emission spectrum.

Antibunching in a second-order correlation (g ⁽²⁾) measurement confirms photons emitted from a source do not overlap in time (or bunch) and the source is therefore a ‘single photon source’. We measured the coincidence counts of fluorescence from a single NV center inside the opal PC using the Hanbury Brown-Twiss setup shown in Fig. 1(a). Figure 3 shows the normalized second-order correlation function

$g^{\left(2\right)}\left(\tau \right)=\genfrac{}{}{0.1ex}{}{〈:I\left(t\right)I(t+\tau ):〉}{{〈I\left(t\right)〉}^2},$

for a NV center in the opal, where I(t) represents the number of incidence counts at time t. The right axis displays the raw coincidence counts and the corrected normalized second-order correlation function is at the left after subtracting the background using the method of Beveratos et al [32]. The most prominent feature of this plot is that g ⁽²⁾(0) is very close to zero, which is the expected signature for a single quantum emitter. Generally, a value of g ⁽²⁾(0)<0.5 indicates the measurement of a single NV center. Here we measure g ⁽²⁾(0)~0.19, which is comparable to values taken for single NV centers measured on a glass substrate [32]. Note that the g ⁽²⁾ curve rises to values greater than unity for |τ|>25 ns. This is due to a longer lived metastable state which causes a bunching effect [33]. It should be noted that having a photonic crystal with low refractive index contrast allows us to identify a well defined site using the confocal detection system. For a strong crystal, this would not be the case.

 

Fig. 3. Normalised second-order correlation function (left axis) and coincidence counts (right axis) for an NV center within an opal. The fit is performed with the model detailed in [33]. The dashed grey line represents g ⁽²⁾(0)=0.5. A value of g ⁽²⁾(0) below this indicates a SPS.

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Time-resolved fluorescence measurements can be used to determine the lifetime of an emitter—the time it spends in the excited state before returning to the ground state by emitting a photon. Photonic crystals are able to modify the fluorescence lifetime by changing the LDOS that an emitter sees, and hence lifetime measurements of sources embedded in a photonic crystal provides information on the strength of the interaction between the source and the photonic crystal [26]. Figure 4 shows time-resolved fluorescence measurements of NV centers inside two opal photonic crystals. The solid circles show the average normalized fluorescence counts for a NV center emitting in an opal with stopband centered at 710 nm. The open triangles show the average normalized fluorescence counts for a NV center emitting from within a second opal, whose stopband is centered at 610 nm (this opal was fabricated using the same method, but with spheres of diameter 0.260±0.010 µm). That is to say that the first stop-gap overlaps with the NV emission spectrum, and the second does not. Both sets of data show an average measurement of five different NV centers in each crystal and the lifetimes were determined to be 13.3±0.8 ns and 10.2±2.0 ns respectively. The uncertainty given in the lifetime values is indicative of the homogeneity of the lifetime measurements, as it represents the lifetime measurement farthest from the mean value. The measurements show that the lifetime of the NV centers is significantly longer when the stopband is overlapping the NV emission spectrum.

 

Fig. 4. Time-resolved fluorescence measurements of the NV centers inside opals. The data represented by solid circles is an average measurement of five different NV centers in an opal with a stopband positioned at 710 nm (overlapping the NV spectrum), and was found to have a lifetime of 13.3±0.8 ns. The data represented by open triangles is an average measurement of five different NV centers in an opal with a stopband positioned at 610 nm (non-overlapping), and was found to have a lifetime of 10.2±2.0 ns. The lifetime measurements were taken from NV center nanocrystals that displayed antibunching, and so contained one or few color centers. Note that the time indicated as t=0 is actually 11 ns after the excitation pulse. This removes any information from the laser pulse in the determination of the lifetime.

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By choosing to take measurements in opals with different stopband positions, we can determine the effect that the photonic stopband has on the lifetime of the embedded NV centers. Since the opals are both made from polystyrene microspheres and they both pack into a face-centered cubic lattice, then Eqn (2) dictates that the average refractive index of the two crystals is identical. Therefore any variation in the lifetime of emitters radiating from within the crystals cannot be explained because of a variation in refractive index. This does however explain why the values of the lifetimes are lower than usual. Although the lifetimes of NV centers in nanocrystals are often reported to be larger than the value in bulk (~12 ns [32]), we are embedding these emitters in a dielectric environment. This has the effect of reducing the lifetime, and in our case it has reduced it to below the bulk diamond value. The variation in the lifetime between NV centers in different opals can be explained through the modification of the LDOS that the NV center sees. In the case of the NV center radiating into the opal with stopband at 610 nm, there is no overlap between the NV emission spectrum and the stopband, and so the LDOS is not altered. When the NV center radiates into the opal with stopband at 710 nm, there is an overlap with the photonic stopband and the LDOS is reduced. As a result, there are less states to emit into, and hence the lifetime will increase. For these experiments, we see an increase in the lifetime of close to 30% in the opal where the bandgap is overlapped with the NV spectrum. While this is a modest change in comparison to some recent results in 2D photonic crystals [15, 16], we are taking measurements from a crystal with a low refractive index contrast (Δn ~0.6) and small spectral overlap with the emitter. When compared to lifetimes measured in other 3D PCs that do not exhibit a full 3D bandgap, these results are of a similar magnitude. Specifically, Lodahl et al. [26] measured an increase of 55% in titania inverse opals and Li et al. [34] measured an increase of 35% in a polymer woodpile structure. Calculations performed by Nikolaev et al. [35] confirm that a reduction in the LDOS and emission rate is expected at the stopband wavelength for an opal fabricated from polystyrene microspheres. The magnitude of this reduction was found to be approximately 20%.

Self-assembled photonic crystals fabricated from polystyrene microspheres provide a good platform for studying the relationship between LDOS and a single photon source. The low index contrast allows for high resolution, low noise, confocal detection that is not possible in stronger crystals that become highly scattering. We have shown through our second-order correlation function that we can measure single NV centers inside the 3D photonic crystal. Time-resolved fluorescent measurements showed that the NV centers emitting inside the opal possess a longer fluorescence lifetime induced by the interaction between the photonic crystal and the NV center. We believe that further modification of the SER is limited by overlap between the emission and stopband spectrum. By working with a SPS with a narrower emission spectrum, the overlap with the stopband would be greater and so too the modification of the lifetime. Furthermore, a spectrally narrower source provides the opportunity to design the photonic crystal such that the emitter would line up on the band edge. In this case, an increase in the SER may be achieved [19]. Suitable sources include NV centers at low temperature where the emission linewidth is much narrower. Other diamond defect centers such as Nickel [11, 36] which possesses a narrow emission at room temperature may also be suitable, although currently these are not readily available in nanocrystal form. Now that we have shown measurements of single NV centers in low index contrast crystals, it would be advantageous to combine these narrow linewidth sources with high index contrast crystals in the future. A higher index contrast may provide a stronger stopband with a sharper band edge, further enhancing the SER of a narrow emitter operating at this edge. Confocal detection techniques may not be suitable for such experiments due to scattering issues.

4. Conclusion

We have demonstrated a simple and effective method of incorporating and measuring NV centers in 3D PCs. The opal stopband can be specifically tailored to overlap the emission of the diamond emitters, and single photon behavior was measured from these sources. Time-resolved fluorescence measurements show an increase in the lifetime of NV centers embedded inside the opal, a clear signature of interaction with the photonic crystal. At room temperature, NV centers are a broad emitter (~100nm) and because of this, we cannot completely overlap the photonic stopband. However, this work shows a clear pathway for integrating narrow linewidth diamond defect centers, where an enhanced SER at the band edge is feasible. Furthermore, since the opal structure can be used as a template for creating an inverse opal with a full 3D bandgap, there are possibilities of emission control in all directions.