Robust, tunable, and high purity triggered single photon source at room temperature using a nitrogen-vacancy defect in diamond in an open microcavity

: We report progress in the development of tunable room temperature triggered single photon sources based on single nitrogen-vacancy (NV) centres in nanodiamond coupled to open access optical micro-cavities. The feeding of ﬂuorescence from an NV centre into the cavity mode increases the spectral density of the emission and results in an output stream of triggered single photons with spectral line width of order 1 nm, tunable in the range 640 - 700 nm. We record single photon purities exceeding 96% and estimated device eﬃciencies up to 3%. We compare performance using plano-concave microcavities with radii of curvature from 25 µ m to 4 µ m and show that up to 17% of the total emission is fed into the TEM 00 mode. Pulsed Hanbury-Brown Twiss (HBT) interferometry shows that an improvement in single photon purity is facilitated due to the increased spectral density.


Introduction
The realisation of a convenient triggered single photon source (SPS) device that operates at ambient temperature remains an outstanding challenge in the field of photonics. Such a device would be an important enabling technology for quantum science and technology in general, with prospects for use in quantum cryptography, metrology and sensing. Many single quantum systems have been shown to exhibit non-classical photon emission characteristics [1][2][3][4], but most suffer fundamental limitations such as instability, or require low temperature operation. Whilst tremendous progress has been made in recent years with the engineering of high quality single photon sources based on semiconductor quantum dots operating at cryogenic temperatures, the first commercial devices of this type will inevitably be quite bulky and costly to manufacture, and so devices with the potential to deliver robust, room temperature sources remain of considerable interest.
Of the available candidate systems for a room temperature SPS, Nitrogen-vacancy (NV) centres in diamond have been shown to be both bright and stable [5], with single photon emission robust to extended optical pumping, modest thermal cycling and exposure to an oxidising atmosphere. NV centres in nanodiamond have been used in a previous commercial single photon source device [6], but the spectrally broad emission from an NV centre emitting into free space or a bulk material (full-width at half-maximum of about 60 nm between 650 nm and 710 nm) is not well suited to most applications. Optical microcavities [7] provide a practical solution to this problem. Coupling of spectrally broad emission to a narrow microcavity mode -the so-called 'bad emitter regime' of cavity quantum electrodynamics -results in the 'feeding' of emitted photons into the cavity mode [8] such that the emission takes on the spectral and spatial properties of the mode without substantial loss of intensity [9]. Since microcavity modes can be engineered to have desirable spatial properties for coupling into external optics and can be tuned spectrally, the emission can also be tailored for practical device applications. In particular the increased spectral density achieved by the feeding process is of benefit for low light level free-space applications where the emitted photons must be distinguished from a broad ambient background. The relatively broad band emission of the NV centre also offers the attraction of a wide spectral tuning range with potential for wavelength division multiplexing of single photon streams.
To maximise the efficiency of a room temperature NV-cavity device it is essential to minimise the cavity mode volume as far as is possible, and with this in mind, cavity coupling using plasmonic structures [26], and ultra small Fabry Pérot cavities with metal mirrors [23] have been demonstrated. These approaches can lead to high out-coupling efficiency but offer little ability to control or tune the spectra, and single photon fidelity can be compromised by autofluorescence from the metal components.
Here we report the performance of room temperature devices in which single NV centres in nanodiamond are coupled to open microcavities consisting one planar and one concave mirror. This particular style of microcavity has become increasingly popular in recent years for their ease of alignment, tunability, and efficient coupling to external optics [10][11][12][13][14][15][16]. A wide range of experiments coupling single photon emitters to open cavities has been reported, including quantum dots [17], diamond colour centres [18][19][20][21][22][23][24], and single molecules [25]. Much of the preceding work has been concerned with coupling NV centres to cavities with relatively high quality factors [18][19][20][21], or with metallic mirrors and much lower cavity quality factors [23]. In the experiments reported here we use dielectric mirrors to produce open microcavities with intermediate finesse, providing a combination of narrow spectral line width, high single photon fidelity, high spectral density, tunability and modest device efficiencies. We use focused ion beam (FIB) milling to achieve precise fabrication of the concave mirror template with radius of curvature (RoC) between 4 µm and 25 µm, thus allowing systematic comparison of performance as a function of microcavity design. We find that best performance is achieved with RoC = 8 µm, providing a balance between strongest cavity feeding and efficient photon extraction from the cavity mode into the external optics. Specifications of these single photon sources are characterised in detail.

Method
The nanodiamonds (NDs) used in this work were commercially available high-pressure hightemperature material (Microdiamant) between 35 nm and 100 nm in diameter, which had been cleaned using a tri-acid mixture and centrifuged to narrow the size distribution. Plano-concave open access microcavities were formed between two decoupled substrates; one planar mirror and one featured mirror (inset, figure 1(d)). Production of the featured mirror begins with a 500 µm thick fused silica substrate (UQG Optics). A silicon dicing saw is used to score trenches ∼200 µm deep across most of the surface, leaving small protruding plinths ∼ 300 × 300 µm in size (figure 1(a)) as reaching cavity lengths ∼ 1 µm is problematic using substrates with larger surface areas. Concave features 600 nm in depth are formed on the plinth using a FIB [13,27] and the substrate is then commercially coated (LaserOptik) with 16 pairs of Distributed Bragg Reflector (DBR) layers yielding a peak reflectivity R f > 99.99% at 640 nm, and a transmission of ∼ 50% at 532 nm. The ion beam sputtered dielectric layers consist of silica (SiO 2 n r = 1.49) and tantalum pentoxide (Ta 2 O 5 n r = 2.1) for a high refractive index contrast as well as a high packing density to minimise absorptive and scattering losses within the DBR. The featured mirror is terminated with Ta 2 O 5 to minimise mode penetration into the mirror as well as minimising the contribution of surface contaminants to intra-cavity scattering due to a node of the resonant field forming at the substrate surface. The planar substrate is coated with 11 pairs of layers to act as the out-coupler of the resonator (R p ∼ 99.7%), and is terminated with a SiO 2 layer to ensure an antinode of the electric field at the mirror surface for strong interaction with the spin-cast nanodiamond. The planar mirrors were marked with a Ga + FIB (FEI FIB200) prior to spin-coating with the ND suspension, to provide a reference 'grid' that allow specific NDs to be located when the mirror is inverted. Characterisation of the NDs and measurement of the device performance was carried out using a home-built scanning confocal microscope based on a steering mirror (Newport FSM 300-01) directing a 532 nm excitation source (Oxxius LCX-532L, 250 mW) through a 4-f telecentric lens pair to an Olympus 0.8 N.A air objective lens. For pulsed excitation an amplified picosecond pulsed laser diode at 531 nm (Picoquant LDH-P-FA-530B) was used. Collected fluorescence was passed through a 50 µm pin hole followed by a free space 50:50 beam splitter with one output directed onto a single photon avalanche diode (SPAD, Excelitas SPCM-AQRH-14-TR) and the other to a multi-mode fibre which could be coupled to either a fibre-coupled SPAD, or a spectrometer.
To identify suitable single NV centres for cavity coupling, fluorescence from the spin-cast nanodiamonds on the planar mirror is first imaged as shown in figure 1(c). Peaks in intensity are identified by an image processing script and an automatic sequence conducts Hanbury Brown and Twiss (HBT) interferometry on each. This was found to be an effective way to both photo-bleach unstable features, and allow the remaining peaks to be rapidly assayed to identify strong and stable single photon emitters. The fluorescence saturation intensity and saturation excitation power (I sat & P sat respectively) were measured for each of these selected NV centres, and the orientation of their axis of symmetry found by rotating the excitation polarisation. The polarisation state of the emitted photons was not investigated during this study however the TEM 00 for the cavities used here is degenerate for orthogonal polarisation states, and so the polarisation properties of the NV centre's emission are thought to be unaffected by its coupling to these cavity modes. The fluorescence spectrum was recorded to ensure that the NV centre remained predominantly in the negative charge state. Time-correlated single photon counting yields the excited state lifetime through time-resolved photoluminescence (TRPL), and HBT measurements were performed with pulsed excitation to establish the single photon emission fidelity.
Once the selected NVs have been fully characterised, the planar mirror is inverted and the same NV centres relocated using the registration marks, allowing a concave mirror to be positioned behind a chosen NV as shown in figure 1(d). The cavity coupling and tuning is then achieved by reducing the cavity length with a piezoelectric actuator. The plano-concave resonators display Hermite-Gauss mode structure, denoted by TEM nm , where n and m are the orders of the Hermite polynomials describing the field distribution in the x and y directions respectively. Figure 2 shows fluorescence spectra and images obtained from coupling the same NV centre (NV1) to cavities with concave mirror RoCs 25, 12, 8 and 4 µm and diameters 10, 7.5, 5.5 and 4 µm respectively. Coupling of the NV emission to multiple cavity modes is observed in each of the spectra in figure 2(a), with the strong, regularly spaced modes corresponding to the transverse excitations of the primary TEM 00 modes. In each case the cavity length was minimised such that only a few field nodes existed between the mirror surfaces. Careful positioning of the NV centre on the axis of the cavity results in optimal coupling to the modes with m,n both even and negligible coupling to modes with odd m or n. In figure 2(a) such optimal alignment is apparent from the RoC 25 and 12 µm cavities whereas for the two smallest cavities some coupling to odd modes is also observed. The TEM 00 mode was found to dominate the measured output increasingly as the RoC was reduced. This observation is explained by the larger numerical apertures of the higher transverse modes in the smaller RoC cavities, such that these modes have higher clipping losses at the edges of the concave mirrors and couple less efficiently into the microscope objective.

Results and analysis
As well as modulating the output spectrum, closing the cavity increases the device efficiency. Figure 3(a) shows the effect of the cavity length on the detected photon count rate from a single NV centre coupled to a RoC 8 µm cavity. As the cavity length is reduced, oscillation in the measured intensity is observed as the modes of successive longitudinal index pass through resonance with the NV emission. The inset for figure 3(a) highlights the first maximum, and indicates approximate locations corresponding to the observed spectra in figure 3(b). A strong device output signal persists over a 40 nm spectral range. In the uppermost spectrum of figure  3(b) the next higher family of TEM mn modes, allows for the free spectral range (FSR) to be ascertained. A 1D transfer matrix approach was used to model this transmission spectrum, revealing that it corresponds to a physical mirror separation of 980 nm. The mode penetration into the mirrors can also be included by taking the value at which the field intensity drops to 1/e of its intra cavity value, yielding a total optical path length of L = 1.77 µm. Lateral mode spacings were calculated using resonator theory, and also by importing AFM topographies into FDTD simulations. Both approaches show the transverse mode spacings to be in excellent agreement with the experimentally recorded data. Calculating the cavity finesse from the FSR and homogeneous linewidth yields F = ∆λ δλ = 270, which is an order of magnitude lower than the value suggested by only considering the average reflectivity of the mirrors (∼ 2200). This implies the other sources of loss which is probably a combination of those associated with the contoured DBR in the mirror feature seen previously [13] and scattering from the ND itself and other surface contaminants. Figure 3(c) shows the spectrum of NV2 observed whilst the DBR was facing towards the objective lens (blue data) with a peak emission intensity at a wavelength of around 660 nm. This peak wavelength is slightly blue-shifted compared with the free-space emission of the NV centre due to the reflection band of the dielectric mirror. Using FDTD simulations to simulate the effect of the mirror on collected fluorescence, we reconstruct the free-space NV emission spectrum (green data) which peaks at a wavelength of 680 nm. This spectrum agrees well with the relative intensities of the TEM 00 modes recorded as the cavity is tuned.
The mode coupling efficiency is established by recording the fluorescence intensity as a function of excitation power and fitting with the function N = P N s at P s at +P + BP. Here N is the measured fluorescence count rate on the SPAD and P is the laser power at the objective back aperture, while the saturation count rate N sat , the saturation power, P sat and the background contribution B are fitting parameters. A power dependence is first recorded from the DBR without an NV present. This region was photo-bleached until stable, and is used to provide an initial value for B when fitting the NV's emission. The final fitted background component is subtracted from both the fits and the plotted data for clarity. Here three cases are considered; first the initial NV fluorescence collected with the DBR facing the objective lens (blue), the full NV-cavity coupled emission spectrum (red), and a single TEM 00 mode (green). In order to collect only a single TEM 00 mode, an 8 nm band pass filter (Semrock FF01-690/8-25) is placed in the fluorescence path, and a cavity mode is tuned into this region. Fits yielded N sat values of 495 kcps, 167 kcps and 88 kcps for the full spectrum on the DBR, the full cavity spectrum and a single TEM 00 mode respectively. Integration of the spectrum shown in figure 3(c) that of the 495 kcps 5.4% of it lies in an 8 nm spectral band centered at 690 nm. This means out of the cavity 26.6 kcps would have been collected through such a filter, in contrast to the 88 kcps measured when the emitter was placed within the cavity. From the ratio of N sat for the cavity-coupled TEM 00 mode and that of the same NV with only the planar mirror present, we estimate that ∼ 17.8% of the emitted fluorescence is output into this single TEM 00 mode. With a measured TEM 00 mode width of 0.35 nm this coupling efficiency corresponds to an increase in spectral density by about a factor of 30. Figure 4 (b) follows the same colour scheme as figure 4(a) and shows measured continuous wave g (2) (τ) datasets for each case. The degree of photon antibunching observed in g (2) (0) gives an indication of single photon purity. A variety of excitation powers were used; 0.1P sat (= 0.15 mW), 1.5P sat (= 0.8 mW) and 2P sat (= 1.1 mW) for the DBR facing the objective, the full cavity spectrum, and the single TEM 00 mode datasets. The lower count rates observed for the full cavity and TEM 00 meant a shift to higher powers facilitated data acquisition. The DBR and full cavity  histograms show very similar g (2) (0) values, while the TEM 00 histogram shows a noticeable reduction in g (2) (0), despite the higher excitation power, as a result of the blocking of broadband background by the bandpass filter.
Quantitative values for device parameters such as the single photon fidelity (ν) and efficiency (η) require pulsed excitation. The laser pulse repetition rate was set to 5 MHz to ensure full decay of the fluorescence between excitation pulses. HBT data to establish the single photon fidelity are shown in figure 4(c) and (d), maintaining the same colour scheme as used in figures 4(a) and (b). The inset shows the central region plotted on a logarithmic scale, with a Gaussian filter applied to remove noise. As with the cw measurements, we find that the presence of the cavity degrades the single photon fidelity if the full spectrum is collected, but the use of a narrow (8 nm) bandpass filter around the TEM 00 mode restores the fidelity and even improves it compared with that observed in the absence of the cavity. The fact that such strong spectral filtering improves the situation shows that background, uncorrelated light diminishes single photon purity in this system. By using a microcavity to concentrate the NV emission spectrally to a TEM 00 mode, the benefits of such filtering can be gained without a significant loss in single photon count rate. Figure 4(d) shows semi-logarithmic plots of curve fits used to quantify the single photon purity in each case. The fitting function comprises rising and falling exponentials, centred at the peak location, upon a time-independent background. This function is fitted to the central peak at τ = 0 and the peak at τ = 200 ns for each measurement. The simple ratio of the peak heights reveals the highest purity one could achieve with this device if time gating is included and the uncorrelated background cannot be removed. For the three situations recorded (DBR, full cavity spectrum, TEM 00 only) we obtain values of ν = 92.7%, 89.1% and 96.3% respectively. The background values provided by the fits for the three situations are 0.041, 0.078 and 0.019 respectively, suggesting that if the uncorrelated signal can be removed fidelities of ν = 96.8%, 96.9% and 98.2% would be achieved.
The device efficiency is estimated by dividing the fitted value of I sat under pulsed illumination by the pulsed excitation rate. This parameter was only measured using the full cavity-coupled spectrum (i.e. with no spectral filter to isolate the TEM 00 ). With the pulsed illumination set at 5 MHz we record I sat = 51 kcps, corresponding to a system efficiency of just over 1%. Using the measured ratio of I sat for the full cavity spectrum to the filtered TEM 00 under cw excitation, we infer a system efficiency for TEM 00 mode of ∼ 0.5%. Subsequent experiments using planar mirrors with peak reflectivities of 97.5% rather than 99.7% have recorded TEM 00 mode I sat values of 45 kcps under the same excitation conditions, providing a system efficiency of 0.9%. Taking into account transmission losses in the microscope optics (excluding the objective lens) and the finite efficiency of the single photon detectors we estimate that this corresponds to a device efficiency approaching 3%.
Finally we obtain a further measure of the cavity coupling by comparing the fluorescence lifetime of an NV centre in and out of the cavity. Figure 5 shows time-resolved photoluminescence measurements taken on NV2 when on the DBR substrate facing the mirror (blue) and when cavity coupled (green). Such measurements are insensitive to filtering of the emission and so the full cavity coupled spectrum was used. This plot shows that cavity coupling leads to a marked decrease in the fluorescence lifetime. For both of these decays, the best fits were given by bi-exponential expressions, with a slightly weaker short time component (τ 1 ) and a longer dominant contribution (τ 2 ). Whilst the shorter component increased from τ 1 = 7.7 ns to τ 1 = 8.9 ns the dominant part of the decay was seen to decrease from a lifetime of τ 2 = 23.6 ns to τ 2 = 18.6 ns, corresponding to a rate enhancement of 26.3%. The weaker component is a factor of 0.9 smaller than the longer component, which drops to 0.8 when placed inside the cavity. From these results it is not clear what the physical origins of decay route responsible for the shorter lifetime are. The longer decay time is close to the value expected for negatively charged NV centres in nanodiamond.
FDTD simulations reveal a mode volume of 4λ 3 , and the effective Q factor of the system is shown from 1 Q e f f = 1 Q c av + 1 Q e mi t = 0.35 690 + 70 690 to be ≈ 10. From the usual expression for the Purcell factor, F p = 3Q e f f 4π 2 V λ n 3 , taking the refractive index of the mode to be 1 corresponding to the air intracavity medium gives F P = 0.2 for the TEM 00 mode alone, and including proportionate contributions from the other transverse modes present in the measured spectrum in figure 2a gives an effective Purcell factor of 0.3, in excellent agreement with the measured value, once the emission into non cavity modes is taken into account by adding 1. The efficiency of coupling into the TEM 00 mode of β = F P /(F P + 1) = 0.17, also in excellent agreement with the coupling efficiency measured from the comparison between the measured fluorescence intensities described earlier.

Conclusions and outlook
In summary we have reported progress in the realisation of robust, room temperature triggered single photon sources based on the coupling of a single NV centre in nanodiamond to open access microcavities with dielectric mirrors. We have demonstrated optimisation of the cavity parameters by the repeatable coupling of the same single NV centre to a series of engineered cavity mirrors. We find that up to 17% of the room temperature emission is coupled into a single TEM 00 mode of width 0.35 nm, corresponding to an increase in spectral density by a factor of 30 and demonstrating the important role that cavity feeding in the bad emitter regime can play in achieving a tunable room temperature single photon source. Single photon fidelity in excess of 96% is recorded, along with a recorded single photon device efficiency of around 3%. Such device specifications hold promise for the realisation of practical triggered single photon sources operating at room temperature.