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Abstract
In this work, the lifetime of nitrogen-vacancy color centers within nanodiamonds is reduced from 550±13 ps to 297±10 ps through the implantation of xenon. Coupled-mode analysis is employed to characterize the mechanism responsible for the reduction in emission lifetime. The observed spectral lineshape is found to be consistent with a Voigt profile consisting of two Lorentzian resonant peaks at 637 nm and 811 nm that are inhomogeneously broadened by a Gaussian distribution. A convolution of the frequency-domain Lorentzian output, with linewidths less than 1 nm, from the coupled-mode system of equations with a Gaussian with standard deviation of 85 nm is performed to generate the Voigt profile. The shortened emission lifetime is found to be consistent with a coupled mode theory model incorporating coupling between nitrogen-vacancy and xenon-vacancy color centers.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Quantum information technology is a rapidly growing field that calls for technologies that prepare, evolve, and measure quantum bits (qubits) to be successful [1]. Evolution technologies that allow qubits to be transferred and interact optically are likely to include solid-state optical quantum emitters [2]. Quantum emitters, comprising a host of technologies such as quantum dots, rare earth impurities, and color centers in diamond have many applications. They can produce indistinguishable single photons on demand [3–7], enable interactions between single photons [8], and can store and process quantum information in the spin states [9–11]. Quantum emitters can also sense electromagnetic fields [12,13] at nanoscale dimensions. The color centers in nanodiamond are an example of a set of quantum emitters that have been studied extensively [14].
Many varieties of nanodiamond color centers have been evaluated, such as iron, titanium, and xenon [14]. Each one exhibits different optical properties. The nitrogen-vacancy (NV) color center is the most commonly studied color center with over 50 years of research [15].
The NV center is a point defect in diamond with ${C_{3v}}$ symmetry consisting of a substitutional nitrogen-lattice vacancy pair oriented along the [111] crystalline direction. It is created in the chemical vapor deposition of diamond, or by radiation damage and annealing, or by ion implantation and annealing in bulk and nanocrystalline diamond. The NV center is known to have negative ($N{V^ - }$) and neutral ($N{V^0}$) charge states. These charge states are identified by their optical zero phonon lines (ZPLs) at 1.945 eV (637 nm) and 2.156 eV (575 nm) respectively [16]. The associated vibrionic bands extend from their ZPLs to higher/lower energy in absorption/emission.
Both charge states of the NV color center have been identified as room temperature single photon sources [17–19]. This was confirmed through statistically-significant antibunching dips observed through second-order autocorrelation measurements [often abbreviated as ${g^{(2 )}}(\tau )$].
While NV color centers offer the attractive feature of room temperature single-photon emission, one of the key obstacles to the utilization of nitrogen vacancy color centers in quantum information technologies are their long bulk emission lifetimes, typically 80 ns [20]. These lifetimes do not support the fast repetition rates necessary for most quantum information applications [21].
Attempts have been made to shorten the emission lifetimes of NVs using various methods, such as coupling to surface plasmons [20], modifying the substrate refractive index [22], or introducing radiation induced lattice defects (RILDS) [23]. These methods have been largely successful, but come with various tradeoffs, such as decreased emitter intensity when applying RILDs, or difficult and irregular construction when plasmonic methods are utilized.
In this work, we describe a precise fabrication method for the shortening of NV color center lifetimes while preserving their broadband emission and intensity.
We discuss first the fabrication and initial optical characterization of nanodiamond films and their subsequent ion implantation with xenon. The post-implant optical characterization is discussed before concluding with an analysis of our findings using coupled mode theory. In our analysis, we create a model of our system using idealized components, and the associated coupled-mode system of equations. Next, we solve the system of equations to obtain analytical expressions for the spectral intensity lifetime before generating a Voigt profile, representing our model’s frequency response, that is in good agreement with the experimentally observed lineshape of our color centers.
2. Methods
We conducted the nanodiamond film assembly process in two stages: film deposition and ion implantation. In the first stage, we created a very dense film to increase the chances of successful ion implantation using the Salt-Assisted Ultrasonic disaggregation (SAUD) [22–28]. In the second stage, ion implantation of xenon was performed at Sandia National Laboratories.
All optical characterization was performed using a custom-made scanning confocal microscope. Further details of all these procedures are included in the Supplement 1 provided.
3. Results and analysis
3.1 Film characterization
Dynamic Light Scattering (DLS) measurements were conducted with the Malvern Zetasizer ZS Nano. Post-SAUD, DLS measurements indicated that the z-average (intensity-weighted mean hydrodynamic size of the particles) decreased from 43 nm to 18 nm, with a polydispersity index decrease from 0.203 to 0.100. After analysis of the surface with a scanning electron microscope, the film was deemed to have good surface coverage.
Photoluminescence spectroscopy was subsequently performed using the fluorescence intensity measurement method on the film with a custom scanning confocal microscopy setup. PL measurements revealed the presence of several nitrogen vacancy color centers. Those color centers were analyzed, and a spectrum matching with that of a typical nitrogen-vacancy (NV) color center was observed from all regions of the film investigated.
3.2 Optical characterization
The film was implanted with xenon ions at Sandia National Laboratories, and subsequently annealed at 500°C for one hour. After implantation, the film was optically characterized using the same custom scanning confocal microscopy setup and was found to still contain several color centers. The spectrum shows a peak at ∼624 nm. This peak is red-shifted by 30 nm with respect to previous experiments involving xenon implantation into diamond. Previous experiments involving photoluminescence spectroscopy performed on nanodiamond agglomerates [24], as well as previous work detailing the size dependence of fluorescent nanodiamond emission [25]. The photoluminescence spectrum from the NV centers can vary depending on the particle size and agglomeration pattern [25]. For certain aggregation patterns, photoluminescence peaks around 630–650 nm can be observed in experiment [24], which is in the same spectral region that was observed in our sample. Previous experiments have shown that the emission spectrum of nitrogen vacancy color centers will vary according to excitation wavelength [26–28] Our excitation wavelength was 532 nm, while the previous xenon-related work was excited at 514.5 nm. In this previous work, a characteristic $N{V^0}$ zero phonon line (575nm) was reported for samples annealed at 700${\circ}{C}$, showing good evidence of the contribution of NV-related emission in samples annealed at these temperatures. Our measured spectrum is also very similar to previous experiments involving the implantation of xenon into type 1A diamond [28]. Combining these papers supports our understanding that the measured spectrum reflects fluorescence from nitrogen-vacancy color centers.
Several scans were conducted, and no photobleaching was observed. Fluorescence lifetime measurements of color centers within the film were conducted at random within the field of view, which was made possible by the abundance of individual color centers. The measured lifetimes of color centers within the film were remarkably short (below 1 nanosecond), and displayed low variance across the sample, as expected, given the fluence rates of the implantation.
In our experiment, the measured fluorescence lifetimes of the color centers within the film typically exhibit a bi-exponential relationship, with two exponential lifetimes ${\tau _1}$ and ${\tau _2}$. The longer lifetime, ${\tau _2}$, is typically associated with color centers within the bulk of the nanodiamond, while the shorter lifetime ${\tau _1}$ is associated with surface effects [20,23].
Results from time-resolved photoluminescence are provided in Fig. 2. We performed a bi-exponential nonlinear least-squares fit on the experimental data to extract the relevant lifetimes and amplitudes, and then calculated the standard error of the lifetimes. The fluorescence lifetime of implanted color centers within the bulk were found to be ${\tau _2} = 297 \pm 10\; \textrm{ps}$, with the surface effect lifetime ${\tau _1} = 42 \pm 14\; \textrm{ps}$. This is a remarkable reduction in lifetime for nitrogen vacancies in nanodiamond, which typically have a fluorescence lifetime on the order of 40–80 ns [23]. A comparison to pre-implantation lifetimes yielded a similar bi-exponential relationship with the surface-associated lifetime ${\tau _1} = 38 \pm 8\; \textrm{ps}$ and the bulk lifetime ${\tau _2} = 550 \pm 13\; \textrm{ps}$. The pre-implant bulk lifetime observed can be attributed to the presence of C-Centers (single nitrogen substitution within the lattice), as has been reported in the literature [23], since the pre-Implant diamonds were type 1A diamonds that are known to contain several C-Centers [23]. The intensity of the post-implant fluorescence compared with the pre-implant fluorescence was also measured, and the post-implant fluorescence intensity was approximately twice that of the pre-implant fluorescence intensity. The two fluorescence measurements are documented in Fig. 1. The observed sharp decay from the pre-implant species is due to the higher contribution of surface effects ($\tau = 38 \pm 8\; \textrm{ps}$) in the observed fluorescence.
Fig. 1. Process flow diagram for Xe color center fabrication. a.) A nanodiamond film is deposited using disaggregated nanodiamonds in solution via electrophoretic deposition prior to ion implantation. b.) The resultant film is characterized via scanning electron microscopy and reveals good surface coverage. c.) The resulting film is implanted with Xe species at a fluence of ${\mathbf{10^{14}}}$ ${\textbf {ions}}/{\textbf c}{{\textbf m}^2}$; the resulting color centers are characterized via scanning photoluminescent (PL) spectroscopy (this image has a field of view of 20 × 20 µm2).
Fig. 2. Lifetime measurements are conducted on pre-implant (gray) and post-implant (blue) color center species. Pre-Implant and post-implant data is represented by the grey and black circles, respectively. Post-Implant color centers show a bulk lifetime of ${{\boldsymbol \tau }_\mathbf 2} = $297${\pm} {\mathbf{10}}$ ps. This is a 43% reduction in bulk lifetime compared to pre-implant color centers. The sharp decline in the pre-implant data is due to the higher contribution of surface effects (${{\boldsymbol \tau }_1} = $ 38${\pm} {\mathbf 8}$ ps) in the observed fluorescence.
Several attempts were made to explain the peculiar fluorescence characteristics of the post-implant film, such as the introduction of additional point C-Centers or other radiation-induced lattice defects. The results, specifically the increase in fluorescence intensity, the relatively unchanged surface lifetime, and shortening of only the bulk lifetime, are contrary to the predictions of prior work. The literature predicts a shortening of both bulk and surface lifetimes, as well as the lowering of the fluorescence intensity of nitrogen vacancy color centers as the number of C-Centers and other lattice defects grows [21]. This quenching effect is from the creation of non-radiative energy transitions within the ground and excited states of the nitrogen vacancy color centers. As these effects are not present here, it is fair to assume a different mechanism is responsible for the decreased lifetime, and increased fluorescence of the color centers. Coupled-mode theory calculations can be employed to help elucidate this mechanism in detail.
4. Discussion
Coupled mode theory was developed in the 1950s to analyze and design of a broad range of devices including microwave traveling-wave tubes, parametric amplifiers, oscillators, and frequency converters. Central to the theory is the analysis of lossless resonances, and their coupling to similarly lossless waveguides, and one-another. The theory serves as an approximate, yet insightful and accurate mathematical description of the electromagnetic oscillations and wave propagation for coupled systems [29–31].
For the purposes of our analysis, we considered only the lifetime reduction associated with the nitrogen-vacancy color center in the bulk. The system was described as a two-resonator system with the field amplitudes of the lowest-order resonator modes in each resonator given by ${A_1}$ and ${A_2}$, corresponding to resonator 1 and 2 respectively. Each resonator possesses a resonant frequency denoted by ${\omega _{1,2}}$. A coupling term representing the weak coupling between the resonators was denoted by ${\tau _{12}}$. In our analysis, resonator 1 represents our pre-implant nitrogen-vacancy color center while resonator 2 represents a typical $Xe$ color center and we consider asymmetric and symmetric coupling between the two resonances. This two-resonator system is symmetrically coupled to two identical waveguides representing the propagation of EM waves in air on one side, and into the substrate on the other. These waveguides are known as waveguides 1 and 2, respectively. The coupling constants of resonance 1 to waveguides 1 and 2 are given by ${\tau _{11W}}$, and $\; {\tau _{12W}}$. The coupling constants of resonance 2 to waveguides 1 and 2 are given by ${\tau _{21}}$ and ${\tau _{22w}}$. All coupling constants are known via experiment or the literature. The resonances and coupling constants give rise to two simultaneous differential equations for symmetric coupling:
The case of asymmetric coupling between resonances 1 and 2, with energy coupling from resonance 1 to resonance 2, was also investigated with corresponding rate equations:
A schematic corresponding to the system is provided in Fig. 3. The solution for the symmetrically coupled resonances involves a second order differential equation. It yields the following roots:
The coupling term, ${\tau _{12}}$, was found by matching the field amplitude ${A_1}$ with our post-implant experimental spectral measurement results shown in Fig. 4, and was found to equal 647.5 ps. The solution for the asymmetrically coupled resonances contains a single exponential term:
Fig. 3. Schematic diagram showing the essential features of our coupled-mode theory model: two single-mode waveguides 1, and 2, with output field amplitudes ${{\boldsymbol s}_{\mathbf{1},\mathbf{2} - }}$; two resonances of field amplitudes ${{\boldsymbol A}_{\mathbf{1},\mathbf{2}}}$ and fequencies ${{\boldsymbol \omega }_{\mathbf{01},\mathbf{02}}}$ coupled to waveguides 1 and 2, and one another with lifetimes ${{\boldsymbol t}_{\mathbf{11}{\boldsymbol w}}}$, ${{\boldsymbol t}_{\mathbf{12}{\boldsymbol w}}}$, ${{\boldsymbol t}_{\mathbf{21}{\boldsymbol w}}}$, ${{\boldsymbol t}_{\mathbf{22}{\boldsymbol w}}}$, and ${{\boldsymbol t}_{\mathbf{12}}}$. ${{\boldsymbol s}_{\mathbf{1},\mathbf{2} - }}$ are normalized so that ${|{{{\boldsymbol s}_{\mathbf{1},\mathbf{2} - }}} |^{\mathbf 2}}$ is power in the waveguide, and ${{\boldsymbol A}_{\mathbf{1},\mathbf{2}}}$ are normalized so that ${|{{{\boldsymbol A}_{\mathbf{1},\mathbf{2}}}} |^{\mathbf 2}}$ is energy in the cavities.
Fig. 4. Photoluminescence spectrum of post-implant color centers (blue) with Voigt profile generated by coupled-mode system of equations overlaid in grey. A good match between our experiment and theoretical analysis is achieved by considering inhomogeneous broadening effects, specifically strain broadening, within the diamond sample.
As in the symmetrically coupled regime, ${\tau _{12}}$ was found to equal 647.5ps. Therefore, we cannot use the decay rate alone to distinguish between the symmetric and asymmetric descriptions.
The decay rate and field amplitude ${A_1}$, when evaluated in the symmetric and asymmetric coupling frameworks, showed a good match with the bulk lifetime decay and intensity measured in our post-implant color centers. The spectral data was also considered. Our measured spectral intensity shown in Fig. 4 features a strong peak at 624 nm that likely results from inhomogeneous broadening, or vibrionic broadening as measured in previous experiments involving NVs [32]. Also, of note is the absence of the zero phonon line. The zero-phonon line of NV centers is not directly measured for nanodiamonds of the size and agglomeration pattern reported in our work. For this information, please see work specializing in this topic, such as Ref. [33]. In both cases of inhomogeneous broadening or vibrionic broadening, we would expect a Gaussian broadening to be induced by the presence of these phenomena. To investigate this, our coupled-mode system of equations was solved in the frequency domain. In both coupling frameworks, this output features two Lorentzian peaks with linewidths less than 1 nm, corresponding to two resonances with peaks at 637 nm and 811 nm. These were then convolved with a single Gaussian with standard deviation of 85 nm, representing inhomogeneous broadening effects, and the resulting Voigt profiles generated for both coupling frameworks shows a good match with our measured results. A Voight profile results from the convolution of two broadening mechanisms, one which would produce a Gaussian profile, typically inhomogeneous broadening, and the other would produce a Lorentzian profile, likely homogeneous broadening. Voigt profiles are common in many branches of spectroscopy.
It is a fair assumption that inhomogeneous broadening effects are prevalent throughout our sample and contribute to the observed lineshape. Nanodiamonds feature several defects with a range of surface functionalizations [34]. These defects give rise to strain broadening, which is an inhomogeneous broadening effect arising from differences in the local environment of emitters at different spatial locations [35]. This Voigt profile generation method has been used previously to describe other diamond color center species, specifically silicon-vacancy color centers [35] where inhomogeneous distributions have also been observed. Therefore, it can be concluded that the observed lineshape is predicted by our coupled-mode analysis. Another explanation may involve vibrational broadening effects observed in previous experiments involving NVs [32]. Vibrational transitions, and their associated lineshape broadening, could also be responsible for our observed photoluminescence spectra. The distinction between these two hypotheses is not resolved by either the time-domain or frequency-domain data, and thus will require additional investigation in future work.
From our results, it appears the coupling of nitrogen-vacancy color centers and xenon color centers within nanodiamonds gives rise to an overall lifetime reduction. This reduction in lifetime is not accompanied by a reduction in intensity, as is typical of shunting effects due to nitrogen-vacancies coupling to other lattice defects, such as C-centers and A-centers. Instead, we observe an almost two-fold increase in intensity. Coupled-mode theory provides a suitable explanation for these effects.
5. Conclusions
In conclusion, we have shown that the implantation of xenon into nanodiamonds and subsequent annealing gives rise to an increase in color center intensity as well as a reduction in color center lifetime. Our measured pre-implant lifetime was 550ps, while our measured post-implant lifetime was 297 ps. This corresponds to a lifetime reduction of 46%. We employed coupled-mode theory to determine that this lifetime reduction is consistent with a coupling between the nitrogen-vacancy and xenon color centers in the bulk, corresponding to a coupling time constant of 647.5 ps. These parameters were also consistent with the observed spectral lineshape, described by a Voigt profile with two Lorentzian peaks at 637 nm and 811 nm that is convolved with a single Gaussian reflecting inhomogeneous broadening effects.
Our method of lifetime shortening lacks many of the drawbacks of other conventional methods, such as a decrease in emitter intensity and difficult fabrication requiring specialized equipment prone to user error. Instead, quantum emitters produced with our method feature increased emitter intensity and simpler fabrication. While prior literature has established that NV centers can be used as single photon emitters, and lifetime shortening may enable faster single photon emission, the measurement technique employed did not allow for 2-photon correlation measurement. Therefore, additional studies are warranted to examine this correlation. Regardless, ion implantation and subsequent annealing serves as an attractive option for the fabrication of room-temperature quantum emitters.
Funding
Office of Naval Research (N000014-15-1-2833, N00014-19-S-B001); National Science Foundation (CBET-1855882, EEC-1227110, EEC1454315-CAREER); U.S. Department of Energy (DEEE0004946).
Acknowledgements
All implantation was performed by Sandia National Laboratories. Photoluminescence spectroscopy materials and equipment were provided by Professor Vladmir Shalaev’s group at Purdue University’s Birck Nanotechnology Center with experiments conducted and overseen by Simeon Bogdanov.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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