Near-field energy transfer between a luminescent 2D material and color centers in diamond

Energy transfer between fluorescent probes lies at the heart of many applications ranging from bio-sensing and -imaging to enhanced photo-detection and light harvesting. In this work, we study F\"orster resonance energy transfer (FRET) between shallow defects in diamond --- nitrogen-vacancy (NV) centers --- and atomically-thin, two-dimensional materials --- tungsten diselenide (WSe$_2$). By means of fluorescence lifetime imaging, we demonstrate the occurrence of FRET in the WSe$_2$/NV system. Further, we show that in the coupled system, NV centers provide an additional excitation pathway for WSe$_2$ photoluminescence. Our results constitute the first step towards the realization of hybrid quantum systems involving single-crystal diamond and two-dimensional materials that may lead to new strategies for studying and controlling spin transfer phenomena and spin valley physics.


I. INTRODUCTION
Förster resonance energy transfer (FRET) is the near-field transfer of energy due to the dipole-dipole interaction in a donor/acceptor pair system-the energy from the excited state of the donor is transferred to the acceptor, initially in the ground state. The transfer does not involve the exchange of photons and occurs at a rate determined by the overlap integral, i.e. the frequency-dependent oscillator strengths of the quantum spectroscopic (fluorescence/absorption) transition dipoles as well as their distance. 1 Realized for a variety of heterogeneous donor-acceptor systems-quantum dots, molecules, chromophores, etc. 2 -FRET constitutes the basis of a wide range of both fundamental effects and practical applications including single-molecule (bio)sensing and (bio)imaging, super-resolution fluorescence microscopy, as well as FRET-enhanced photodetection and light harvesting.
Evidently, the characteristics of the donor/acceptor systems are key to the practical realization of any FRET-based application. As fluorescent dye molecules traditionally used in FRET may bleach, recent work has focused on exploring resonant energy transfer processes in luminescent solid-state systems which show superior stability and much broader versatility for many of the proposed sensing, imaging and optoelectronic applications. Luminescent point defects in diamond 3 including the well-studied nitrogen vacancy (NV) center, 4 are long-term stable, fluorescent probes with established nanoscale sensing capabilities for magnetic 5 and electric fields, 6 as well as temperature. 7 Furthermore, FRET processes involving NV centers in nanodiamonds have already been demonstrated with organic molecules 8,9 and graphene. 10,11 Simultaneously-and relevant to this study-there is an entire family of fluorescent probes in atomically-thin two-dimensional (2D) transition metal dichalcogenide (TMDs) materials which exhibit ultra-bright luminescence. 2D-TMDs are leading candidates for emerging applications in optoelectronics, photodetection and valleytronics 12-14 rendering them significant for quantum technologies. 15 So far, FRET involving luminescent 2D-TMDs has been demonstrated with organic dye molecules 16 and colloidal quantum dots. 17,18 Notably, electrical gating of 2D-TMDs has been shown to enable control over the efficiency of the energy transfer process. 19 Conventionally, the rate of energy transfer between a pair of point dipoles such as molecules and chromophores scales with the distance z between the dipoles like 1 z 6 . Unlike this conventional scaling, FRET between a 2D material and a quantum dot or an atomic-scale quantum system like a color center scales with 1 z 4 . 10,20 In this work, we report FRET between two solid-state, stable, luminescent quantum systems-an ensemble of shallowly implanted NV centers in single-crystal diamond (SCD) and a 2D WSe 2 monolayer. This is the first observation of FRET involving color centers in SCD. In the process, NV centers act as donor dipoles which non-radiatively transfer their excitation energy to excitons in WSe 2 . WSe 2 is an optimal FRET partner in this case, as its broad absorption band (500-800 nm) largely overlaps with the NV photoluminescence (PL) band between 640 and 750 nm. We employ fluorescence lifetime imaging to measure lifetime changes due to FRET between WSe 2 flakes and NV centers. We also observe enhanced excitation of WSe 2 via FRET processes. We estimate the FRET radius for the NV-WSe 2 pair to be 13 nm, and we show that the spin-based magnetic sensing capabilities of NV centers are conserved also when FRET takes place.

II. SAMPLE PREPARATION AND EXPERIMENTAL SETUP
We use high-purity, (100)-oriented, synthetic, single-crystal diamond (SCD) from Element Six (electronic grade quality, [N] s < 5 ppb, B < 1 ppb). The SCD sample (size 2 × 4 mm 2 ), is polished to a roughness of R a < 3 nm by Delaware Diamond Knives. We first employ reactive ion etching 21 to remove the top 15 µm of the SCD; this is done to avoid creating NV centers in the diamond top layers which are potentially damaged as a result of the mechanical polishing. We then form a homogeneous layer of NV centers by shallowly implanting nitrogen ions with an implantation density of 4 × 10 11 cm −2 and an energy of 4 keV. The SCD sample is then annealed in vacuum at 800 • C and cleaned in boiling acids (1:1:1 mixture of sulfuric acid, perchloric acid and nitric acid). Using Monte Carlo simulations, 22 we estimate a resulting depth of the NV centers of (6.5 ± 2.7) nm below the SCD surface. Using photoluminescence (PL) measurements, we show the creation of a spatially homogeneous ensemble of NV centers. We also employ reactive ion etching onto a target area of the diamond to remove selectively all NV centers (area size ≈ 1 × 0.4 mm 2 ).
This functions as the control area as it allows for the characterization of the properties of the WSe 2 flakes on SCD independently of the interaction with the NV centers.
We synthesize WSe 2 monolayer flakes on a sapphire (0001) substrates via chemical vapor deposition following Ref. 23 and then transfer them onto the SCD sample using the method described below and depicted in Fig. 1(a). We first spin coat poly(methyl methacrylate)

III. PHOTOLUMINESCENCE AND LIFETIME MEASUREMENTS
First, we characterize the hybrid NV/WSe 2 system depicted in Fig. 2(a) under continuous excitation. The inset in Fig. 2(b) shows a typical PL map of a triangular WSe 2 flake which we localize due to its strong excitonic PL at 760 nm [see Fig. 2 To further investigate the hybrid NV/WSe 2 system, we perform PL lifetime measurements. In the area in which all NV centers have been removed, we find a lifetime of the WSe 2 exciton recombination PL of τ W Se 2 = 0.41(5) ns which is consistent with the value for pristine WSe 2 flakes before transfer. Figure 3 PL (τ W Se 2 ), we attribute the slower decay to the NV ensemble interacting with the WSe 2 flake (τ N V ). In contrast, in areas not covered by WSe 2 flakes we consistently measure a much longer NV lifetime with an average value of τ bulk N V ∼ 12(1) ns, typical for NV centers in bulk diamond. 24 For shallowly implanted NVs, slightly longer lifetimes of ∼ 16-17 ns have been previously reported. 25 We point out that, in our experiment, residuals from the transfer process might slightly reduce the NV lifetime in-between the flakes. For NV centers coupled to WSe 2 flakes, we find a value for the lifetime that is halved compared to the non-coupled NVs in our sample. This finding proves the occurrence of non-radiative energy transfer-FRET-between NV centers in SCD and excitons in the WSe 2 flake. The WSe 2 provides the NV centers with a non-radiative decay channel-mediated by dipole-dipole interaction-which reduces τ N V .
To further investigate FRET between WSe 2 and NV centers, we perform PL lifetime imaging of different areas of the SCD sample [see Fig. 3(a), (c) and (d)]. We fit a double exponential decay to the measured data and extract τ N V and τ W Se 2 . We consistently observe τ N V < 6 ns in areas where the SCD surface is covered by a WSe 2 flake, as discernible from comparing the PL map in Fig. 3(a) and the lifetime map in Fig. 3(c). In contrast, we find τ bulk N V on all other positions. The pattern of the WSe 2 flakes is furthermore confirmed when plotting τ W Se 2 [see Fig. 3(d)].
Below, we interpret these results in detail and highlight the peculiarities of the FRET process between an ensemble of NV centers and a WSe 2 flake. In our case, the FRET process is non-trivial as FRET strongly depends on the distance between the donor and the acceptor and our NV centers show a spread of depths z in the SCD. Assuming the flake is in direct contact with the SCD surface, each specific NV center of the ensemble lies at a different distance z from the WSe 2 and we thus would expect a complicated multi-exponential PL decay corresponding to a spread of NV lifetimes. Experimentally, however, we find that the NV lifetime is very well described by a single exponential decay with time constant τ N V . To simulate the PL decay expected from the NV ensemble coupled to the WSe 2 flake, we first calculate τ N V as a function of z. To this end, we need to determine the non-radiative decay rate γ non−rad due to the FRET process. We assume that the WSe 2 flakes have infinite size compared to the atomic-sized NV centers; we find 10 where R is the Förster radius, i.e. the distance at which the efficiency of the FRET mechanism is 50 %. The quantity R depends on the quantum efficiency of the donor and on the spectral overlap between the donor's emission and the acceptor's absorption, as well as their dipole moments. We furthermore assume that the radiative decay rate γ rad is constant for all NV centers and equal to the reference bulk value (τ bulk N V ) −1 . For each NV center at a specific depth z, we should find a mono-exponential decay with τ N V (z). Equation 1 shows that FRET is more efficient if z is smaller; consequently NV centers very close to the surface will be strongly quenched and emit less photons. We calculate the PL intensity I(z) of an NV center at a depth z as where I 0 is the non-quenched PL intensity, and γ rad and γ non−rad are the radiative and non-radiative decay rates, respectively.
To obtain the resulting PL decay of the ensemble, we weight each of the mono-exponential decay curves for each depth z with the intensity I(z) (Eq. 2) and with the depth distribution D(z) of NV centers resulting from the implantation process. We extract the depth distribution D(z) using Monte Carlo Simulations (SRIM), which produce a depth profile of (6.5 ± 2.7) nm. As we observe all NV centers in the ensemble simultaneously, we integrate over the whole implantation profile to retrieve the observed PL decay.
Notably, the calculated PL decay of the NV ensemble indicates a decay which is wellrepresented with a mono-exponential function with an effective τ ef f N V (assuming R > 5 nm) in full agreement with our experimental observations. Figure 3(e) shows the expected value of τ ef f N V for 5 nm < R < 30 nm-which we now use to estimate R for the NV/WSe 2 pair and find R N V /W Se 2 = 13 nm. To further confirm the agreement between the measured data and our model, we reduce the data to the time range in which the NV's mono-exponential decay is dominating. We do not include data from the first 3 ns-as this signal mainly represent PL from WSe 2 -and we do not consider the long time tail-i.e. all the data points with count rates below 1 % of the NV centers' peak value. This data treatment leads to the black line in [Fig. 3(f)] which agrees very well with the calculated PL decay (red line), assuming R N V /W Se 2 = 13 nm, and resulting in τ ef f N V = 5.2 ns. We note that τ N V = 5.2 ns in this situation is expected for NV centers in a depth of ∼ 12 nm. Our value for R N V /W Se 2 is thus comparable to that reported for the NV-graphene system, R N V /graphene , 10 strongly supporting the hereby observation of FRET between NV centers and WSe 2 .
To further investigate the energy transfer mechanism between NV centers and WSe 2 flakes, we study how the WSe 2 PL intensity depends on the excitation wavelength λ exc . Negativelycharged NV centers act as donors for WSe 2 . Consequently, FRET from excited NV centers constitutes an excitation path for WSe 2 PL which adds to laser excitation of WSe 2 PL.
Recording PL spectra of ensembles of NVs at positions not covered by WSe 2 flakes, we find that the NV PL is only significantly excited for λ exc > 465 nm. Consequently, our NV centers can only contribute as donors to the excitation of WSe 2 PL for λ exc > 465 nm. We thus investigate this excitation wavelength range in detail. We investigate the PL rate of the To check for consistency, we furthermore investigate two areas without NV centers separated by more than 0.5 mm. We also correct the WSe 2 PL intensity for NV center and background PL. As we compare the WSe 2 PL intensity with and without NV centers, changes in the excitation laser power when changing λ exc affect both measurements in the same way. Consequently, we did not correct for variations of the laser power. Figure 4(a) displays a clear tendency of an enhanced excitation of WSe 2 PL for flakes coupled to the shallow NV ensemble. We note that the enhanced excitation cannot be due to the absorption of NV PL by the WSe 2 flakes for the PL is too weak to induce the observed enhancement. The observed excitation enhancement of WSe 2 in the presence of NV centers constitutes additional strong evidence for FRET between NV centers and WSe 2 .
We now investigate the electronic spin properties for NV centers under the WSe 2 flakes.
We use lifetime-gating to separate NV PL and WSe 2 PL to enhance the measurement contrast when performing optically detected magnetic resonance (ODMR) measurements under pulsed laser excitation. Fig. 5(a) and (b) show the ODMR of the NV ensemble underneath  the WSe 2 flake in the absence and presence of an external magnetic field, respectively. We observe an ODMR contrast of 10 % without external field, which is typical for shallow NV centers, and which proves clear separation of NV and WSe 2 PL. Observing ODMR with a magnetic-field-dependent splitting for NV centers undergoing FRET indicates that they can serve as multi-functional sensors: while using FRET processes to monitor the presence of other dipoles, NV centers can simultaneously sense magnetic fields. This observation renders NV centers promising as multi-functional sensors in biological systems or for the investigation of novel materials where they can operate as nanoscale probes for nuclear magnetic resonance spectroscopy 26 that simultaneously couple to excitons via FRET.
We finally investigate how precisely we can localize the edge of a WSe 2 flake using the spatial variation of τ N V . We measure τ N V along a line perpendicularly crossing the edge of a WSe 2 flake [see Fig. 4(b)]. We fit τ N V using a Gaussian function approximating the point spread function of our setup. We find a FWHM of 620 nm which is closely matching the point-spread-function of our setup which we estimated by imaging single color centers This leads to a minimum integration time per pixel of < 15 ms.

IV. SUMMARY AND OUTLOOK
In conclusion, we have demonstrated FRET between shallow NV centers in SCD and WSe 2 flakes with an estimated Förster radius of 13 nm. The FRET process strongly reduces τ N V to around 6 ns, whereas the coupling to the NV centers enhances the excitation of WSe 2 for λ exc below 500 nm. We show that NVs undergoing FRET retain their ODMR and are applicable as multi-functional sensors.
In the future, we will investigate the transfer of WSe 2 flakes onto SCD photonic structures e.g. nanopillars with single NV centers. The first tests conducted during this work prove that typical SCD nanopillars are robust in the applied transfer process. Using such photonic structures will enhance the PL rates from single NV centers and will also allow for the modification of the excitonic properties of 2D materials via inducing local strain. 28 While traditionally FRET pairs are formed by attaching FRET partners to larger molecules or nanoparticles 8,29 or directly within a biological specimen 29 , the extension to stable solidstate systems could enable the realization of scanning devices where FRET is established between a single quantum probe scanning the system under investigation. Consequently, the distance between sample and probe can be varied continuously, which allows for indepth characterization of the FRET process and imaging the sample on the nanoscale.
Such techniques termed FRET-Scanning near field optical microscopy (FRET-SNOM) 30 will highly-profit from stable probes like NV centers in SCD. The first demonstration of FRET-SNOM enabled nanoscale imaging of graphene flakes using a scanning NV center in a nanodiamond. 10 Moreover, hybrid systems involving NV centers and 2D materials are potential candidates for spin transfer and spin valley physics. The latter has triggered intense research in TMDs and has potential for quantum information and sensing applications. 31