ARTICLE https://doi.org/10.1038/s41467-020-17899-7 OPEN Fast electrical modulation of strong near-field interactions between erbium emitters and graphene Daniel Cano 1, Alban Ferrier 2,3, Karuppasamy Soundarapandian1, Antoine Reserbat-Plantey1, Marion Scarafagio2, Alexandre Tallaire2, Antoine Seyeux2, Philippe Marcus2, Hugues de Riedmatten1,4, Philippe Goldner2, Frank H. L. Koppens 1,4 ✉ & Klaas-Jan Tielrooij 5 ✉ 1234567890():,; Combining the quantum optical properties of single-photon emitters with the strong near- field interactions available in nanophotonic and plasmonic systems is a powerful way of creating quantum manipulation and metrological functionalities. The ability to actively and dynamically modulate emitter-environment interactions is of particular interest in this regard. While thermal, mechanical and optical modulation have been demonstrated, electrical modulation has remained an outstanding challenge. Here we realize fast, all-electrical modulation of the near-field interactions between a nanolayer of erbium emitters and gra- phene, by in-situ tuning the Fermi energy of graphene. We demonstrate strong interactions with a >1000-fold increased decay rate for ~25% of the emitters, and electrically modulate these interactions with frequencies up to 300 kHz – orders of magnitude faster than the emitter’s radiative decay (~100 Hz). This constitutes an enabling platform for integrated quantum technologies, opening routes to quantum entanglement generation by collective plasmon emission or photon emission with controlled waveform. 1 ICFO – Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain. 2 Institut de Recherche de Chimie Paris (IRCP), Université PSL, Chimie ParisTech, CNRS, 75005 Paris, France. 3 Faculté des Sciences et Ingénierie, Sorbonne Universités, UFR 933, 75005 Paris, France. 4 ICREA - Institució Catalana de Reçerca i Estudis Avancats, 08010 Barcelona, Spain. 5 Catalan Institute of Nanoscience and Nanotechnology (ICN2), BIST and CSIC, Campus UAB, 08193 Bellaterra (Barcelona), Spain. ✉email: frank.koppens@icfo.eu; klaas.tielrooij@icn2.cat NATURE COMMUNICATIONS | (2020)11:4094 | https://doi.org/10.1038/s41467-020-17899-7 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17899-7 O ne of the major accomplishments of nanophotonics interactions, the erbium emitters should be located at nanoscale research is the accurate control of the near-field inter- distances from the 2D material—ideally within the sub- actions between light emitters and their environment. wavelength volume occupied by the highly confined plasmons These interactions typically lead to a modification of the (<15 nm). A sufficiently thin layer with erbium emitters is decay rate and emission properties, with decay-enhancement therefore required. However, crystals of nanoscale dimensions factors FP up to 1000 for emitters in the near-field of metallic typically suffer from detrimental non-radiative losses due to nano-antennas1. Such systems, however, do not easily allow for surface defects25. Removing this loss mechanism is crucial, as it active modulation of the emitter–environment interactions. constitutes a competing energy flow channel for Active and dynamic control of emitter–environment interactions erbium–graphene interactions that would hinder the observation has been achieved in photonic crystal cavities and nano- of these interactions. We overcome this experimental bottleneck electromechanical systems through modulation of the effective by using atomic layer deposition (ALD)26 with optimized post- refractive index of the environment, using electromechanical treatment—a technique that produces few-nanometer-thick rare- actuation2, mechanical oscillations3,4, or photoexcitation of free earth-doped Y2O3 films with atomic scale thickness control and carriers5. These techniques, however, either only work with one emission quality as in bulk crystals (see Supplementary Note 1, fixed modulation frequency or require optical fields for fast Supplementary Figs. 1 and 2, and Supplementary Table 1). The modulation. Furthermore, the achieved decay-enhancements are results we will show are obtained with a sample containing an typically moderate, with FP ~ 10. erbium layer of 12 nm thickness, as measured through white light An effective solution can be found in graphene, a two- interferometry (see Supplementary Note 2 and Supplementary dimensional (2D) material that combines a high degree of electro- Figs. 3 and 4 for more sample characterization). optical tunability at high speeds (tens of GHz6) with strong near- With the aim of dynamically controlling the erbium–graphene field light–matter interactions. Graphene not only provides a wide interactions through the Fermi energy of graphene EF, we range of electrical tunability through its Fermi energy. At suffi- combine a backgate of p-doped silicon with a polymer electrolyte ciently high Fermi energy, it supports plasmons with much topgate27 (see Fig. 1). The backgate, with a smaller alternating stronger field confinement than noble metals: the wavelength of current (AC) impedance than the topgate, is very suitable for graphene plasmons λpl is ~100 times smaller than that of free- high-frequency modulation. We use it to modulate EF at high space photons λ0, whereas in metallic thin films λ0/λpl is typically frequencies over a range of ~0.3 eV. On the other hand, the <3, see ref. 7. For pristine graphene, this leads to a mode volume topgate allows Fermi energy tuning over a range >1 eV, which is confinement of ðλ0 =λpl Þ3 ’ 106 , according to ref. 8. Moreover, it sufficiently high to launch plasmons in resonance with the is possible to reach a mode volume confinement up to 109 in photons emitted by erbium, whose energy is EEr = 0.8 eV (see graphene-metal grating structures9 and 1010 in cube-grating Fig. 1a). We use the topgate to provide a high base Fermi energy structures10, with potential for very strong near-field interactions during high-frequency modulation of the backgate. The Fermi with nearby emitters. Many suggested plasmon-based technolo- energies induced by both gates are calibrated by Hall measure- gies, where the fields of photonics and electronics merge11,12, ments and resistance measurements (see Supplementary Note 3 would benefit from fast temporal control of emitter–plasmon and Supplementary Fig. 5). Thus, using our dual-gated, hybrid interaction, including applications such as single-photon nano- erbium–graphene system, we can modulate EF, for example, antennas13, and sub-diffraction-limited sensors14. Experimen- between 0.6 and 0.3 eV, (Fig. 1b). This modulates the system tally, however, active electrical tunability of emitter–graphene between two regimes, where the erbium emitters decay by interaction has only been demonstrated with low decay- transferring energy to graphene, leading to intraband absorption enhancement (FP < 3) and in a non-dynamic fashion15,16. (Fig. 1a) and interband absorption (Fig. 1c), respectively. The Here we present a hybrid system made of a nanoscale layer of intraband regime is mainly associated with plasmon generation in erbium emitters in an oxide matrix, and graphene, in which the graphene, whereas in the interband regime mainly electron–hole near-field interactions can be efficiently controlled on-chip, at high pair creation occurs. modulation frequencies, and by means of moderate electrical gate voltages (on the order of a few volt). Rare-earth erbium ions are technologically highly relevant as they emit photons at 1.54-μm Emission contrast and decay enhancement. The intraband and wavelength, within the C-band of optical communication systems. interband absorption regimes can be experimentally distinguished Furthermore, rare-earth oxide crystals have a proven relevance in because they are associated with different local densities of optical photonic quantum memories17 and spin–photon interfaces18, while states (LDOS), leading to distinct decay rates for the emitters nanoscale rare-earth materials are currently gaining interest19. We interacting with graphene. Our calculations following refs. 28,29 will show highly efficient erbium–graphene interaction with decay- show that the decay-enhancement factor FP for an emitter at 5 enhancement factors FP >1000 for ~25% of the ions, which means nm from graphene is ~100 in the intraband regime (EF = 0.6 eV) that >99.9% of the energy of these excited ions flows to graphene and >1000 in the interband regime (EF = 0.3 eV). In order to through near-field interactions. Importantly, we demonstrate observe these regimes experimentally, we excite the erbium ions modulation of the erbium–graphene interaction on a much shorter with a 532-nm laser and detect their emission at 1.54 μm in a time scale than the lifetime of the single-photon emitters. In this scanning confocal microscope (see “Methods”), while varying the special dynamical case, the quantum regime emerges, with exciting Fermi energy using the topgate. Figure 2a shows the measured possibilities such as generation of single photons with controlled emission contrast, defined as the emission without graphene waveform20,21, Dicke phases22,23, and quantum entanglement (measured by shining the laser outside the graphene channel) generation by collective plasmon emission24. divided by the emission with graphene (measured by shining the laser on graphene; see also Supplementary Fig. 3). The excitation power is sufficiently low (fluence of 104 W cm−2) to ensure that Results the ion transition is not saturated (see Supplementary Fig. 4). We Hybrid erbium–graphene system with dual-gate modulation. indeed identify two different regimes: at low Fermi energies (EF < We show the design of our hybrid system schematically in Fig. 1. 0.4 eV), energy transfer is mostly caused by interband transitions The central part consists of a graphene monolayer on a nanoscale in graphene. Above 0.4 eV, interband transitions become sup- layer of erbium-doped Y2O3 (2%). To achieve strong near-field pressed by Pauli blocking, because EF > EEr/2, and intraband 2 NATURE COMMUNICATIONS | (2020)11:4094 | https://doi.org/10.1038/s41467-020-17899-7 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17899-7 ARTICLE a Intraband regime (plasmons) Graphene Y 2O3, 12 nm Vbg SiO 2, 285 nm high p-Doped Si Excited erbium ion b EEr Fermi energy (eV) 0.6 1000 enhancement Decay- 100 0.3 Interband regime Time (e–h pairs) c Vbg low EEr Fig. 1 Concept of dynamic modulation of hybrid erbium–graphene system. a Schematic illustration of the hybrid erbium–graphene system when the Fermi energy of graphene is tuned to ~0.6 eV and the erbium–graphene interaction leads to intraband transitions, mainly associated with launching of propagating graphene plasmons (red waves). The system contains, from top to bottom, a monolayer of graphene, a thin film (~12 nm) of Y2O3 containing erbium ions (white spheres), a 285-nm-thick SiO2 layer, and a p-doped silicon backgate. A backgate voltage, Vbg, is applied between the backgate and a gold electrode in contact with graphene for fast modulation. The SiO2 layer serves as electrical isolation between graphene and the p-doped silicon. On top of graphene, there is a transparent topgate made of polymer electrolyte (not shown in the image). b Sinusoidal time evolution of the Fermi energy of graphene (dashed black line, left vertical axis) and the corresponding decay-enhancement factor FP for an erbium emitter located at z = 5 nm from graphene (solid purple line, right vertical axis). The modulation of the Fermi energy, calculated following refs. 28,29, leads to a modulation of FP by more than one order of magnitude—from <100 in the intraband regime to >1000 in the interband regime. c Schematic illustration of the hybrid erbium–graphene system for EF ~ 0.3 eV, which corresponds to interband transitions, mainly creating electron–hole pairs (red–blue spheres). transitions become the dominant energy decay pathway of the even faster decay in the interband regime (e−1 time of ~1 ms), ions. The positive slope of the emission contrast for EF > 0.6 eV is compared to the decay without graphene (e−1 time of ~6 ms), in a clear signature of the presence of plasmons. The slope is positive qualitative agreement with the emission contrast measurements, because the decay length of the plasmon field is approximately the which show less emission in the interband regime than in the same as the plasmon wavelength, λpl, which scales linearly with intraband regime. EF. Therefore, as EF increases, the volume occupied by the plas- Strikingly, the decay curves are multi-exponential, with a large mon field increases, thus increasing the number of ions inter- negative slope in the beginning of the decay (see inset of Fig. 2b). acting with plasmons, and thereby decreasing the amount of This multi-exponential behavior stems from the different decay emitted light. rates γ of the emitters, depending on their distance to graphene z, To obtain more insight into the dynamics of the since γ scales with z−4 in the interband regime and with erbium–graphene interactions, we measure the erbium emission expð4πz=λpl Þ in the intraband regime28,30. The ions located decay curves. We modulate the excitation laser into pulses and furthest away from graphene have the lowest energy transfer use single-photon counting electronics to create emission rates, thus emitting more photons and extending the decay curves histograms (see “Methods”). Figure 2b shows the decay curves to long times. The strongly negative slope in the beginning of the measured with the laser shining on graphene for the interband decay curves (with an estimated decay time <100 μs; see inset of transition regime (EF ~ 0.2 eV) and for the intraband regime Fig. 2b and Supplementary Fig. 10) is due to the high energy (EF ~ 0.8 eV), as well as in a region without graphene. We observe transfer rate for small z and indicates the presence of a significant faster decay in the intraband regime (e−1 time of ~3 ms) and fraction of ions with very strong erbium–graphene interactions. NATURE COMMUNICATIONS | (2020)11:4094 | https://doi.org/10.1038/s41467-020-17899-7 | www.nature.com/naturecommunications 3 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17899-7 a 8 b 100 Measurements 7 Simulation Emission contrast 6 PL instensity Interband 5 Intraband 0 1 2 4 Ba re In Int e t ra rbi 3 10–1 erb um ba nd an 2 d 0.2 0.4 0.6 0.8 1 0 5 10 15 Fermi energy, EF (eV) Time, t (ms) c 1 d 1 Er density distribution, P (z ) TOF-SIMS P (J) 0.8 0.8 Emission In te rb P (FP > p) 0.6 an 0.6 d 102 103 104 105 0.4 Int J (s–1) 0.4 rab an d 0.2 0.2 Y2O3 SiO2 0 0 10 20 30 40 50 60 70 100 101 102 103 104 Distance, z (nm) p Fig. 2 Efficient energy flow from erbium emitters to graphene. a Measured emission contrast, defined as the emission with the excitation laser shining outside graphene divided by the emission with the laser on graphene, as a function of the Fermi energy (black dots). The black solid line represents the calculated emission contrast from N erbium ions located at different distances zi from graphene (see “Methods”), using the total graphene conductivity. The red (blue) dotted line represents the calculated emission contrast by only considering the conductivity of the intraband (interband) excitation, showing the different microscopic origins of the emitter–graphene interactions at high and low EF. The interband contribution (blue) quickly drops when EF > 0.4 eV, due to Pauli blocking, whereas the intraband contribution (red) steadily rises with EF. b Measured decay curves of erbium ions for three cases: graphene in the interband regime (EF = 0.3 eV, blue dots), graphene in the intraband regime (EF = 0.8 eV, red dots), and without graphene (orange dots). The black solid lines are the best-fit stretched-exponential functions. The inset focuses on the beginning of the decay curves, illustrating the multi-exponential behavior. c Erbium density distribution (normalized to maximum) vs. erbium–graphene distance obtained from the combined analysis of the emission contrast and the decay curve of the interband regime (blue) and from TOF-SIMS measurements (black). d Cumulative distribution of the decay enhancement factor calculated for the interband (blue) and the intraband (red) regimes. These curves show that about 80% (50%) of the ions have FP > 10 for the interband (intraband) regime, and approximately 25% of ions have FP > 1000 for both regimes. The inset shows the total decay rate distributions directly obtained from the multi-exponential fitting of the experimental decay curves (see “Methods”). The colors are the same as in b. Thus the decay curves provide information of the z-dependence graphene, leading to the largest decrease in emission. Together, of the interactions, while the emission contrast measurements the decay curves and emission contrast measurements yield the reflect the overall (distance-integrated) graphene-induced decay- density of erbium ions as a function of z (see Fig. 2c). enhancement FP, which is ~7 (~2.5) in the interband (intraband) In detail, we extract the distribution for ions with z > 7 nm regime. This indicates that an overall fraction of η ≈ (FP − 1)/ directly from the decay curves of Fig. 2b, by describing each multi- FP ≈ 85% (60%) of the energy of excited erbium emitters exponential decay curve by a continuous sum of exponentially flows to interband (intraband) transitions in graphene. We note decaying functions, whose probability amplitudes are given by the that we have reproduced these decay curves with multiple decay-rate distribution P(γ). In terms of the ion dynamics, the erbium–graphene samples (see Supplementary Note 4 and distribution P(γ) can be interpreted as the likelihood that a given Supplementary Fig. 9). ion decays with a certain decay rate γ. The inset of Fig. 2d clearly shows that the decay-rate distribution P(γ) is shifted toward higher values of γ in the regions of the device with graphene, indicating Quantifying erbium–graphene interaction. Given the strong z- that the decay rate increases due to energy transfer to graphene. dependence of the emitter–graphene interaction, it is crucial to From the analysis of these decay-rate distributions, we extract the determine the distribution of erbium ions in order to quantita- distribution of decay-enhancement factors P(FP), following the tively understand the energy transfer efficiency of the different numerical procedure described in the “Methods” section. Then we erbium ions in the nanolayer. We analyze the emission contrast convert P(FP) into the distribution of erbium–graphene distances and the decay curves (Fig. 2a, b) together because they provide P(z), i.e., the density distribution, by using the theoretical relation complementary information. The decay curves provide with high between FP and the emitter–graphene distance z. accuracy the distribution of ions with relatively low FP factors It turns out that the distributions P(FP) and P(z) obtained from (large z), as these are the ions that emit the largest number of the decay curves are accurate up to FP = 103, corresponding to z photons during lifetime measurements. On the other hand, the ≳ 7 nm. For higher values of FP, the decay is so fast and has such emission contrast measurements of Fig. 2a reveal more accurately a small amplitude that we cannot resolve it experimentally in our the effect of the ions with relatively large FP (small z), as these are decay curves (see Supplementary Note 5). However, we can the ions that transfer the highest fraction of their energy to obtain the distribution of the ions with z < 7 nm using the 4 NATURE COMMUNICATIONS | (2020)11:4094 | https://doi.org/10.1038/s41467-020-17899-7 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17899-7 ARTICLE emission contrast measurements of Fig. 2a. For this, we use a 0.6 a Fermi energy, computational model of N ions at different distances from EF (eV) graphene, zi (i = 1, ..., N), and find the ion density distribution 0.45 P(z) that best reproduces the measurements of Fig. 2a, b (see “Methods”). This is how we obtain the ion density distribution in 0.3 Fig. 2c. 0 1/4 1/2 3/4 1 We compare the ion distribution extracted from optical t · fmod measurements P(z) with the density distribution measured by means of time-of-flight secondary ion mass spectrometry (see “Methods” and Supplementary Note 6). The similarity between 1.5 b 20 Hz the two density distributions confirms the validity of our analysis. Normalized emission Interestingly, our results indicate that some ions have diffused Intraband 1 (plasmon) from the Y2O3 layer into the underlying SiO2 layer. This has likely occurred during the annealing post-treatment of the films. These Interband diffused ions interact less strongly with graphene and lead to the 0.5 moderate overall emission contrast we observe in Fig. 2a. 0 50 ms Importantly, our analysis of the experimental data of Fig. 2a, b provides evidence of very strong emitter–graphene interactions at 1.3 c 200 Hz the shortest distances. Figure 2d shows the calculated cumulative Normalized distribution of P(FP), emission Z 1 1 PðF P > pÞ ¼ PðF P ÞdF P ; ð1Þ p 0.7 which describes the probability that an ion has a decay- 0 5 ms enhancement factor larger than p. In this way, the cumulative distribution P(FP > p) provides the fraction of ions with FP > p. Using Eq. (1), we find that about 80% (50%) of the ions have 1.05 d 2 kHz decay enhancement factor FP > 10 for the interband (intraband) Normalized emission regime, and approximately 25% of ions have FP > 1000 for both 1 regimes, which means that >99.9% of the energy from these ions flows to graphene. 0.95 Fast electrical modulation of near-field interactions. Having 0 0.5 ms established the occurrence of highly efficient erbium–graphene interactions in our system, we now demonstrate dynamic control e 1.004 30 kHz of these interactions on a time scale that is much shorter than the Normalized emitter’s lifetime of ~10 ms31. We induce a fast temporal var- 1.002 emission iation in the LDOS experienced by the emitters by modulating the 1 Fermi energy of graphene. To this end, we apply an AC voltage to 0.998 the backgate and verify the effect of this modulation on the excited state populations of erbium by measuring the temporal 0.996 variations of photon emission using a single-photon counting set- 0 33.3 µs up. In these experiments, we keep the excitation laser power constant. In Fig. 3, we modulate the Fermi energy between f 300 kHz 0.3 and 0.6 eV at different modulation frequencies f mod between 1.0005 Normalized 20 Hz and 300 kHz. This corresponds to a modulation of the emission erbium decay pathway between interband and intraband transi- 1 tions, as in Fig. 1. In these measurements, we thus establish control over the timing of plasmon launching from erbium ions 0.9995 down to the microsecond range, which is remarkable for emitters with millisecond natural lifetime. We verified that there is no 0 3.33 µs dynamic response outside graphene and that a backgate voltage Time, t of <10 V is sufficient for complete modulation between the two Fig. 3 Dynamic modulation between interband and intraband regimes. emitter–graphene interaction regimes (see Supplementary Fig. 6). a Fermi energy as a function of time t using a sinusoidal function of frequency As f mod increases and becomes higher than the emitter decay f mod (schematic). The slow topgate is used to tune to EF ~ 0.45 eV, whereas the rate, the internal dynamics of the ions are not able to follow the fast backgate provides the modulation between 0.3 and 0.6 eV. b–f Time- temporal variations of the environment. This results in a gradual resolved photon emission while the Fermi energy is modulated at different delay of the maximum and minimum of the time-dependent frequencies between 20 Hz and 300 kHz (green dots). Every time-modulated emission with respect to the sinusoidal oscillation of the Fermi emission measurement is normalized to its mean value, so that the modulation energy and the reduction of the emission modulation amplitude, does not depend on the excitation laser power or the photon collection which depends on 1=f mod whenever f mod  γ. Interestingly, efficiency. The black solid curves show the dynamic simulations of N ions these modulation frequencies surpass not only the decay rate of located at the distribution of distances from graphene P(z), obtained from the the ions but also the quantum coherence decay rate of erbium in emission contrast measurements and decay curves (see “Methods”). Note that Y2O3 (11 kHz; measured at 2.5 K in a bulk ceramic sample and f shows modulation on a time scale of microseconds, whereas the radiative under a small external magnetic field of 0.65 T)32. lifetime of erbium ions in Y2O3 is ~10 ms, a difference of 4 orders of magnitude. NATURE COMMUNICATIONS | (2020)11:4094 | https://doi.org/10.1038/s41467-020-17899-7 | www.nature.com/naturecommunications 5 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17899-7 In a second series of measurements, shown in Fig. 4, we 0.9 a Fermi energy, modulate the Fermi energy between 0.7 and 0.9 eV. Here we EF (eV) apply a higher voltage to the polymer electrolyte topgate than in 0.8 the previous modulation experiment, while modulating the backgate again with a voltage of <10 V. In this situation, the system is always in the intraband regime, where plasmon 0.7 launching is the dominant energy decay pathway, and we 0 1/4 1/2 3/4 1 therefore modulate the strength of the emitter–plasmon interac- t · fmod tion. Note that an increase in backgate voltage now leads to a decrease in emission, because stronger emitter–plasmon interac- tion leads to less emission (see also Supplementary Fig. 7). This is b in contrast with the case in Fig. 3, where an increase in backgate 1.02 Normalized voltage leads to a transition from the interband absorption regime emission to the intraband regime, giving more emission. 1 We model the temporal modulation of photon emission by simulating the dynamics of N ions using the distribution of ion 0.98 20 Hz distances P(z) obtained from the emission contrast measurements and decay curves. For every ion i at distance zi, we numerically solve the rate equation with the time-dependent FP factor and for 0 50 ms the corresponding Fermi energy modulation (see “Methods”). We find good agreement between experimental data and numerical c simulations, which do not contain any freely adjustable fit 1.02 parameters (see “Methods”), adding credibility to our computa- Normalized emission tional approach. We note that, only in the case of Fig. 4e, we 1 observe a larger modulation amplitude in the experiment than in the simulation. We speculate that this could be related to 0.98 200 Hz additional (e.g., non-local) effects in the plasmonic local field at very short distances from graphene. 0 5 ms Discussion We have demonstrated a material platform that integrates the d optical properties of erbium quantum emitters with the strong 1.01 Normalized near-field interactions of graphene, providing the conditions for emission quantum manipulation and metrological functionalities33,34. In 1 particular, our hybrid erbium–graphene platform enables fast temporal control over the strong near-field interactions, thus 0.99 1 kHz providing an efficient way to manipulate quantum states in nanoscale solid-state devices by means of conventional elec- tronics. The control over the dynamics of single-photon emitters 0 1 ms on a much shorter time scale than their lifetime is an essential ingredient toward observing intriguing effects, such as Dicke e phase transitions22,23, non-linear light–matter interactions at 1.01 the quantum level35, and multi-particle entanglement genera- Normalized emission tion24. In addition, such a fast control over the near-field 1 interactions will expand existing functionalities of plasmonic nanodevices integrating graphene waveguides and 0.99 cavities28,29,36–38. It enables the control of the waveform of 5 kHz photons and plasmons emitted into a guided mode21,39, which is a required capability for distributed quantum systems. It fur- 0 0.2 ms thermore facilitates the connection of optical transistors40,41 Time, t based on quantum emitters in integrated plasmonic circuits, with the possibility to attenuate or amplify the plasmon emis- Fig. 4 Dynamic modulation within the intraband regime. a Fermi energy sion by means of a gate voltage. These promising applications as a function of time t using a sinusoidal function of frequency f mod will be boosted by the prospects of coupling plasmonic modes to (schematic). The slow topgate is used to tune to EF ~ 0.8 eV, whereas the the far field through optical nanoantennas or through optical fast backgate provides the modulation between 0.7 and 0.9 eV, thus waveguides42, thus enabling controlled photon emission modulating the interaction strength within the intraband regime. b–e Time- enhancement for optical communications. Overall, these pro- resolved photon emission while the Fermi energy is modulated at different spects will stimulate the development of emitter–graphene frequencies between 20 Hz and 5 kHz (red dots). Every time-modulated interfaces as a building block for hybrid systems with applica- emission measurement is normalized to its mean value, so that the tions in optoelectronic quantum technologies. modulation does not depend on the excitation laser power or the photon collection efficiency. The black solid curves show the dynamic simulations of N ions located at the distribution of distances from graphene P(z) Methods obtained from the emission contrast measurements and decay curves (see Fabrication of erbium–graphene hybrid devices. The erbium–yttria thin-film depositions are carried out by ALD with a commercial reactor using conventional “Methods”). Note that the modulated emission is out of phase with the β-diketonate precursors: Er(tmhd)3 and Y(tmhd)3. The precursors are held at modulating Fermi energy, because a higher Fermi energy gives lower 160 °C and delivered using N2 as a carrier gas and O3 as an oxidizing agent. The emission in the intraband regime. 6 NATURE COMMUNICATIONS | (2020)11:4094 | https://doi.org/10.1038/s41467-020-17899-7 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17899-7 ARTICLE precursors are flown sequentially with 3-s injection time into the thermalized zi ≳ 7 nm are obtained by discretization of the density distribution P(z) calculated deposition chamber at 350 °C. The number of cycles is adjusted in order to obtain from the decay curves. The positions zi ≲ 7 nm are free parameters that we vary to the desired thickness (circa 12 nm here). The films are annealed at high tem- find the distribution of distances, fz i gi¼1;:::;N , that best reproduces the emission perature (950 °C) for 2 h in air prior to measurement in order to improve crys- contrast measurements of Fig. 2a. This variational procedure assumes that the tallinity. More details about the optimization of the growth procedure are discussed density distribution is smooth. The calculations are accomplished by considering in Supplementary Note 1. We use a moderate erbium concentration of 2% in order that the emission from every ion is proportional to its excited-state population, to avoid possible non-radiative decay channels induced by erbium–erbium inter- which in turn is proportional to 1/(FPγed + γmd + γnr), where the theoretical decay- actions. Single-layer graphene, grown by chemical vapor deposition on copper, is enhancement factor FP(zi) is computed from the methods of refs. 28,29 (see above). transferred directly onto the surface of the 12-nm-thick Y2O3:Er3+ layer using the Here we assume that γnr = 10 Hz for all ions (see Supplementary Note 1). The standard wet transfer method. Graphene is patterned into a Hall-bar geometry by discrete distribution fz i gi¼1;:::;N is converted into a continuous distribution, P(z), laser writing optical lithography and subsequent reactive ion etching (see Sup- and vice versa, by integration and discretization, respectively. We typically use N = plementary Fig. 3). The whole surface is covered with a transparent polymer 50, where the density distribution already nicely converges. electrolyte that serves as topgate. The electrolyte is made of polyethylene oxide and LiClO4 with 8:1 weight ratio in a solution of methanol27. The device contains six electrical contacts to graphene and two electrical contacts to apply the topgate Simulation of the dynamic response to gate modulation. We simulate the voltage Vtg to the polymer electrolyte. The electrical contacts consist of a 50-nm- quantum-state population dynamics for every ion i of our N-ion model by thick gold layer deposited on a 5-nm-thick chromium sticking layer and patterned numerically solving the rate equations44, by laser writing optical lithography. There is a 50-nm-thick SiO2 protection layer dN ðiÞ h i ðiÞ ð2Þ between the gold electrodes and the electrolyte in order to isolate the gold elec- e ¼ N ðiÞ ðiÞ e F P γed þ γmd þ γnr þ N g γexc ; trodes from the polymer electrolyte. dt N ðiÞ ðiÞ g þ N e ¼ 1; ð3Þ Experimental set-up for optical measurements. The experiments are carried out in a home-built scanning confocal microscope set-up, with the sample mounted where N ðiÞ g and N ðiÞ e are, respectively, the populations in ground and excited states, ðiÞ inside a vacuum chamber at a pressure of 5–10 mbar for optimal operation of the F P is the time-dependent decay-enhancement factor at the position zi, and γexc is polymer electrolyte gate. The optical set-up uses an infrared objective (Olympus the excitation rate, which depends on the excitation laser power. The results of the LCPLN-50X-IR, numerical aperture 0.65), which provides a spatial resolution of simulations do not depend on γexc since every measurement is normalized to its ~1 μm. A focused 532-nm laser beam, with typically a power of ~0.2 mW at the mean value, although we need to assume a certain value of γexc to do the com- sample, excites the ions into the short-lived state 2H11/2, from which the erbium ðiÞ putation. To calculate F P , we first obtain the oscillating energy EF that corresponds population rapidly decays into the metastable first excited state 4I13/2 via non- to the applied gate voltages using the calibration described in Supplementary radiative multiphonon emission. The emission of the 4I13/2 → 4I15/2 transition at Note 3. The Fermi energy amplitude as a function of the back-gate voltage the characteristic wavelength 1.54 μm is collected, spectrally filtered with a narrow amplitude is ΔEF = BΔVbg, where B = 15 eV mV−1 (13 eV mV−1) in the experi- bandpass filter (Thorlabs FB1550-40), and directed into a near-infrared single- ments of Fig. 3 (Fig. 4). We then convert EF into FP using the methods of refs. 28,29 photon detector (ID Quantique id210) with very low level of dark counts (~9 Hz). (see above). For time-resolved measurements, emission histograms are obtained using photon- counting electronics (PicoHarp 300) in time-tagged time-resolved acquisition mode, recording the arrival times of all photons. During lifetime measurements, Time-of-flight secondary ion mass spectrometry (ToF-SIMS). We use a dual- the excitation laser intensity is modulated into square pulses by switching on and beam ToF-SIMS spectrometer (IONTOF GmbH, Műnster, Germany) to measure off the signal of an acousto-optic modulator. All measurements were carried out at the density profile of the yttrium and erbium ions at a sufficiently low primary ion room temperature. We verified that, during measurements that can take up to dose density to keep static conditions. The spectrometer was operated at a pressure several hours, the Fermi energy did not vary significantly (see Supplementary of 10−9 mbar. A pulsed 25 kV Bi+ primary ion beam delivering 1 pA over a 100 × Fig. 8). 100 μm2 area is used to etch the chemical species from the surface. The masses of the removed chemical species are determined by ToF-MS. The sputtering of the surface was done using a 2-keV Cs+ sputter gun giving a 100-nA target current Decay-rate distributions from the decay curves. The decay rate in the regions over a 300 × 300 μm2 area. The interlacing between Bi+ and Cs+ guns allows to of the device without graphene is γEr = γed + γmd + γnr, where γed ~ 75 Hz and record TOF-SIMS depth profiles. We used the profile of the removed YO− particles γmd ~ 50 Hz correspond to the electric and magnetic dipole moments, respec- to extract the Er3+ density distribution. This approximation is justified since the tively31, and γnr represents the non-radiative decay channels of the erbium thin diffusion coefficients of yttrium and erbium are practically the same (see Supple- film. In the regions with graphene, the total decay rate is γ = γEr + γgr, where γgr is mentary Fig. 11). the rate of energy transfer to graphene. Every experimental decay curve, n(t), is R1 γt described as a continuous sum of exponential decays, nðtÞ ¼ 0 PðγÞ γ e dγ, where P(γ) is the probability distribution that describes the likelihood that a given ion Data availability The data that support the findings of this study are available from the corresponding decays at a certain rate γ. Here we have considered that the excited erbium population, and thus the emission, is inversely proportional to the decay rate. The authors upon reasonable request. integral has the form of a Laplace transformation, so we can extract P(γ) by inverse Laplace transformation using the numerical techniques of ref. 43 (see the inset of Received: 20 March 2020; Accepted: 14 July 2020; Fig. 2d). Next, we calculate the energy transfer rate distribution R1 Pgr(γgr) by numerically solving the convolution equation, PðγÞ ¼ 0 PEr ðγ  γgr ÞPgr ðγgr Þdγgr . Here PEr(γEr) denotes the decay-rate distribution in the regions of the device without graphene (we write the subindex Er to indicate that the distribution only includes the intrinsic decay mechanisms of the erbium film). In doing the deconvolution, we filter out the small effect of the undesired non-radiative decay channels γnr, thus obtaining the pure contribution of the erbium–graphene inter- References 1. Akselrod, G. et al. Probing the mechanisms of large Purcell enhancement in actions, γgr. The distribution Pgr(γgr) can be easily converted into the distribution of decay-enhancement factors, P(FP), by using the relation γgr = (FP − 1)γed. Next, we plasmonic nanoantennas. Nat. Photonics 8, 835–840 (2014). translate P(FP) into the density distribution, P(z) = P(FP)dFP/dz. For this, the 2. Cotrufo, M. et al. 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Ltd., Singapore, 020-17899-7. 2016). 30. Gaudreau, L. et al. Universal distance-scaling of nonradiative energy transfer Correspondence and requests for materials should be addressed to F.H.L.K. or K.-J.T. to graphene. Nano Lett. 13, 2030–2035 (2013). 31. Weber, M. J. Radiative and multiphonon relaxation of rare-earth ions in Y2O3. Peer review information Nature Communications thanks the anonymous reviewers for Phys. Rev. 171, 283 (1968). their contribution to the peer review of this work. Peer review reports are available. 32. Zhang, H. et al. Transparent Er3-doped Y2O3 ceramics with long optical coherence lifetime. ACS Omega 2, 3739–3744 (2017). Reprints and permission information is available at http://www.nature.com/reprints 33. Schoelkopf, R. & Girvin, S. Wiring up quantum systems. Nature 451, 664–669 (2008). Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in 34. Kurizki, G. et al. Quantum technologies with hybrid systems. Proc. Natl Acad. published maps and institutional affiliations. Sci. USA 112, 3866–3873 (2015). 35. Cox, J. D. & García de Abajo, F. J. Nonlinear atom-plasmon interactions enabled by nanostructured graphene. Phys. Rev. Lett. 121, 257403 (2018). 36. Tame, M. S. et al. Quantum plasmonics. Nat. Phys. 9, 329–340 (2013). Open Access This article is licensed under a Creative Commons 37. Alonso Calafell, I. et al. Quantum computing with graphene plasmons. NPJ Attribution 4.0 International License, which permits use, sharing, Quant. Inf. 5, 37 (2019). adaptation, distribution and reproduction in any medium or format, as long as you give 38. Christensen, J., Manjavacas, A., Thongrattanasiri, S., Koppens, F. H. L. & appropriate credit to the original author(s) and the source, provide a link to the Creative García de Abajo, F. J. Graphene plasmon waveguiding and hybridization in Commons license, and indicate if changes were made. The images or other third party individual and paired nanoribbons. ACS Nano 6, 431–440 (2012). material in this article are included in the article’s Creative Commons license, unless 39. Morin, O., Körber, M., Langenfeld, S. & Rempe, G. Deterministic shaping and indicated otherwise in a credit line to the material. If material is not included in the reshaping of single-photon temporal wave functions. Phys. Rev. Lett. 123, article’s Creative Commons license and your intended use is not permitted by statutory 133602 (2019). regulation or exceeds the permitted use, you will need to obtain permission directly from 40. Hwang, J. et al. A single-molecule optical transistor. Nature 460, 76–80 (2009). the copyright holder. To view a copy of this license, visit http://creativecommons.org/ 41. Geiselmann, M., Marty, R., García de Abajo, F. J. & Quidant, R. Fast optical licenses/by/4.0/. modulation of the fluorescence from a single nitrogen-vacancy centre. Nat. Phys. 9, 785–789 (2013). 42. Tiecke, T. G. et al. Efficient fiber-optical interface for nanophotonic devices. © The Author(s) 2020 Optica 2, 70–75 (2015). 8 NATURE COMMUNICATIONS | (2020)11:4094 | https://doi.org/10.1038/s41467-020-17899-7 | www.nature.com/naturecommunications