Abstract

Hexagonal boron nitride (hBN), a wide-bandgap 2D material, is rapidly emerging as a promising candidate for quantum optics experiments. In this work, we demonstrate, to the best of our knowledge, the first signature of Rabi oscillations, the time-domain analogue of the Mollow triplet, from a resonantly driven hBN quantum emitter. Resonant photoluminescence excitation measurements reveal that the emitter undergoes strong spectral diffusion with a time scale of 37±25ms, resulting in a 0.6 GHz spectral diffusion broadened linewidth at the weak excitation limit. We further realize resonance fluorescence from the same emitter using a cross-polarized setup. The results shown here present an important step toward utilizing coherent optical control in 2D materials for the realization of scalable quantum information processing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Coherent control of a quantum mechanical two-level system is at the heart of quantum information processing [14], nanoscale quantum sensing [5,6], and quantum communication. Due to their long spin coherence times even at room temperature, nitrogen-vacancy (NV) centers in diamond have been widely used in coherent control schemes. Even though semiconductor quantum dots (QDs) are promising candidates for studying coherent light–matter interactions at cryogenic temperatures [711], fast decoherence times significantly limit their use at room temperature. Recently, spin-based room temperature coherent control in other systems such as silicon carbide (SiC) [12] has been realized.

The discovery of quantum emitters in atomically thin materials has opened up unique opportunities for device integration and efficient light–matter interactions [1319]. Among others, quantum emitters in hexagonal boron nitride have received significant attention due to their remarkable properties, including room-temperature single-photon emission [2023], ultrabrightness [21], and narrow emission lines [24]. The rapid progress in understanding this system has been supported by studies in defect engineering [2529], emission wavelength tuning using electric fields [30], and strain [31]. However, to date, there have been no reports of coherent optical control of quantum emitters in hexagonal boron nitride (hBN).

In this work, we report Rabi oscillations and resonance fluorescence from a single hBN quantum emitter at 10 K. After performing nonresonant characterization including photon antibunching, we use photoluminescence excitation (PLE) measurements to study the defect’s resonant absorption by its zero phonon line (ZPL). We find that in the limit of low optical intensity, the single emitter has a linewidth as low was 0.6 GHz. In the limit of large intensity, however, second-order photon correlation measurements reveal coherent optical Rabi oscillations. Finally, we demonstrate resonance fluorescence of the emitter in which we optically pump and detect the coherent photons emitted from the ZPL using a cross-polarized setup. This work highlights that hBN quantum emitters can display optical coherence at low temperature, making them a significant resource for quantum optics.

2. PHOTOLUMINESCENCE CHARACTERIZATION OF THE EMITTER

The hBN sample is mounted in an attocube attoDRY cryostat, and a frequency tunable Ti:sapphire laser is used for the optical excitation. We identify a bright and relatively stable hBN emitter using the confocal PL setup illustrated in Fig. 1(a) (see Appendix A for details). The fluorescence from the emitter is coupled into a single-mode fiber and then directs the signal to either a grating spectrometer for spectral measurements or a fiber-based Hanbury Brown and Twiss (HBT) interferometer to study photon statistics.

 figure: Fig. 1.

Fig. 1. PL measurements. (a) Schematic representation of the cryogenic PL setup. BS, beam splitter; λ/2, half-wave plate; LP, linear polarizer; SPAD, single-photon avalanche diode. (b) PL spectrum of a hBN emitter with 725 nm laser excitation of 400 μW, showing ZPL and PSB. Note that the dark green line is multiplied by 100 to see the features clearly. The inset shows the spectral wandering of the emitter. (c) Polar maps of the excitation (blue open circles) and emission (red open circles). The solid lines are fits obtained using I(θ)=a+bcos2(θθ0). (d) Second-order correlation function of the spectrum shown in (a) measured with a HBT setup. The red solid line is a fit obtained using Eq. (1). The measured antibunching dip at zero time delay is 0.75. The black dashed line represents the limit for a single-photon source.

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Figure 1(b) shows the PL spectrum of a selected hBN emitter, recorded at 725 nm laser excitation. A bright ZPL near 796.3 nm and a weaker PSB (880 nm–915 nm) can be clearly identified. The intensity ratio of the ZPL and PSB is a constant for a given emitter at a given temperature, and is described by the Debye–Waller factor [32]. Using the PL spectrum shown in Fig. 1(b), we calculate the intensity ratio ZPL/(ZPL+PSB) to be 0.89 at 10 K, which is typical for hBN emitters [20]. The inset in Fig. 1(b) illustrates the spectral wandering of the ZPL measured with a high-resolution 1800 lines/mm grating. The ZPL energy is sensitive to emitter’s local electric field fluctuations due to the Stark effect. Spectral diffusion has been a major issue in quantum optics experiments based on semiconductor QDs [33] as well as NV centers in diamond [34].

To characterize the polarization properties of the emitter, we perform polarization-dependent measurements for both excitation (blue trace) and emission (red trace) [Fig. 1(c)]. The solid lines are obtained by fitting the experimental data to the function I(θ)=a+bcos2(θθ0), where a and a+b are the minimum and maximum values of the PL intensity, respectively, and θ0 is the angle of polarization of the emitter. The calculated polarization contrasts for the excitation and emission are 0.85 and 0.7, respectively. Such a high degree of linear polarization suggests that the emitter corresponds to a single-dipole transition. The misalignment of the excitation and emission dipoles have been previously reported and can be attributed to the presence of additional electronic states [35].

To verify that a single-hBN emitter is responsible for the detected signal, the second-order intensity autocorrelation function is recorded by sending the collected photons to the HBT setup, which consists of a 50:50 beam splitter and two single-photon avalanche photodiodes (SPADs) [Fig. 1(d)]. The measurement shows a clear signature of short time-delay bunching, which indicates the presence of a nonradiative relaxation path through a metastable state. To describe these observations, we use a second-order correlation function relevant for a three-level system, which is given by [27]

g2(τ)=1ρ2[(1+a)e|τ|/τ1ae|τ|/τ2],
where τ is the correlation time, a is the photon bunching amplitude, and τ1 and τ2 are the lifetimes of the excited states. ρ accounts for the presence of Poissonian light. After fitting the experimental data using Eq. (1), the antibunching dip at zero time delay, g(2)(0), is determined to be 0.75. It should be noted that the criteria for determining single-photon emission for a three-level system is g(2)(0)=12(1+ρ2a) [27], which reduces to the quantum limit of a two-level system (0.5) when the photon bunching amplitude a approaches zero. Using the fitting parameters (a=4.7,ρ=0.5), we calculate the latter to be 1.1 (>0.75); thus, this confirms the single-photon emission. Furthermore, the data is not corrected to account for the background emission and/or instrument response function (IRF) of the detectors that would result in a more pronounced antibunching dip at the zero time delay.

3. PLE CHARACTERIZATION OF THE EMITTER

Recently, acoustic-phonon-broadened ZPL linewidth of hBN emitters has been studied in the high-temperature limit [36]. At the lowest temperatures, however, linewidth measurements are primarily limited by the instrument resolution. The knowledge of the fundamental linewidth limits of hBN quantum emitters will be very useful for developing next-generation hBN-based indistinguishable single photons. In this regard resonant PLE, in which we excite the emitter with a tunable laser energy in resonance with the quantum emitter’s optical transition and collect photons from the phonon sideband (PSB), is a useful approach to characterize hBN emitters at cryogenic temperatures [37,38]. In this section of the article, we provide a detailed analysis of the emitter using PLE measurements.

The schematics of the experimental setup are shown in Fig. 2(a), where we use two long-pass filters to select only PSB counts (see Appendix A for details). Figure 2(b) shows a time trace of the PSB counts when the wavelength of the excitation laser is fixed and near resonant with the ZPL. The data is acquired with 10 ms time bins at 100 nw laser power. The fluorescence intensity exhibits frequent abrupt jumps due to spectral wandering as seen in the inset of Fig. 1(b). Using the data shown in Fig. 2(b), we build a histogram to find out the associated time scale of these fluctuations. The corresponding histogram is shown in the inset of Fig. 2(b). Here it is assumed that the emitter is on-resonance if the count rate is equal or greater than 50, and off-resonance, otherwise. Based on this assumption, the emitter is off-resonance more than half of the measurement time (τon/τoff=0.4). We further estimate the average spectral diffusion time scale τSD for this particular emitter to be 37±25ms.

 figure: Fig. 2.

Fig. 2. PLE measurements. (a) Schematics of the detection system. (b) Single photon APD time trace of the PSB when the excitation laser is on-resonant with the ZPL. (c) Excitation spectra of the emitter measured at 36 nW and 1.5 μW. Solid red lines are Lorentzian fits. (d) Saturation of the fluorescence intensity acquired by monitoring the integrated PSB counts. The error bars represent the standard error of the detected peak fluorescence intensity at each laser power. The solid red line is a theoretical fit to the data using Eq. (2). The inset displays the power broadening of the emitter. The fit was obtained using Eq. (3). The actual power that corresponds to p¯=1 is 13 nW. The error bars in the inset are the standard errors of the FWHM of the Lorentzian fits shown in Fig. 2(c).

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PLE is an absorption measurement; thus we obtain spectral resolution for a finely scanned laser energy. Figure 2(c) shows excitation spectra measured at two different laser powers. In these measurements, the laser is scanned across the ZPL while collecting fluorescence photons at the PSB. The full width at half-maximum (FWHM) of the excitation spectrum in weak excitation regime is found to be 0.6GHz. We further confirm that the detected signal is indeed due to the PSB counts by sending the collected signal into a grating spectrometer. These measurements are presented in Section 1 of Supplement 1.

 figure: Fig. 3.

Fig. 3. Rabi oscillations. (a) Second-order correlation function measured using the PSB photons as a function of excitation powers. Traces are vertically shifted for clarity. The solid red lines represent the corresponding theoretical traces (κ21/2π=148±3MHz, κ23/2π=0.72±0.25MHz, κ31/2π=0.007±0.002MHz). Theoretical traces are convolved with the instrument response function (IRF) of the detector. (b) Comparison of second-order correlation functions for PSB photons (green) and white light with the same average count rate (black). The indicated uncertainties are standard deviations of the two curves. (c) Decay rates [1/τ1 in Eq. (1)] extracted from nonresonant second-order correlation measurements versus excitation power. The solid red line is a linear fit to the data to estimate the spontaneous decay rate of the emitter. (d) Estimated Rabi frequency from (a) as a function of square root of the laser intensity.

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 figure: Fig. 4.

Fig. 4. Resonance fluorescence measurements. (a) Simultaneous time traces of ZPL+PSB (red line) and PSB (dark green), recorded at 10 nW laser power. Traces are shifted vertically for clarity. Also, note that PSB counts are multiplied by a factor of 10. The dashed line represents the average laser background during the measurement. (b) Second-order correlation function of ZPL+PSB. The background is recorded separately and subtracted out. Data acquisition time is 1 h. The solid red line is a fit obtained using Eq. (1).

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Figure 2(d) presents the fluorescence intensity at the PSB as a function of normalized excitation laser power. The saturation behavior of a resonantly driven two-level system can be described by [39,40]

I=Isatp¯(1+p¯),
where I denotes the fluorescence intensity at a given excitation power, Isat is its saturation value, and p¯ corresponds to a normalized excitation power. Equation (2) is used to fit the power-dependent fluorescence data in Fig. 2(d). The actual power corresponding to p¯=1 is 13 nW. The broadening of the absorption linewidth with increasing excitation power, power broadening, is a direct consequence of the saturation of the absorption in a two-level system under high excitation intensities [41]. The inset in Fig. 2(d) presents an analysis of linewidth versus normalized excitation power (p¯) obtained by averaging five PLE scans recorded at each excitation power. The power broadened linewidth Γ (FWHM) can be related to its homogeneously broadened linewidth Γ0 via
Γ=Γ01+p¯.
To be consistent with the data shown in Fig. 2(d), here we have used the same scaling factor for the horizontal axis. As can be seen, a reasonable agreement is found between the experimentally measured linewidths and the theory.

4. RABI OSCILLATIONS

The photon statistics of the PLE signal are studied by recording the second-order correlation function using a HBT setup. Figure 3(a) shows a series of such traces recorded with increasing excitation power. One can clearly identify the first peak of an oscillatory signal and its linewidth narrowing when the excitation power is increased. These oscillations arise due to laser-induced coherent population cycling between the ground and optically excited state. The oscillations occur at a characteristic frequency called the Rabi frequency. Since these oscillations are imprinted into the PSB, PLE allows us to study Rabi oscillations in the PSB signal without direct access to the resonance fluorescence signal. However, the low count rate available at the PSB (<104counts/s on average) together with the timing resolution of the detectors make it difficult to resolve complete Rabi oscillations. The traces shown in Fig. 3(a) were recorded for more than 8 h to improve statistics. To further verify that the observed oscillatory nature is due to Rabi oscillations, we have compared the second-order correlation function of PSB photons with that of white light, having the same average count rates [Fig. 3(b)]. The calculated standard deviations of the white light and PSB photons are 0.096 and 0.124, respectively. As shown in Fig. 3(b), the bunching peaks near zero delay reach 1.35, which is 23σ above the uncertainty in g(2)(τ). Furthermore, the amplitude and spacing of these features evolve systematically with optical power, consistent with the expected signature of Rabi oscillations. Finally, we note that these short-time bunching features are not present in the nonresonant photon correlation measurements. Therefore, we conclude that we indeed observe optical Rabi oscillations.

The solid red lines in Fig. 3(a) are theoretical traces obtained by integrating optical Bloch equations relevant for a two-level system with an additional metastable state. More information on the theoretical traces can be found in the Section 2 of Supplement 1. To determine the spontaneous decay rate to be used for the theoretical traces (κ21), we record second-order correlation function using the PL signal for a range of excitation powers [42,43]. After fitting the data with Eq. (1), we extract 1/τ1(=κ12+κ21) and plot against the excitation power [Fig. 3(c)]. Linear extrapolation of the data (solid red line) is used to find 1/τ1 at zero excitation power at which κ12 is zero. In this way, κ21/2π=148±3MHz (lifetime of 1ns) is estimated and used for the theoretical fits. Additionally, theoretical traces are convolved with the IRF to account for the limited time resolution of the detectors. From the power-dependent second-order correlation measurements similar to what is shown in Fig. 3(a), we also extract the corresponding Rabi frequency at each laser intensity and plot as a function of square root of the laser intensity [Fig. 3(d)]. The plot shows a linear dependence, which is expected for a resonantly driven two-level system. Lifetimes of hBN quantum emitters at cryogenic temperatures (5 K) have previously been studied and compared with coherence times [44]. We find that the measured linewidths are consistent with those reported in [38,44].

5. OBSERVATION OF RESONANCE FLUORESCENCE

The generation of high-quality single photons is a key requirement for many applications in quantum information science [45]. Even though direct resonant excitation is challenging to realize in solid-sate systems, resonance fluorescence is known to generate single photons with optimal coherence and indistinguishablity properties [46]. Resonance fluorescence has been extensively studied in semiconductor QDs either using an optical microcavity [11,40,47,48] or the cross-polarized approach to minimize the background laser scattering [9]. More recently, resonance fluorescence has been reported in tungsten diselenide (WSe2) quantum emitters [17].

To study resonance fluorescence, here we employ a cross-polarized excitation and detection setup using two linear polarizers and a quarter-wave plate (see Appendix A for details). Although this approach is known to provide well over 106 extinction on smooth substrates [49], we managed to get a 2.5×104 extinction ratio in our measurements. Figure 4(a) shows the time traces of ZPL+PSB (red line) and PSB (dark green line) recorded at 10 nW excitation power for 30 min. While background counts (dashed black line) fluctuate from 2000 to 6000 counts/s, well-aligned peaks in the two traces can be clearly identified. One can estimate the expected count rate at the ZPL based on the PSB counts, and Debye–Waller factor, calculated from the PL spectrum. According to Fig. 4(a), we have 2,000counts/s at the PSB, and thus the expected ZPL count rate is 20,000counts/s. The measured ZPL count rate agrees well with this estimate, and hence confirms the observation of resonance fluorescence.

To further verify that the detected signal is due to resonance fluorescence, the second-order correlation function is measured by sending the collection (without any spectral filtering, i.e., ZPL+PSB+laser) to the HBT setup. Even though we have achieved a 4:1 signal to background ratio when the emitter is on-resonance, spectral diffusion determines how much time the emitter spends on-resonance compared to off-resonance. For this particular emitter, we find that it is off-resonance for minutes. Therefore, background laser scattering plays a significant role in determining the dip at zero delay in the second-order correlation function. To account for that, background laser scattering is recorded separately on the Si substrate for the same amount of time and subtracted out. Since the polarizers in the cross-polarized setup are very sensitive to wavelength changes, tuning the laser wavelength spoils the extinction ratio significantly. Therefore, a better approach for background correction is to tune the emission wavelength using an external electric field [30,50,51]. The resultant histogram is shown in Fig. 4(b). Here the fit (red solid line) is again obtained using Eq. (1). The presence of the pronounced antibunching dip with g(2)(0)=0.17 is a clear indication of a single-photon source.

6. CONCLUSION

In conclusion, we have observed Rabi oscillations which demonstrate the potential for coherent optical manipulation of hBN quantum emitters. We find a close agreement between the theory and the experimental traces, and, in particular, the observed Rabi oscillation can be successfully reproduced when the experimentally measured spontaneous decay rate is used in the theory. PLE measurements reveal that the emitter saturates near 100 nw and has a narrow linewidth reaching 0.6 GHz at the weak excitation limit. This work also demonstrates the possibility of accessing direct resonance fluorescence counts, carrying improved coherence and indistinguishable properties that are useful for quantum science applications. We find that the spectral diffusion results in abrupt intensity fluctuations happening at a millisecond timescale. These fluctuations introduce unnecessary complications and hinder the use of hBN emitters in any application where a constant flux of photons is needed. Therefore, it will be important to minimize these effects in future experiments. One possibility is to use a passivation technique based on high-quality atomic layer epitaxy-grown Al2O3, which is known to reduce the spectral diffusion from the substrate significantly [24]. In particular, one potential route to achieve coherent control and indistinguishable photons is to use strain-induced hBN quantum emitters [52], combined with resonance fluorescence [33].

APPENDIX A: METHODS

1. Sample Preparation

The hBN flakes we investigated are commercially available from Graphene Supermarket. The as-received flakes are suspended in a 50–50 water–ethanol solution. We drop cast 25 μL of solution onto a thermally oxidized silicon substrate and anneal the samples at 850°C for 30 min under continuous nitrogen flow. We have previously prepared samples in this way, and have characterized those hBN flakes via Raman spectroscopy and energy-dispersive x-ray spectroscopy [36].

2. Optical Characterization

In resonance fluorescence measurements, two orthogonally oriented linear polarizers (one in the excitation arm and the other in the collection arm) are used to filter out the direct laser scattering from the substrate. An additional quarter-wave plate is also introduced into the common arm for correcting any ellipticity introduced by the sample. The input linear polarizer and quarter-wave plate are carefully adjusted to optimize the extinction using high-precision attocube piezo rotators (ANR 101). The fluorescence signal is split into two paths, and counts in each arm are simultaneously read using a National Instrument multifunction DAQ card, which allows us to study the count rates of the ZPL+PSB and PSB separately. Since the intensity ratio between ZPL and PSB remains approximately the same, in this way, one can easily identify if there are any significant laser fluctuations.

Funding

NSF Directorate for Mathematical and Physical Sciences (MPS) (CAREER-DMR-1553788, EFRI-EFMA-1542707); the Cornell Center for Materials Research with funding from the NSF MRSEC program (DMR-1719875); Air Force Office of Scientific Research (AFOSR) (FA9550-19-1-0074).

 

See Supplement 1 for supporting content.

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35. N. R. Jungwirth and G. D. Fuchs, “Optical absorption and emission mechanisms of single defects in hexagonal boron nitride,” Phys. Rev. Lett. 119, 057401 (2017). [CrossRef]  

36. N. R. Jungwirth, B. Calderon, Y. Ji, M. G. Spencer, M. E. Flatté, and G. D. Fuchs, “Temperature dependence of wavelength selectable zero-phonon emission from single defects in hexagonal boron nitride,” Nano Lett. 16, 6052–6057 (2016). [CrossRef]  

37. T. T. Tran, M. Kianinia, M. Nguyen, S. Kim, Z.-Q. Xu, A. Kubanek, M. Toth, and I. Aharonovich, “Resonant excitation of quantum emitters in hexagonal boron nitride,” ACS Photon. 5, 295–300 (2017). [CrossRef]  

38. A. Dietrich, M. Bürk, E. S. Steiger, L. Antoniuk, T. T. Tran, M. Nguyen, I. Aharonovich, F. Jelezko, and A. Kubanek, “Observation of Fourier transform limited lines in hexagonal boron nitride,” Phys. Rev. B 98, 081414 (2018). [CrossRef]  

39. H. J. Krenner, S. Stufler, M. Sabathil, E. C. Clark, P. Ester, M. Bichler, G. Abstreiter, J. J. Finley, and A. Zrenner, “Recent advances in exciton-based quantum information processing in quantum dot nanostructures,” New J. Phys. 7, 184 (2005). [CrossRef]  

40. A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99, 187402 (2007). [CrossRef]  

41. M. L. Citron, H. R. Gray, C. W. Gabel, and C. R. Stroud, “Experimental study of power broadening in a two-level atom,” Phys. Rev. A 16, 1507–1512 (1977). [CrossRef]  

42. M. Berthel, O. Mollet, G. Dantelle, T. Gacoin, S. Huant, and A. Drezet, “Photophysics of single nitrogen-vacancy centers in diamond nanocrystals,” Phys. Rev. B 91, 035308 (2015). [CrossRef]  

43. N. R. Jungwirth, Y. Y. Pai, H. S. Chang, E. R. MacQuarrie, K. X. Nguyen, and G. D. Fuchs, “A single-molecule approach to ZnO defect studies: single photons and single defects,” J. Appl. Phys. 116, 043509 (2014). [CrossRef]  

44. B. Sontheimer, M. Braun, N. Nikolay, N. Sadzak, I. Aharonovich, and O. Benson, “Photodynamics of quantum emitters in hexagonal boron nitride revealed by low-temperature spectroscopy,” Phys. Rev. B 96, 121202 (2017). [CrossRef]  

45. D. Bouwmeester, The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation (Springer, 2000).

46. C. Matthiesen, A. N. Vamivakas, and M. Atatüre, “Subnatural linewidth single photons from a quantum dot,” Phys. Rev. Lett. 108, 093602 (2012). [CrossRef]  

47. E. B. Flagg, A. Muller, J. W. Robertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, G. J. Salamo, and C. K. Shih, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5, 203–207 (2009). [CrossRef]  

48. A. Ulhaq, S. Weiler, S. M. Ulrich, R. Roßbach, M. Jetter, and P. Michler, “Cascaded single-photon emission from the Mollow triplet sidebands of a quantum dot,” Nat. Photonics 6, 238–242 (2012). [CrossRef]  

49. A. V. Kuhlmann, J. Houel, D. Brunner, A. Ludwig, D. Reuter, A. D. Wieck, and R. J. Warburton, “A dark-field microscope for background-free detection of resonance fluorescence from single semiconductor quantum dots operating in a set-and-forget mode,” Rev. Sci. Instrum. 84, 073905 (2013). [CrossRef]  

50. A. N. Vamivakas, Y. Zhao, S. Fält, A. Badolato, J. M. Taylor, and M. Atatüre, “Nanoscale optical electrometer,” Phys. Rev. Lett. 107, 166802 (2011). [CrossRef]  

51. C. Chakraborty, K. M. Goodfellow, S. Dhara, A. Yoshimura, V. Meunier, and A. N. Vamivakas, “Quantum-confined Stark effect of individual defects in a van der Waals heterostructure,” Nano Lett. 17, 2253–2258 (2017). [CrossRef]  

52. N. V. Proscia, Z. Shotan, H. Jayakumar, P. Reddy, C. Cohen, M. Dollar, A. Alkauskas, M. Doherty, C. A. Meriles, and V. M. Menon, “Near-deterministic activation of room-temperature quantum emitters in hexagonal boron nitride,” Optica 5, 1128–1134 (2018). [CrossRef]  

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    [Crossref]
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    [Crossref]
  44. B. Sontheimer, M. Braun, N. Nikolay, N. Sadzak, I. Aharonovich, and O. Benson, “Photodynamics of quantum emitters in hexagonal boron nitride revealed by low-temperature spectroscopy,” Phys. Rev. B 96, 121202 (2017).
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  45. D. Bouwmeester, The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation (Springer, 2000).
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    [Crossref]
  47. E. B. Flagg, A. Muller, J. W. Robertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, G. J. Salamo, and C. K. Shih, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5, 203–207 (2009).
    [Crossref]
  48. A. Ulhaq, S. Weiler, S. M. Ulrich, R. Roßbach, M. Jetter, and P. Michler, “Cascaded single-photon emission from the Mollow triplet sidebands of a quantum dot,” Nat. Photonics 6, 238–242 (2012).
    [Crossref]
  49. A. V. Kuhlmann, J. Houel, D. Brunner, A. Ludwig, D. Reuter, A. D. Wieck, and R. J. Warburton, “A dark-field microscope for background-free detection of resonance fluorescence from single semiconductor quantum dots operating in a set-and-forget mode,” Rev. Sci. Instrum. 84, 073905 (2013).
    [Crossref]
  50. A. N. Vamivakas, Y. Zhao, S. Fält, A. Badolato, J. M. Taylor, and M. Atatüre, “Nanoscale optical electrometer,” Phys. Rev. Lett. 107, 166802 (2011).
    [Crossref]
  51. C. Chakraborty, K. M. Goodfellow, S. Dhara, A. Yoshimura, V. Meunier, and A. N. Vamivakas, “Quantum-confined Stark effect of individual defects in a van der Waals heterostructure,” Nano Lett. 17, 2253–2258 (2017).
    [Crossref]
  52. N. V. Proscia, Z. Shotan, H. Jayakumar, P. Reddy, C. Cohen, M. Dollar, A. Alkauskas, M. Doherty, C. A. Meriles, and V. M. Menon, “Near-deterministic activation of room-temperature quantum emitters in hexagonal boron nitride,” Optica 5, 1128–1134 (2018).
    [Crossref]

2018 (7)

C. Chakraborty, L. Qiu, K. Konthasinghe, A. Mukherjee, S. Dhara, and N. Vamivakas, “3D localized trions in monolayer WSe2 in a charge tunable van der Waals heterostructure,” Nano Lett. 18, 2859–2863 (2018).
[Crossref]

T. Vogl, G. Campbell, B. C. Buchler, Y. Lu, and P. K. Lam, “Fabrication and deterministic transfer of high-quality quantum emitters in hexagonal boron nitride,” ACS Photon. 5, 2305–2312 (2018).
[Crossref]

Z.-Q. Xu, C. Elbadawi, T. T. Tran, M. Kianinia, X. Li, D. Liu, T. B. Hoffman, M. Nguyen, S. Kim, J. H. Edgar, X. Wu, L. Song, S. Ali, M. Ford, M. Toth, and I. Aharonovich, “Single photon emission from plasma treated 2D hexagonal boron nitride,” Nanoscale 10, 7957–7965 (2018).
[Crossref]

G. Noh, D. Choi, J.-H. Kim, D.-G. Im, Y.-H. Kim, H. Seo, and J. Lee, “Stark tuning of single-photon emitters in hexagonal boron nitride,” Nano Lett. 18, 4710–4715 (2018).
[Crossref]

P. C. Humphreys, N. Kalb, J. P. J. Morits, R. N. Schouten, R. F. L. Vermeulen, D. J. Twitchen, M. Markham, and R. Hanson, “Deterministic delivery of remote entanglement on a quantum network,” Nature 558, 268–273 (2018).
[Crossref]

A. Dietrich, M. Bürk, E. S. Steiger, L. Antoniuk, T. T. Tran, M. Nguyen, I. Aharonovich, F. Jelezko, and A. Kubanek, “Observation of Fourier transform limited lines in hexagonal boron nitride,” Phys. Rev. B 98, 081414 (2018).
[Crossref]

N. V. Proscia, Z. Shotan, H. Jayakumar, P. Reddy, C. Cohen, M. Dollar, A. Alkauskas, M. Doherty, C. A. Meriles, and V. M. Menon, “Near-deterministic activation of room-temperature quantum emitters in hexagonal boron nitride,” Optica 5, 1128–1134 (2018).
[Crossref]

2017 (8)

C. Chakraborty, K. M. Goodfellow, S. Dhara, A. Yoshimura, V. Meunier, and A. N. Vamivakas, “Quantum-confined Stark effect of individual defects in a van der Waals heterostructure,” Nano Lett. 17, 2253–2258 (2017).
[Crossref]

T. T. Tran, M. Kianinia, M. Nguyen, S. Kim, Z.-Q. Xu, A. Kubanek, M. Toth, and I. Aharonovich, “Resonant excitation of quantum emitters in hexagonal boron nitride,” ACS Photon. 5, 295–300 (2017).
[Crossref]

B. Sontheimer, M. Braun, N. Nikolay, N. Sadzak, I. Aharonovich, and O. Benson, “Photodynamics of quantum emitters in hexagonal boron nitride revealed by low-temperature spectroscopy,” Phys. Rev. B 96, 121202 (2017).
[Crossref]

N. R. Jungwirth and G. D. Fuchs, “Optical absorption and emission mechanisms of single defects in hexagonal boron nitride,” Phys. Rev. Lett. 119, 057401 (2017).
[Crossref]

A. L. Exarhos, D. A. Hopper, R. R. Grote, A. Alkauskas, and L. C. Bassett, “Optical signatures of quantum emitters in suspended hexagonal boron nitride,” ACS Nano 11, 3328–3336 (2017).
[Crossref]

G. Grosso, H. Moon, B. Lienhard, S. Ali, D. K. Efetov, M. M. Furchi, P. Jarillo-Herrero, M. J. Ford, I. Aharonovich, and D. Englund, “Tunable and high-purity room temperature single-photon emission from atomic defects in hexagonal boron nitride,” Nat. Commun. 8, 705 (2017).
[Crossref]

T. V. Lam, Y. Lu, and P. Koy, “Room temperature single photon source using fiber-integrated hexagonal boron nitride,” J. Phys. D 50, 295101 (2017).
[Crossref]

X. Li, G. D. Shepard, A. Cupo, N. Camporeale, K. Shayan, Y. Luo, V. Meunier, and S. Strauf, “Nonmagnetic quantum emitters in boron nitride with ultranarrow and sideband-free emission spectra,” ACS Nano 11, 6652–6660 (2017).
[Crossref]

2016 (8)

S. Choi, T. T. Tran, C. Elbadawi, C. Lobo, X. Wang, S. Juodkazis, G. Seniutinas, M. Toth, and I. Aharonovich, “Engineering and localization of quantum emitters in large hexagonal boron nitride layers,” ACS Appl. Mater. Interfaces 8, 29642–29648 (2016).
[Crossref]

N. Chejanovsky, M. Rezai, F. Paolucci, Y. Kim, T. Rendler, W. Rouabeh, F. Fávaro de Oliveira, P. Herlinger, A. Denisenko, S. Yang, I. Gerhardt, A. Finkler, J. H. Smet, and J. Wrachtrup, “Structural attributes and photodynamics of visible spectrum quantum emitters in hexagonal boron nitride,” Nano Lett. 16, 7037–7045 (2016).
[Crossref]

T. T. Tran, K. Bray, M. J. Ford, M. Toth, and I. Aharonovich, “Quantum emission from hexagonal boron nitride monolayers,” Nat. Nanotechnol. 11, 37–41 (2016).
[Crossref]

T. T. Tran, C. Elbadawi, D. Totonjian, C. J. Lobo, G. Grosso, H. Moon, D. R. Englund, M. J. Ford, I. Aharonovich, and M. Toth, “Robust multicolor single photon emission from point defects in hexagonal boron nitride,” ACS Nano 10, 7331–7338 (2016).
[Crossref]

L. J. Martnez, T. Pelini, V. Waselowski, J. R. Maze, B. Gil, G. Cassabois, and V. Jacques, “Efficient single photon emission from a high-purity hexagonal boron nitride crystal,” Phys. Rev. B 94, 121405 (2016).
[Crossref]

N. R. Jungwirth, B. Calderon, Y. Ji, M. G. Spencer, M. E. Flatté, and G. D. Fuchs, “Temperature dependence of wavelength selectable zero-phonon emission from single defects in hexagonal boron nitride,” Nano Lett. 16, 6052–6057 (2016).
[Crossref]

S. Kumar, M. Brotóns-Gisbert, R. Al-Khuzheyri, A. Branny, G. Ballesteros-Garcia, J. F. Sánchez-Royo, and B. D. Gerardot, “Resonant laser spectroscopy of localized excitons in monolayer WSe2,” Optica 3, 882–886 (2016).
[Crossref]

C. Chakraborty, K. M. Goodfellow, and A. N. Vamivakas, “Localized emission from defects in MoSe2 layers,” Opt. Mater. Express 6, 2081–2087 (2016).
[Crossref]

2015 (5)

C. Chakraborty, L. Kinnischtzke, K. M. Goodfellow, R. Beams, and A. N. Vamivakas, “Voltage-controlled quantum light from an atomically thin semiconductor,” Nat. Nanotechnol. 10, 507–511 (2015).
[Crossref]

A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, and A. Imamoglu, “Optically active quantum dots in monolayer WSe2,” Nat. Nanotechnol. 10, 491–496 (2015).
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M. Koperski, K. Nogajewski, A. Arora, V. Cherkez, P. Mallet, J.-Y. Veuillen, J. Marcus, P. Kossacki, and M. Potemski, “Single photon emitters in exfoliated WSe2 structures,” Nat. Nanotechnol. 10, 503–506 (2015).
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2014 (1)

N. R. Jungwirth, Y. Y. Pai, H. S. Chang, E. R. MacQuarrie, K. X. Nguyen, and G. D. Fuchs, “A single-molecule approach to ZnO defect studies: single photons and single defects,” J. Appl. Phys. 116, 043509 (2014).
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2013 (3)

A. V. Kuhlmann, J. Houel, D. Brunner, A. Ludwig, D. Reuter, A. D. Wieck, and R. J. Warburton, “A dark-field microscope for background-free detection of resonance fluorescence from single semiconductor quantum dots operating in a set-and-forget mode,” Rev. Sci. Instrum. 84, 073905 (2013).
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H. Bernien, B. Hensen, W. Pfaff, G. Koolstra, M. S. Blok, L. Robledo, T. H. Taminiau, M. Markham, D. J. Twitchen, L. Childress, and R. Hanson, “Heralded entanglement between solid-state qubits separated by three metres,” Nature 497, 86–90 (2013).
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H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, “Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor,” Science 339, 557–560 (2013).
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2012 (4)

K. Konthasinghe, J. Walker, M. Peiris, C. K. Shih, Y. Yu, M. F. Li, J. F. He, L. J. Wang, H. Q. Ni, Z. C. Niu, and A. Muller, “Coherent versus incoherent light scattering from a quantum dot,” Phys. Rev. B 85, 235315 (2012).
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K. Konthasinghe, M. Peiris, Y. Yu, M. F. Li, J. F. He, L. J. Wang, H. Q. Ni, Z. C. Niu, C. K. Shih, and A. Muller, “Field-field and photon-photon correlations of light scattered by two remote two-level inas quantum dots on the same substrate,” Phys. Rev. Lett. 109, 267402 (2012).
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A. Ulhaq, S. Weiler, S. M. Ulrich, R. Roßbach, M. Jetter, and P. Michler, “Cascaded single-photon emission from the Mollow triplet sidebands of a quantum dot,” Nat. Photonics 6, 238–242 (2012).
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C. Matthiesen, A. N. Vamivakas, and M. Atatüre, “Subnatural linewidth single photons from a quantum dot,” Phys. Rev. Lett. 108, 093602 (2012).
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2011 (3)

A. N. Vamivakas, Y. Zhao, S. Fält, A. Badolato, J. M. Taylor, and M. Atatüre, “Nanoscale optical electrometer,” Phys. Rev. Lett. 107, 166802 (2011).
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2010 (2)

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys. 6, 249–253 (2010).
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A. J. Ramsay, “A review of the coherent optical control of the exciton and spin states of semiconductor quantum dots,” Semicond. Sci. Technol. 25, 103001 (2010).
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2009 (2)

A. Nick Vamivakas, Y. Zhao, C.-Y. Lu, and M. Atatüre, “Spin-resolved quantum-dot resonance fluorescence,” Nat. Phys. 5, 198–202 (2009).
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E. B. Flagg, A. Muller, J. W. Robertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, G. J. Salamo, and C. K. Shih, “Resonantly driven coherent oscillations in a solid-state quantum emitter,” Nat. Phys. 5, 203–207 (2009).
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2008 (1)

J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J. M. Taylor, P. Cappellaro, L. Jiang, M. V. G. Dutt, E. Togan, A. S. Zibrov, A. Yacoby, R. L. Walsworth, and M. D. Lukin, “Nanoscale magnetic sensing with an individual electronic spin in diamond,” Nature 455, 644–647 (2008).
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2007 (1)

A. Muller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, “Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity,” Phys. Rev. Lett. 99, 187402 (2007).
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2006 (1)

J. Wrachtrup and F. Jelezko, “Processing quantum information in diamond,” J. Phys. Condens. Matter 18, S807 (2006).
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2005 (1)

H. J. Krenner, S. Stufler, M. Sabathil, E. C. Clark, P. Ester, M. Bichler, G. Abstreiter, J. J. Finley, and A. Zrenner, “Recent advances in exciton-based quantum information processing in quantum dot nanostructures,” New J. Phys. 7, 184 (2005).
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2001 (2)

T. H. Stievater, X. Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “Rabi oscillations of excitons in single quantum dots,” Phys. Rev. Lett. 87, 133603 (2001).
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H. Kamada, H. Gotoh, J. Temmyo, T. Takagahara, and H. Ando, “Exciton rabi oscillation in a single quantum dot,” Phys. Rev. Lett. 87, 246401 (2001).
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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. PL measurements. (a) Schematic representation of the cryogenic PL setup. BS, beam splitter; λ / 2 , half-wave plate; LP, linear polarizer; SPAD, single-photon avalanche diode. (b) PL spectrum of a hBN emitter with 725 nm laser excitation of 400 μW, showing ZPL and PSB. Note that the dark green line is multiplied by 100 to see the features clearly. The inset shows the spectral wandering of the emitter. (c) Polar maps of the excitation (blue open circles) and emission (red open circles). The solid lines are fits obtained using I ( θ ) = a + b cos 2 ( θ θ 0 ) . (d) Second-order correlation function of the spectrum shown in (a) measured with a HBT setup. The red solid line is a fit obtained using Eq. (1). The measured antibunching dip at zero time delay is 0.75. The black dashed line represents the limit for a single-photon source.
Fig. 2.
Fig. 2. PLE measurements. (a) Schematics of the detection system. (b) Single photon APD time trace of the PSB when the excitation laser is on-resonant with the ZPL. (c) Excitation spectra of the emitter measured at 36 nW and 1.5 μW. Solid red lines are Lorentzian fits. (d) Saturation of the fluorescence intensity acquired by monitoring the integrated PSB counts. The error bars represent the standard error of the detected peak fluorescence intensity at each laser power. The solid red line is a theoretical fit to the data using Eq. (2). The inset displays the power broadening of the emitter. The fit was obtained using Eq. (3). The actual power that corresponds to p ¯ = 1 is 13 nW. The error bars in the inset are the standard errors of the FWHM of the Lorentzian fits shown in Fig. 2(c).
Fig. 3.
Fig. 3. Rabi oscillations. (a) Second-order correlation function measured using the PSB photons as a function of excitation powers. Traces are vertically shifted for clarity. The solid red lines represent the corresponding theoretical traces ( κ 21 / 2 π = 148 ± 3 MHz , κ 23 / 2 π = 0.72 ± 0.25 MHz , κ 31 / 2 π = 0.007 ± 0.002 MHz ). Theoretical traces are convolved with the instrument response function (IRF) of the detector. (b) Comparison of second-order correlation functions for PSB photons (green) and white light with the same average count rate (black). The indicated uncertainties are standard deviations of the two curves. (c) Decay rates [ 1 / τ 1 in Eq. (1)] extracted from nonresonant second-order correlation measurements versus excitation power. The solid red line is a linear fit to the data to estimate the spontaneous decay rate of the emitter. (d) Estimated Rabi frequency from (a) as a function of square root of the laser intensity.
Fig. 4.
Fig. 4. Resonance fluorescence measurements. (a) Simultaneous time traces of ZPL + PSB (red line) and PSB (dark green), recorded at 10 nW laser power. Traces are shifted vertically for clarity. Also, note that PSB counts are multiplied by a factor of 10. The dashed line represents the average laser background during the measurement. (b) Second-order correlation function of ZPL + PSB . The background is recorded separately and subtracted out. Data acquisition time is 1 h. The solid red line is a fit obtained using Eq. (1).

Equations (3)

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g 2 ( τ ) = 1 ρ 2 [ ( 1 + a ) e | τ | / τ 1 a e | τ | / τ 2 ] ,
I = I sat p ¯ ( 1 + p ¯ ) ,
Γ = Γ 0 1 + p ¯ .

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