Abstract
Singlephoton emission from the nitrogenvacancy defect in diamond constitutes one of its many proposed applications. Owing to its doubly degenerate ^{3}E electronic excited state, photons from this defect can be emitted by two optical transitions with perpendicular polarization. Previous measurements have indicated that orbitalselective photoexcitation does not, however, yield photoluminescence with welldefined polarizations, thus hinting at orbitalaveraging dynamics even at cryogenic temperatures. Here we employ femtosecond polarization anisotropy spectroscopy to investigate the ultrafast electronic dynamics of the ^{3}E state. We observe subpicosecond electronic dephasing dynamics even at cryogenic temperatures, up to five orders of magnitude faster than dephasing rates suggested by previous frequency and timedomain measurements. Ab initio molecular dynamics simulations assign the ultrafast depolarization dynamics to nonadiabatic transitions and phononinduced electronic dephasing between the two components of the ^{3}E state. Our results provide an explanation for the ultrafast orbital averaging that exists even at cryogenic temperatures.
Introduction
Among the known colour centres of diamond, the negatively charged nitrogenvacancy (NV^{−}) defect has attracted the most attention^{1}, motivated by its potential to serve as a building block for novel quantum technologies. Remarkable advances in their magnetic and optical manipulation, performed even at the singledefect level^{2}, herald their application to spinbased quantum computing^{3,4} and photonics^{5}, as well as nanoscale magnetic field^{6,7,8} and temperature sensors^{9,10,11}.
Buried deep within the band gap of diamond are the NV^{− 3}A_{2} electronic ground state and the doubly degenerate ^{3}E excited state, which are optically coupled by a narrow zerophonon line (ZPL) transition at 1.95 eV (637 nm wavelength, Fig. 1a). This optical transition has been identified as a potential quantum emitter for single photons^{1,5}. Vibronic coupling between the ^{3}E electronic state and a quasilocalized vibrational mode at ∼68 meV gives rise to a broad phonon sideband^{12}. The E_{x} and E_{y} sublevels of the ^{3}E state have orthogonal electronic alignment, evidenced by the computed orbital densities in Fig. 1b, hence yielding two perpendicularly polarized ^{3}A_{2}→^{3}E transitions^{1}.
As a result of its orbital degeneracy, the ^{3}E state couples to a doubly degenerate vibrational mode of e symmetry to form an E⊗e JahnTeller (JT) system^{1}. The JTactive mode involves the displacement of the carbon atoms that surround the vacancy. The initially degenerate E_{x} and E_{y} states are displaced along the JTactive mode Q_{JT}, creating a conical intersection (CI, see Fig. 1b). At the same time, the potential minimum energy is reduced by the JT stabilization energy E_{JT}. For the NV^{–} defect, the theoretically predicted JT stabilization energy E_{JT} of 25 meV is smaller than the tunnelling splitting of 34 meV, therefore rendering the system a dynamic JT distortion^{13}.
In the vicinity of CIs, the BornOppenheimer approximation breaks down, allowing exceptionally fast nonadiabatic (NA) transitions between potential energy surfaces^{14,15}. In molecular photochemistry, for example, CIs between electronic excited and ground states are known to promote ultrafast internal conversion on femtosecond timescales^{16}. In the case of the NV^{−} defect, the CI exists only between the excited state E_{x} and E_{y} orbitals, thereby potentially enabling ultrafast NA transitions between them. In addition, the JT effect has been invoked to explain the asymmetry between the absorption and photoluminescence (PL) lineshapes^{1}, the broadening of the ^{3}E→^{3}A_{2} ZPL transition linewidth with increasing temperature and the concomitant reduction in the polarization contrast of its PL^{17}. These JT effects have important ramifications. The nonunity polarization contrast, observed even at cryogenic temperatures, for example, impairs coupling of NV^{−} photon sources to plasmonic waveguides and decreases the interference visibility of emitted single photons, thus impeding its use in quantum information processing^{5}.
The coherent dynamics of the orbital doublet at the E⊗e JT CI are encoded in the optical dephasing times. From the PL excitation linewidths of single defects, dephasing times of ∼10 ns at sub10 K and <0.3 ps at temperatures beyond 200 K have been inferred^{17}. The former is substantiated by an orbital coherence time of ∼6–7 ns, directly determined from timedomain Ramsey fringe interferometry^{18}. However, the low PL polarization contrast of ≲0.5 at 4 K indicates the existence of ultrafast dynamics that precede the nanosecond electronic dephasing processes that have been uncovered so far^{17,18,19}.
Here we use femtosecond polarization anisotropy (PA) spectroscopy to resolve the ultrafast coherent orbital dynamics of the ^{3}E state. We observe biphasic electronic dephasing dynamics occurring on subpicosecond to fewpicosecond timescales, even at cryogenic temperatures, up to five orders of magnitude faster than dephasing rates suggested by previous frequency and timedomain measurements^{17,19,20}. Ab initio molecular dynamics (AIMD) simulations assign the dynamics to NA transitions around the CI and phononinduced electronic dephasing between components of the ^{3}E state.
Results
PA spectroscopy
The femtosecond PA measurements employ a narrowband linearly polarized pump pulse to excite the ZPL transition of the NV^{−} defect (Fig. 1a), following which a broadband linearly polarized probe pulse measures the pumpinduced change of the normalized transmission spectrum ΔT/T. Excitation of the ZPL as opposed to the phonon sideband avoids complications introduced by ultrafast vibrational relaxation^{21}. Varying the pump–probe time delay and relative polarization yields the timeresolved ΔT/T signal (Fig. 1b) for parallel (S^{}) and perpendicular (S^{⊥}) relative polarization between pump and probe pulses. The PA signal S_{aniso}(λ,t) is then obtained from the relation S_{aniso}(λ,t)=(S^{}−S^{⊥})/(S^{}+2S^{⊥}) (see Methods).
Photoexcitation leads to increased transmission of the NV^{−} sample, as can be seen from the positive ΔT/T signal over the entire probe spectrum (Fig. 1c). Features on the blue side of the ZPL arise from depletion of the ^{3}A_{2} ground state by the photoexcitation pump pulse, resulting in the bleaching of the ^{3}A_{2} groundstate absorption spectrum. The positive ΔT/T signal on the red side of the ZPL is because of Stokesshifted stimulated emission from the level of the ^{3}E state, populated by the pump pulse, to the various levels on the ^{3}A_{2} ground state. As such, the former signal is sensitive to groundstate dynamics, whereas the latter is sensitive to excited state dynamics. Note that excitedstate absorption from the ^{3}E state, which would give negative ΔT/T signals, is negligible because of the small oscillator strength of excitedstate absorption into the conduction band.
S_{aniso}(λ,t) provides information on the alignment dynamics after photoexcitation (see Methods and Supporting Information). In molecular spectroscopy, for instance, this is used to measure the reorientation of molecules in solution^{22}, an effect that does not occur here because the NV^{−} defects are fixed in the diamond lattice. In addition, for probe transitions involving doubly degenerate excited states with perpendicular transition dipoles, as is the case here, the PA signals also reflect electronic reorientation. In such instances, the PA signal reports on electron motion around a CI^{23,24}, and its decay yields the dephasing time between the E_{x} and E_{y} states^{25}. Since the measurements are performed on an ensemble of differently oriented NV^{−} centres, linearly polarized photoexcitation does not selectively populate only one component of the orbital doublet, but instead, prepares a coherent superposition of the E_{x} and E_{y} states. As such, both population transfer and loss of phase coherence between the orbital doublet states—collectively referred to as orbital dephasing herein—lead to electronic dealignment and, hence, the decay of the PA^{23,25}. The observation of dephasing dynamics in the timedomain complements frequencydomain measurements, particularly when dephasing is fast and spans multiple timescales, which make the broad linewidths associated with ultrafast depolarization challenging to discern in the frequency domain.
The PA spectrum S_{aniso}(λ,t) collected as a function of pump–probe time delay at 77 K is shown in Fig. 2a. The anisotropy value obtained on the blue side of the ZPL transition, where groundstate bleaching dominates, is found to be constant to within experimental error (S_{aniso}∼0.1). On the other hand, a pronounced decay (Fig. 2b) is observed for the PA recorded at the ZPL (whitedashed line) and to its red side, where stimulated emission occurs. Anisotropy dynamics only appearing through stimulated emission indicates that they originate from the ^{3}E excited state. The PA decay at the ZPL can be fit to the function , where the offset A_{0}, amplitudes A_{1} and A_{2}, and exponential decay constants τ_{1} and τ_{2} are all fit parameters. The time constants of both the fast (τ_{1}) and slow (τ_{2}) decay components exhibit distinct temperature dependencies (Fig. 2c). Furthermore, τ_{2} is evident only below 150 K. τ_{1} is constant to within experimental error, varying between 0.15±0.03 and 0.10±0.02 ps for all measured temperatures. On the other hand, τ_{2} decreases markedly from 14.4±1.7 ps at 10 K to 0.70±0.11 ps at 150 K. It is noteworthy that S_{aniso} does not completely decay to 0.10 within the maximum time delay of 20 ps employed in our measurements. This asymptotic value of 0.10 for S_{aniso} would be expected for an electronic system that comprises a nondegenerate ground state and a doubly degenerate excited state with orthogonal transition dipoles, as is the case here^{23,25}. We note that S_{aniso} does not vanish to zero, as it would for molecules in solution by rotational diffusion^{22} because the defects are fixed in the diamond lattice. We believe that the deviation of the final S_{aniso} value from the theoretical isotropic value of 0.10 is indicative of longlived orbital coherence surviving beyond 20 ps, consistent with nanosecond dephasing dynamics that have been observed at cryogenic temperatures via singledefect lineshape measurements^{17} and timedomain Ramsey fringe interferometry^{18}. The subpicosecond to picosecond dynamics observed herein precede the previously reported dephasing timescales.
Subpicosecond τ_{1} electronic depolarization dynamics
NA AIMD simulations are performed to elucidate the origin of the observed subpicosecond depolarization dynamics. The computed decay profiles reveal depolarization via population transfer from the initially populated E_{x} state to the E_{y} state (Fig. 2d). The ∼100fs timescale for electronic equilibration (Fig. 2e) is in agreement with the experimental τ_{1} values. The inverse relation between the computed τ_{1} and the electron–phonon coupling strength (Fig. 2e) indicates that the fast component of the electronic depolarization dynamics is driven by NA transitions. The relatively weak temperature dependence is partly due to the stiff and extended diamond structure, and is qualitatively different from the strong temperature dependence that appears, for example, in semiconductor quantum dots, which have finite nanoscale size and thus a large surfacetovolume ratio^{26}. Fourier transforms of the realtime fluctuations of the E_{x} and E_{y} energies yield the frequencies of the phonon modes that mediate the electronic equilibration (Fig. 2f). Within the theoretical framework of AIMD, these phononinduced fluctuations arise from incoherent vibrational motions of the thermal bath (see Supplementary Figs 1 and 2), unlike coherent phonons launched by impulsive excitation, which manifest themselves as oscillatory features in the ΔT/T signals. The fast fourier transform (FFT) power spectrum obtained at 77 K reveals several prominent peaks at 47, 69, 90, 120, 130 and 150–160 meV. These modes have been identified and assigned by earlier ab initio calculations to the various quasilocalized vibrational modes of the NV^{−} defect^{27}, including one at 69 meV that coincides with the energy of the JTactive e mode^{13}. Interestingly, the presence of multiple phonon frequencies in the FFT power spectrum suggests that the depolarization dynamics are driven not only by the JTactive modes, but also by a collection of other vibrational modes that are anharmonically coupled to the JTactive modes.
Picosecond τ_{2} electronic depolarization dynamics
The conspicuous temperature dependence of τ_{2} suggests phononmediated electronic depolarization as its origin. The vanishing NV^{−} defect phonon density of states^{13,27,28} at phonon energies <20 meV prevents onephonon transitions from effecting population transfer between the E_{x} and E_{y} states^{29}. Nevertheless, onephononmediated electronic depolarization is still possible via phononinduced fluctuations of the orbital doublet, or even transitions from the lowestenergy E_{x} and E_{y} vibronic levels of the ^{3}E electronically excited state to higherlying, nondegenerate vibronic levels of A_{1} and/or A_{2} symmetry, for which electronic alignment does not exist. In either case, the onephonon transition rate Γ(T)=1/τ_{2}(T) follows the relation^{30}
where Γ_{0} is the temperatureindependent offset, σ (Γ_{c}) characterizes the electron–phonon coupling strength for phonon energies ℏω<<k_{B}T (ℏω≳k_{B}T) and ω_{c} represents the effective frequency of a group of phonons with energies ℏω≳k_{B}T that induces depolarization. Fitting the experimental data to equation (1) gives Γ_{0}=0.070±0.013 ps^{−1}, σ∼0 (to within experimental uncertainty), Γ_{c}=9.9±3.4 ps^{−1} and ℏω_{c}=26±3 meV (Fig. 2c). The vanishing σ coefficient is consistent with the paucity of lowenergy phonons with ℏω<<k_{B}T in the phonon density of states. Interestingly, ω_{c} closely approaches the calculated E—A_{1} tunnelling splitting^{13} of 35 meV, suggesting possible electronic depolarization via the phonondriven population transfer from the E_{x} and E_{y} vibronic levels to the totally symmetric A_{1} vibronic level within the ^{3}E electronically excited state. Excitedstate AIMD simulations based on a microcanonical trajectory generated at 10 K furnish a dephasing time of 8 ps, in good agreement with the experimentally measured value of 14.4±1.7 ps (see Supplementary Fig. 3). The correlated phononinduced fluctuations of the E_{x} and E_{y} states support the long dephasing time. We note, however, that the experimental uncertainty in the measured τ_{2} values does not allow depolarization via onephonon transitions to be distinguished from twophonon Ramantype population transfer^{17} between the E_{x} and E_{y} states (see Supplementary Fig. 4). The latter, whose rate scales as T^{5}, has been invoked to explain the temperaturedependent population transfer and electronic dephasing rates obtained from measurements of singledefect linewidths^{17,31}, decoherence of Rabi oscillations^{29} and ensemble photonecho spectroscopy^{32}.
Discussion
Previous frequency and timedomain measurements were performed on highpurity Type 2a diamond samples, which have defect densities that are in the partsperbillion (p.p.b.) regime, and thus orders of magnitude lower than the Type 1b sample (∼100 p.p.m.) used in the present study. Therefore, a natural question that arises is the extent to which the observed ultrafast dynamics are intrinsic to a single defect. Fluctuations of the charge bath and defect–defect interactions could presumably lead to the enhanced dephasing rates observed herein. First, we note that previous singledefect measurements on samples with similarly high defect densities^{33,34} yield microsecond timescales for spectral diffusion, orders of magnitude longer than the picosecond and subpicosecond dynamics observed here. Second, considering the quasilocalized nature of the vibrational modes^{27}, the modification of the phonon density of states of a given NV^{−} centre by an adjacent defect is expected to be negligible. Finally, and most importantly, we point out that the AIMD simulations were performed on a 215atom supercell, which corresponds to an effective defect density of 4,650 p.p.m., >40 × larger than the actual ∼100 p.p.m. defect density of the sample used in the measurements. The fact that the observed dephasing timescales are reproduced by the AIMD simulations strongly suggests that the ultrafast dephasing dynamics are intrinsic to the isolated NV^{−} centre. This claim can be verified by future measurements on defects with varying NV^{−} densities.
Our combined experimental–theoretical investigation affords the following unified picture of the ultrafast electronic depolarization dynamics following ZPL photoexcitation of the ^{3}E excited state. Photoexcitation by a linearly polarized laser pulse at the ZPL creates a NV^{−} defect that is electronically aligned in the excited state along the polarization axis of the laser field, leading to a coherent superposition of the E_{x} and E_{y} states (Fig. 3a). Because of the energetic proximity of the vibronic levels to the JT CI, where the electron–phonon coupling strength is maximal, the nonvanishing phonon velocities of the heat bath promote efficient NA transitions between the E_{x} and E_{y} states, leading to rapid electronic depolarization on the τ_{1}∼0.1ps timescale (Fig. 3b). On longer timescales spanning τ_{2}∼1−10 ps, orbital dephasing is promoted by electron–phonon scattering involving phononinduced fluctuations, transitions to totally symmetric, higherenergy vibronic levels and/or twophonon population transfer between the E_{x} and E_{y} states (Fig. 3c).
The subpicosecond to picosecond electronic depolarization dynamics unravelled here provide an explanation for the hitherto unaccounted loss of polarization fidelity of the NV^{−} defect PL at cryogenic temperatures^{17,19}, that is, the fact that orbital averaging occurs even at such low temperatures. This ultrafast biphasic dephasing could have eluded previous frequencydomain measurements since, insofar as multiple disparate dephasing timescales are involved, it is conceivably challenging to identify in a lineshape analysis the broad pedestal that is associated with subpicosecond dephasing. Note that timedomain photon echo measurements have elucidated similar biphasic dephasing dynamics spanning two to three orders of magnitude for excitons in selfassembled^{35} and colloidal^{36} quantum dots. In the case of the NV^{−} centre, our results, together with earlier frequency^{17,19} and timedomain studies^{18,32}, demonstrate that electronic dephasing at a given cryogenic temperature spans an unprecedented five decades in time, from 10^{−13} to 10^{−8} s.
Methods
Sample
The investigated NV^{−} sample is a highpressure hightemperaturegrown Type 1b diamond (Element Six) measuring 4 × 4 × 0.3 mm^{3}. NV^{−} defects are introduced by irradiation with 1MeV electrons at a flux of 10^{18} cm^{−2} and subsequent annealing in vacuum for 2 h at a temperature of 800 °C. The resulting NV^{−} density is ∼10 p.p.m., whereas the density of remaining N_{s} defects is 100 p.p.m. The pure diamond used for artefact subtraction is a CVDgrown type IIa diamond of similar size (Element Six).
Ultrafast polarizationresolved optical spectroscopy
Femtosecond PA measurements were performed on two ultrafast transient absorption setups: a broadband setup that furnishes probe pulses spanning 550–750 nm and wavelengthtunable narrowband pump–pulses (10nm bandwidth), and a twocolour setup that uses tunable narrowband pulses (10nm bandwidth) for both the pump and probe. The narrow pumppulse bandwidth of both setups allows the selective excitation of the ZPL transition at 637 nm, after which the linearly polarized probe pulse measures the pumpinduced change of the normalized transmission spectrum ΔT/T. The time resolution is 80 fs (Supplementary Fig. 5). Signals for parallel (S^{}) and perpendicular (S^{⊥}) relative polarization between pump and probe pulses are recorded. The PA signal S_{aniso}(λ,t) is then obtained from the relation S_{aniso}(λ,t)=(S^{}−S^{⊥})/(S^{}+2S^{⊥}). The typical pump fluence is ∼1 mJ cm^{−2}, which yields a ΔT/T signal of 0.036 at the ZPL transition wavelength (Fig. 1c). Such a small ΔT/T value confirms that our measurements are performed in the weakperturbative limit and higherorder contributions to the signal are negligible. The sample was mounted in either a liquidnitrogencooled cryostat (broadband setup, 77–400 K) or a closedcycle heliumcooled cryostat (twocolour setup, 10–300 K). Further details on the experimental setup, as well as data processing and analysis procedures, can be found in the Supplementary Methods and Supplementary Figs 4–8.
AIMD simulations
We performed realtime atomistic simulations for anisotropy decay of an initially created dipole moment in the NV^{−} defect. The electronic structures of both ground and excited states as well as their statespecific MD simulations were obtained with the VASP software package using the PerdewBurkeErnzerhof (PBE) density functional and projectoraugmentedwave pseudopotentials. The geometry of the NV^{−} defect comprises 1 nitrogen atom and 214 carbon atoms with an additional single electron to achieve the negatively charged NV^{−} centre. The NV^{−} defect was heated up to various temperatures ranging from 10 to 300 K by repeated velocity rescaling, and a 5ps microcanonical trajectory at each temperature was calculated on the ground and excited E_{x} states using the Verlet algorithm with a 1fs time step. In the excited state, we forced a spindown electron to be located at the orbital and removed symmetry constraints of the geometry. Realtime simulations for the PA decay were performed with the timedependent NA electron–phonon coupling and orbital energies updated at every time step. Further details on the simulations can be found in the Supplementary Methods and Supplementary Figs 1–3,9 and 10.
Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.
Additional information
How to cite this article: Ulbricht, R. et al. JahnTellerinduced femtosecond electronic depolarization dynamics of the nitrogenvacancy defect in diamond. Nat. Commun. 7, 13510 doi: 10.1038/ncomms13510 (2016).
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Acknowledgements
This work is supported by a startup grant from NTU, funding from the A*Star Science and Engineering Research Council (122PSF0011 and 122 360 0008) and the Ministry of Education (MOE2014T22052), and the award of a Nanyang Assistant Professorship to Z.H.L. K.H.D. thanks the financial support from JST (PRESTO) and GrantinAids for Scientific Research from Japan Society for the Promotion of Science (KAKENHI), Grant No 15K05386. R.U. acknowledges support by a Rubicon Grant of the Netherlands Organization for Scientific Research (NWO). We are grateful to D.M. Jonas, O.V. Prezhdo, H. Köppel, A. Gali, W. Peters and M. Cho for useful discussions, to R.U.A. Khan, Z. Wang and C. Soci for experimental assistance and to J. Schwartz for providing the sample.
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R.U. and Z.H.L. conceived and designed the project. R.U., S.D. and B.M.K.M. performed the experiments. R.U. and Z.H.L. analysed the data. I.Y.C. and K.H.D. performed the simulations. R.U., K.H.D. and Z.H.L. wrote the manuscript, with input from all authors.
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Supplementary Figures 110, Supplementary Methods and Supplementary References (PDF 819 kb)
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Ulbricht, R., Dong, S., Chang, IY. et al. JahnTellerinduced femtosecond electronic depolarization dynamics of the nitrogenvacancy defect in diamond. Nat Commun 7, 13510 (2016). https://doi.org/10.1038/ncomms13510
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DOI: https://doi.org/10.1038/ncomms13510
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