ARTICLESPUBLISHED ONLINE: 29 SEPTEMBER 2013 | DOI: 10.1038/NPHYS2753

Vibrational and electronic dynamics ofnitrogen–vacancy centres in diamond revealed bytwo-dimensional ultrafast spectroscopyV. M. Huxter1†, T. A. A. Oliver1, D. Budker2 and G. R. Fleming1*The optical and material properties of negatively charged nitrogen–vacancy (NV) centres in diamond make them attractive forapplications ranging from quantum information to electromagnetic sensing. These properties are strongly dependent on thevibrational manifold associated with the centre, which determines phenomena associated with decoherence, relaxation andspin–orbit coupling. Despite its paramount importance in tuning these properties, the role of the vibrational bath and its effecton the electronic-state dynamics of NV centres in diamond is not fully understood. To elucidate the role of the bath, we presenttwo-dimensional electronic spectroscopic studies of ensembles of negatively charged NV defect centres in diamond (NVD). Weobserve picosecond non-radiative relaxation within the phonon sideband and find that strongly coupled local modes dominatethe vibrational bath. These findings provide a starting point for new insights into dephasing, spin addressing and relaxation inNVD with broad implications for magnetometry, quantum information, nanophotonics, sensing and ultrafast spectroscopy.

Diamond can stably accommodate a variety of defects, each ofwhich has its own characteristic properties. One particulardefect, called the NV centre, consists of a nitrogen substitu-tion with a nearest-neighbour-vacancy point defect in the carbonlattice. When negatively charged, the NV centre has a unique com-bination of spin and optical properties, accommodating remarkablespin coherences of up to one second at room temperature1. As aquantum solid-state system, NV centres are particularly promisingowing to their optically and magnetically addressable spin coher-ences, fast spin manipulation2, and coupling to adjacent electronicand nuclear spins3. These systems have wide ranging applicationsincluding solid-state qubits1,3,4, ultrasensitive magnetometers5,6,single-photon emitters7 and ultraresolution imaging8.

In a diamond system containing negatively charged NV centres,the spin states can be initialized and read out by accessing an opticaltransition between triplet states due to an intersystem-crossingpathway. Whereas the nanosecond decay of the electronic statehas been investigated in earlier work9–11, ultrafast picosecond andfemtosecond dynamics associatedwith coherent vibrationalmotionand internal conversion pathways remain entirely unexamined.In addition to the electronic levels, NVD systems have significantphonon sidebands. The vibrational modes in these sidebands arestrongly coupled to the NV centre12–14, influencing the decoherenceof the spin state and dephasing in the excited state9, the flowof energy through the system, and the optical transitions15.Understanding the dynamics of the vibrational bath is critical tounderstanding the optical dephasing of the system and thus toapplications involving optically driven quantum effects. Beyondapplications related to the quantum mechanical properties, theinteraction between electronic states and vibrational modes in theNVD system provides us with critical information on its funda-mental properties with implications for its use in nanophotonics,sensing, magnetometry and NMR.

1Department of Chemistry, University of California, Berkeley and Physical Bioscience Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, USA, 2Department of Physics, University of California, Berkeley and Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley,California 94720, USA. †Present address: Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA.*e-mail: grfleming@lbl.gov

To elucidate the relaxation pathways of this solid-state quantumsystem, we present ultrafast optical measurements on NVD. Usingtwo-dimensional electronic spectroscopy16–18 (2DES), the dynamicsof both the electronic and vibrational relaxation pathways in NVDare measured on femtosecond timescales. This time resolutionallows us to observe coherent vibrational dynamics and relaxationthrough the phonon sideband in real time. 2DES allows us to createan energy-dynamic map of the system, tracing out the vibrationaland electronic relaxation pathways through coherences and popu-lations of vibrational and electronic states. 2DES is a powerful spec-troscopic technique that provides a means of correlating the initialabsorption interaction with the final emission. Using the 2DES ex-periment, we find that the spectrum of the NV centre is dominatedby individual local vibrational modes. By constructing a discretespectral density using the experimentally determined frequencieswe model the linear and nonlinear optical signals and demonstratethe importance of the localmodes in the vibrational bath.

A simplified schematic of the NVD energy-level structure isshown in Fig. 1a. The 3A and 3E states are split into ms =±1 andms = 0 spin sublevels. Although the spin states are not directlyobservable in the electronic optical measurements, they are affectedby the electronic and vibrational transitions that are the subject ofthe present work. Singlet states, with an energy gap correspondingto the near infrared11,19, are not optically excited or probed inthe present measurement. The absorption spectrum of the NVDsample used in the experiment is shown in Fig. 1b. The zero-phonon line (ZPL), which in a linear measurement corresponds totransitions between the ground and excited state occurring withoutthe assistance of a vibration, is at 15,700 cm−1 (638 nm) and persistsat room temperature in NVD. The broad feature to the high-energyside of the ZPL is the phonon sideband that spans more than300meV at room temperature. In the linear absorption spectrumsome vibronic structure, associated with vibrational states that are

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ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS2753

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Figure 1 | Properties of the negatively charged NVD. a, The level structure of the negatively charged NVD including the vibrationally broadened spin triplet3E excited state and the 3A ground state. The lowest energy, zero-phonon transition between the ground and the excited state produces a ZPL in theabsorption spectrum that persists to room temperature. b, Room-temperature absorption spectrum of the NVD sample and the laser spectrum centred at16,000 cm−1 (625 nm) used in 2DES data collection. c, Second derivative of the absorption spectrum, emphasizing the vibronic structure of the phononsideband. d, An absolute-value 2DES plot of NVD with a waiting time (t2) of 5 ps. The intensity scale is in arbitrary units. The 2DES signal is plotted withrespect to the detection axis, ω3, and the absorption axis, ω1. e, The sequence of three pulses used to generate the third-order heterodyne nonlinear signal.f, A slice through the 2DES plot in d along ω1 at ω3= 15,700 cm−1 or the energy of the ZPL transition. The dotted, dashed and solid lines in b–d,f indicatethe ZPL, and the first and the second vibronic peaks, respectively, as observed in the linear absorption.

strongly coupled to the electronic transition, is apparent in thephonon sideband. This structure is clearly highlighted in the secondderivative of the absorption spectrum shown in Fig. 1c.

As a chromophore, the NV defect can be described as a stronglyvibrationally broadened two-level system. The only electronictransition is from the ground to the triplet excited state. The broadline shape observed in the linear absorption arises solely from thephonon sideband associated with this transition. The vibrationalstructure in the phonon sideband, seen in the linear absorptionand emphasized in its second derivative (Fig. 1b,c), is evident inthe 2DES data shown in Fig. 1d. The vibrational contributionsto the signal appear in the 2DES experiment because it followsexcitation dynamics. The 2DES signal is generated by the nonlinearinteraction of three ultrafast pulses with the NVD sample. At eachwaiting time, t2, the data are collected as a function of the timedelay between the first two interactions, t1, which are labelled asshown in Fig. 1e. The first pulse generates a coherence betweenthe ground and excited state that evolves during the time t1.The second pulse puts the system in an excited or ground-statepopulation that evolves for the duration of the time delay t2. Ateach waiting time, the data are Fourier transformed with respectto t1, producing the conjugate variable ω1, and plotted relative tothe frequency-dispersed emission axis, ω3, correlating the initialabsorption event with the emission. This correlation allows us tofollow the evolving system through vibrational and electronic states.The 2DES plot in Fig. 1d was collected for a time delay, t2 of5 ps. At this t2 delay, the directly observable coherent evolution ofvibrational modes has been damped out but relaxation throughvibrational pathways is still apparent. These components can beseen by taking a slice at fixed ω3 through the 2DES plot at theenergy of the ZPL transition (15,700 cm−1). This slice, presented inFig. 1f, frequency resolves the contributions to the emission at theZPL energy, showing three peaks. The peak at ω1 = 15,700 cm−1 isattributed to stimulated emission at the same energy as the initialabsorption. The other two peaks correspond to signal contributionsthat absorb at energies of ω1 = 16,180 and 16,780 cm−1 and emitat the energy of the ZPL. These two peaks are associated withthe first and second vibronic transitions observed in the linearabsorption, indicating that relaxation from the phonon sidebandand emission at the ZPL transition energy involves participation ofvibrational components.

The 2DES experiment correlates the initial absorptive inter-action with the signal emission, creating a map of absorption

and emission events. Diagonal features arise when the energiesof absorption and emission are the same; off-diagonal features(cross peaks) originate when they are different. In an absolutevalue spectrum, the features above the diagonal can arise from anexcited-state absorption contribution (requiring the participationof a third electronic state) or from the action of a vibrational modeexcited at different points along its wavepacket trajectory20,21. Thepeaks below the diagonal are primarily associatedwith energy trans-fer and redistribution among the nuclear degrees of freedom. InNVD, the defect centres (chromophores) are electronically isolatedfrom each other. In this system, the off-diagonal contributions donot originate from inter-chromophore energy transfer but fromvibrational contributions. In Fig. 1d and the corresponding slicein Fig. 1f, the peaks below the diagonal along the ZPL transitionenergy for fixed ω3 arise from energy moving from the phononsideband to the lowest-energy excited state through the stronglycoupled electronic–vibrational transitions.

The ability to resolve the individual vibrational contributions tothe emission at the energy of the ZPL is one of the main advantagesof two-dimensional spectroscopy. The 2DES experiment allows usto separate out the origins of the zero-phonon emission, revealingthe diagonal contribution along with cross peaks associated withthe vibronic modes. Spectral resolution of the signal contributionsdoes not necessarily mean that, in a nonlinear experiment suchas 2DES, all of the signal that appears at the energy of the ZPL isstrictly associated with a zero-phonon transition. Instead, the 2DESplot reports nonlinear absorption and emission energies and anysignal with the same emission energy gap as the ZPL will appearat that energy. By correlating the initial absorption and emissionevents we can isolate different contributions to the signal, providingsignificant advantages as comparedwith other experiments.

Figure 1d demonstrates that the primary relaxation channelfor a waiting time of t2 = 5 ps is through vibronic channels tothe energy associated with the ZPL. At shorter waiting times,the energy is redistributed amongst multiple strongly coupledvibrational modes that beat, modifying the frequency dependenceof the observed 2DES signal. This dynamic vibrational responseis shown in a series of absolute-value 2DES surfaces at differentwaiting times in Fig. 2. At waiting times of less than 2 ps (Fig. 2a–c),the amplitude of the spectrum above and below the diagonaloscillates in response to the action of the vibrational modes stronglycoupled to the NV defect. These amplitude oscillations define aregime of vibrational coherence in the system. After approximately

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Figure 2 | 2DES measurement of NV defect centres. a–e, Representative absolute-value total 2DES surfaces of NVD at different waiting times, t2,indicated in white. The intensity scale is in arbitrary units that are self-consistent within a set of experiments. At short waiting times (t2 < 2 ps), the actionof the vibrational modes is evident in the oscillating amplitudes across absorption and emission axes as the energy is redistributed amongst the vibrationaldegrees of freedom. After approximately 2 ps, the coherent vibrational dynamics driving the amplitude oscillations have relaxed and the 2DES signalassumes an asymptotic form dominated by the excited-state population decay. The black rectangles in a–e highlight the position of a vibronic cross peak,whose intensity oscillates with respect to the waiting time. f, The short-waiting-time oscillatory behaviour of the outlined region obtained from the 2DESsurfaces. The bottom part presents the signal obtained by integrating the outlined region over the ω1 axis and plotting it relative to the ω3 emission axis,and the top part shows the total integrated intensity of the same region.

2 ps, the oscillatory motion is mostly damped leaving clear peaksassociated with vibronic levels.

Many vibrational contributions appear in the 2DES data andcan be seen by looking at different regions of the 2DES plot. Theappearance of these modes is further complicated because theyappear on top of a nanosecond decay associated with the excited-state lifetime. To clearly show the oscillatory behaviour observedin the 2DES surfaces, we have selected a subregion associatedwith the first vibronic cross peak, labelled in Fig. 2a–e using ablack rectangle. The short-waiting-time oscillatory behaviour of thisregion is presented in Fig. 2f. The bottom part of Fig. 2f presentsthe specified region integrated over the ω1 axis and plotted withrespect to the ω3 emission axis, and the top part plots the intensityof the total integrated region defined by the black rectangle. Fig. 2fshows that there are strong, complex oscillations associated withvibrational modes in just this small subregion of the 2DES surface.By integrating over other regions or whole axes, it is possible toobtain the vibrational spectrum of the NVD system.

As shown in Fig. 2, the overall 2DES signal intensity decays on atimescale of picoseconds associated with non-radiative relaxationin the phonon sideband and nanoseconds associated with theexcited-state lifetime. At waiting times longer than 2 ps, the 2DESsignal has a square shape with a distinct band at the ZPL transitionenergy on the emission axis. The square shape of the signal arisesfrom the contributions of the vibronic levels. The laser spectrumused to excite the NVD sample (shown in Fig. 1b) is peaked at16,000 cm−1, which means that most of the excitation is intothe phonon sideband.

The timescales associated with population dynamics (diagonalcomponents of the density matrix) were recovered from the 2DESdata by integrating over the two-dimensional (2D) surfaces ateach waiting time, t2. Plotting the 2DES integrated intensity versuswaiting time produces a transient grating signal (analogous topump–probe spectroscopy). These data were then fitted to anexponential decay with a picosecond and nanosecond component,

where the latter is associated with excited-state relaxation. Thepicosecond decay associated with non-radiative relaxation orinternal conversion within the phonon sideband was foundto be 4.2 ± 0.9 ps on the basis of an average of five repeatmeasurements. This timescale is slower than expected given thedensity of the vibrational states22, which suggests that individualstrongly coupled vibrational modes dominate the relaxationprocess resulting in a reduced apparent density of states. Furtherdetails regarding recovery of the transient grating signal and themeasurement of the internal conversion timescale are available inthe Supplementary Information.

As Fig. 2 reveals, the vibrational dynamics in NVD are complex,involving a significant number of individual and overlappingvibrational modes. To resolve the vibrational modes coupled to theNV defect, we isolate the region of the 2DES spectrum associatedwith emission at the energy of the ZPL. A significant portion ofthe energy absorbed by the NV centre relaxes through vibrationalchannels to the ZPL energy, providing a sub-region of the spectrumthat can be analysed to clearly isolate the vibrational modeseven at long waiting times. This includes energy absorbed intothe phonon sideband that relaxes to the lowest-energy excitedstate before emission. The strong vibrational coupling to the ZPLtransition and the fast non-radiative rate associated with internalconversion is essential to the potential applications of the NVDsystem, especially those that rely on near-monochromatic emissionor optical addressing of states, because these processes rely onrelaxation to the band edge and subsequent emission or relaxationthrough an intersystem crossingmechanism.

The specific frequencies and dynamics of the vibrational modesassociated with emission at the energy of the ZPL are shown inFig. 3. The black rectangle in Fig. 3a indicates the subregion ofthe plot associated with emission (along the ω3 axis) at the ZPLenergy. By integrating over the emission axis of the subregion,we obtain a single trace for each waiting time consisting of thefeatures emitting at the ZPL energy dispersed along the axis of

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Figure 3 |Vibrational modes associated with emission at the ZPL transition energy. a, The 2DES signal at t2= 2 ps with a black rectangle indicating theZPL emission region. By integrating over the ω3 axis for the ZPL emission region, vibrational dynamics associated with emission at the energy of the ZPLtransition can be isolated from the 2D signal. b,c, Representative plots of the integrated regions as a function of the waiting time, t2. b, The oscillations inthe ZPL region to 100 ps with low-frequency oscillations out to tens of picoseconds. c, The short time t2 region of the same data presented in b exhibitingrich oscillations. The black lines indicate the diagonal peak (dotted line), first (dashed line) and second (solid line) vibronic cross peaks emitting at the ZPLtransition frequency. Note that the pattern of black lines is the same as used in Fig. 1. d, The fast Fourier transform (FFT) of the data in c integrated over theω1 axis.

the initial absorptive event, ω1. This procedure effectively isolatesand projects the contributions of the signal emitting at the ZPLenergy onto the ω1 axis. As shown in Fig. 3b, these traces forindividual waiting times are stacked together to create a plot thatshows the evolution of the different spectral components to theemission relative to the entire range of waiting times out to 100 ps.The signal along the waiting time axis provides information onthe population dynamics. Contributions associatedwith coherencesare recovered because the signal is dispersed along the ω1 axisand thus includes off-diagonal parts of the spectrum. In Fig. 3bclear oscillations associated with low-frequency modes, most likelyarising from acoustic phonons in the diamond lattice, are apparenteven out to tens of picoseconds. The shorter waiting time dynamics,shown in Fig. 3c, reveal a rich pattern of higher-frequency coherentvibrations associated with the NV defect.

To resolve the vibrational components, the signal in Fig. 3b wasFourier transformed, producing the plot in Fig. 3d. The Fouriertransform revealed a number of distinct vibrational components atfrequencies in the range of 200–1,800 cm−1. Other higher-frequencymodes are probably present in the system; however, they are outsidethe bandwidth of the laser pulse. A number of vibrations were alsopresent at lower frequency, forming a structured continuum ofclosely spaced modes. These lower-frequency modes are associatedwith the acoustic modes of the diamond lattice. The higher-frequency modes are strongly coupled to the defect and have asignificant influence on its optical properties.

The frequencies obtained from the average of five independent2DES experiments are listed in Table 1 along with comparisonsto literature values determined theoretically and experimentally.The calculated values were obtained using different theoreticalmethodologies to determine the predicted frequencies of modeslocal to the NV centre. Although this comparison is not meantto be definitive, most of the experimentally observed modesmatch closely with calculated local modes. The frequenciesobtained by previous, mostly luminescence, experiments havealso been associated with local mode dynamics. Local modes areassociated with deformations in the lattice within a few unitcells of the defect. The presence of the NV defect leads to amodification of the elastic moduli similar to that experienced bythe dangling bonds in semiconductor nanocrystals23. These localmodes dominate the bath comprising amajor part of the dissipativeresponse of the system.

Table 1 |Discrete frequency components obtained from the2DES measurements and comparison to literature values.

ωmeasured (cm−1)* ωliterature (cm−1) ωtheory (cm−1)

182± 21 – –259± 19 – 255 (ref. 15)337± 31 355 (ref. 13) 336 (ref. 15)457± 18 490 (ref. 13) 481.5, 476, 477 (ref. 34)558± 16 560† (ref. 35) 574, 582, 577 (ref. 15)644± 21 677 (ref. 13) 621, 620 (ref. 34)736± 18 – 734 (ref. 24)1,028± 22 1,040 (ref. 36) 1,030 (ref. 24)1,166± 22 1,130 (ref. 13,36) 1,182 (ref. 24)1,339± 31 1,332‡ (refs 26,36) –

or 1344 (refs 13,36)1,525± 26 1,510§ (ref. 26) 1,555 (ref. 24)

*The error estimates are based on five independent repeat measurements. †Axial mode. ‡Ramanmode. §There are a number of vibrations in this region associated with NV defects or Ramanmodes.

As is evident in Table 1, there is excellent agreement betweenvibrational modes measured in the present experiment and those inthe literature either determined theoretically or experimentally. Insome cases, there are multiple closely spaced modes that could beassociated with the frequencies observed in the 2DES experiment.It is possible that all of those modes are present but are notunambiguously resolvable. The previously observed experimentalvibrational frequencies listed in Table 1 were obtained entirelyfrom steady-state experiments, whereas the values obtained fromthe 2DES experiments were measured as they evolved in realtime. This allowed direct observation of vibrational coherencesand the dynamics of vibrational relaxation pathways, impossible toretrieve from previous experimental work. In addition, observationof vibrational modes in the 2DES experiment requires that thevibration be strongly coupled to the electronic transition, providinga direct link between the optically excited NV defect and theobserved frequencies.

On the basis of the tentative assignment to theoretical valueslisted in Table 1, the experimentally observed modes are acombination of ground- and excited-state, a and e symmetry types.

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The peaks at 457, 558 and 1,028 cm−1 correspond to the vibronicstructure in the linear absorption. The only mode without anassignment is the lowest frequency vibration at 182 cm−1. Thetwo highest frequency modes listed, 1,339 and 1,525 cm−1, areprobably associatedwith delocalized diamond lattice dynamics. The1,525 cm−1 mode is an e symmetry mode24 or an sp2 phase Ramanemission25. The contribution at 1,339 cm−1 is most likely a Ramanmode from the bulk diamond matrix26 although a local mode at1,344 cm−1 has been experimentally observed.

From the 2DES data, we have measured a series of vibrationalmodes that are strongly coupled to the NV centre. To understandthe involvement of the individual vibrational modes in themeasured spectra, we used the experimental vibrational frequenciesto model the 2DES signal. We calculate the linear and third-ordernonlinear optical response of the NVD by modelling it as avibrationally broadened two-level system. Following a responsefunction formalism based on the work of refs 27,28, the vibrationalmodes were explicitly included in the spectral density, which can bewritten as a sum of individual contributions29. The spectral densityof the system was constructed using a Drude–Lorentz form for thequasi-continua of low-frequency modes (sub 100 cm−1). A form ofthe multimode Brownian oscillator model adapted to the case ofone oscillator30,31 was used to include the individual frequenciesobtained from the 2DES experiment. (Further details are given inthe Supplementary Information.)

Simulated 2DES and linear absorption spectra are presented inFig. 4a,b, respectively. The corresponding experimental data areshown in Fig. 4c,d. The simulation closely agrees with the experi-mental results with some deviation at higher energy. This is becausethe input frequencies were cut off and an approximation of the ex-perimental laser pulse spectrum was used. Calculations performedfor shorter waiting times also reproduce the oscillating amplitudesacross the 2DES spectra shown in Fig. 2. In the simple two-levelelectronic system model, all of the broadening and structure comesfrom the experimentally obtained frequencies used as inputs in thespectral density. These strongly coupled local vibrational modesthat dominate the vibrational bath of the NVD system are sufficientto recover both the linear and the nonlinear optical response.

The vibrational modes coupled to the NV centre influence spin–orbit coupling, dephasing and relaxation and are critical for theapplication of NVD to quantum information and memory, single-photon sources, imaging and sensing. Using 2DES measurements,we have revealed the interaction between the optically excited NVdefect and the vibrational bath, showing that the response of thesystem is determined by strongly coupled local modes. Accessingthe dominant components of the vibrational bath will allow usto tune the properties of the system, providing new avenues forresearch. For example, by optically pumping the NV centres wecould specifically excite phonon modes based on their couplingfactors, allowing the development of an NVD material that can beused for quantum storage and information processing based onboth phonons and spin.

Methods2DES measurements were performed using an apparatus described in detailpreviously32 and are only briefly summarized here. The output from a home-builtTi:sapphire oscillator/regenerative amplifier was used to pump a non-collinearoptical parametric amplifier (NOPA), generating pulses in the visible wavelengthrange. The NOPA output was tuned for wavelength and bandwidth to excitethe sample at the energy of the ZPL and the first two strongly coupled vibronictransitions. The spectrally tuned NOPA pulses were used for the 2DES experiment,which was performed using a diffractive-optic-based design, where four passivelyphase-stabilized beams were focused into the sample using a box geometry.The signal radiated in the ks =−k1+ k2+ k3 phase-matching direction wasmixed with a weak local oscillator reference beam, spectrally dispersed usinga Princeton Instruments SP2300A spectrometer and heterodyne-detected ona PIXIS 100 camera.

The 2DES data at each waiting time, t2, were collected as a function the timedelay between the first two interactions, t1, which are labelled as shown in Fig. 1e.To obtain the 2DES data, the time delay t1 was scanned using matched glass wedgepairs that allow for attosecond time-step resolution without beam deviation33.The interferograms generated by the mixing of the signal and the local oscillatorwere collected for the scanned delay t1 and Fourier transformed to produce thefrequency-domain 2D spectrum for a single delay t2. Population dynamics wereobtained by repeatedly scanning t1 for different waiting times, t2. All of the 2DESplots shown here are absolute-value total signals. A total (or relaxation) 2DESsignal consists of both the rephasing and the non-rephasing components that areexperimentally separated by the relative time ordering of pulses one and two. Therephasing portion is a properly time-ordered signal where pulse one arrives beforepulse two and the non-rephasing is collected when pulse two arrives before pulse

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ARTICLES NATURE PHYSICS DOI: 10.1038/NPHYS2753

one. As pulses one and two have different k vectors, the signal produced in the−k1+k2+k3 signal direction corresponds to a photon echo for the rephasingand a free induction decay for the non-rephasing signal. The total signal is asum of both parts, producing a non-phase-twisted signal revealing the relaxationdynamics of the system.

The NVD sample was synthesized (by Element Six) using a high-pressure andhigh-temperature method with an approximately 50 ppm nitrogen concentration.The sample was irradiated with 3 MeV electrons with a dose of 2×1019 cm−2and annealed at 1,325K for two hours. This produced negatively charged NVcentres with an optical density at room temperature of 0.06 at the ZPL (638 nm,15,700 cm−1) with an optical path length of 20 µm, as shown in Fig. 1b. Theoptical density was determined from the linear absorption of the NVD samplemeasured using a Varian Cary 50 ultraviolet–visible spectrophotometer. The2DES experiments were performed using 60 nm or 1,600 cm−1 full-width athalf-maximum spectral bandwidth pulses with a central wavelength of 625 nmor 16,000 cm−1 and compressed to near-transform-limited sub-20 fs pulses at thesample position. The pulse was characterized using a frequency-resolved opticalgating technique on a fused-silica plate. The data were minimally processed andno interpolation or smoothing was applied to the 2D plots. 2DES measurementson a model dye system, oxazine 720 in methanol, were performed before andafter the experiments on the NVD sample to ensure experimental consistency.The t1 time delay was scanned over ±120 fs and 2DES surfaces were collectedfor t2 time delays from 0 to 310 fs in 10 fs steps, from 325 to 400 fs in 25 fs steps,from 400 to 1.5 ps in 100 fs steps, at 1.8 ps, from 2 to 5 ps in 500 fs steps, from5 to 10 ps in 1 ps steps, from 10 to 50 ps in 5 ps steps and from 50 to 100 ps in10 ps steps. Each t2 time was repeated a minimum of three times and the entireexperiment was independently repeated five times. All experiments were performedat room temperature.

Received 4 January 2013; accepted 13 August 2013;published online 29 September 2013

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AcknowledgementsThe authors thank A. Gali for initially suggesting ultrafast measurements withnitrogen–vacancy-diamond, A. Jarmola for preparing the nitrogen–vacancy-diamondsample, and N. Manson and P. Kehayias for helpful discussions. V.M.H. thanks theNational Science and Engineering Research Council of Canada for a postdoctoralfellowship. D.B. was supported by NSF and the AFOSR/DARPA QuASAR programme.Thework byV.M.H., T.A.A.O. andG.R.F. was supported byNSF grantCHE-1012168.

Author contributionsV.M.H., D.B. and G.R.F. conceived the experiment. D.B. and G.R.F. supervised theproject. V.M.H. determined the experimental protocol, wrote and performed thesimulation, analysed the data and wrote the manuscript. V.M.H. and T.A.A.O. collectedthe data. All authors discussed the results and implications and commented on themanuscript at all stages.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints. Correspondenceand requests for materials should be addressed to G.R.F.

Competing financial interestsThe authors declare no competing financial interests.

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Vibrational and electronic dynamics of nitrogen--vacancy centres in diamond revealed by two-dimensional ultrafast spectroscopyMethodsFigure 1 Properties of the negatively charged NVD.Figure 2 2DES measurement of NV defect centres.Figure 3 Vibrational modes associated with emission at the ZPL transition energy.Figure 4 Comparison between calculated and measured 2DES and linear absorption signals.Table 1 Discrete frequency components obtained from the 2DES measurements and comparison to literature values.ReferencesAcknowledgementsAuthor contributionsAdditional informationCompeting financial interests