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Room temperature coherent control of defect spin

LETTER

doi:10.1038/nature10562 Room temperature coherent control of defect spin qubits in silicon carbide

William F.Koehl1,Bob B.Buckley1,F.Joseph Heremans1,Greg Calusine1&David D.Awschalom1

Electronic spins in semiconductors have been used extensively to explore the limits of external control over quantum mechanical phenomena1.A long-standing goal of this research has been to identify or develop robust quantum systems that can be easily manipulated,for future use in advanced information and com-munication technologies2.Recently,a point defect in diamond known as the nitrogen–vacancy centre has attracted a great deal of interest because it possesses an atomic-scale electronic spin state that can be used as an individually addressable,solid-state quantum bit(qubit),even at room temperature3.These exceptional quantum properties have motivated efforts to identify similar defects in other semiconductors,as they may offer an expanded range of functionality not available to the diamond nitrogen–vacancy centre4.Notably,several defects in silicon carbide(SiC) have been suggested as good candidates for exploration,owing to a combination of computational predictions and magnetic res-onance data4–10.Here we demonstrate that several defect spin states in the4H polytype of SiC(4H-SiC)can be optically addressed and coherently controlled in the time domain at temperatures ranging http://www.sodocs.net/doc/03bad489e53a580216fcfeb5.htmling optical and microwave techniques similar to those used with diamond nitrogen–vacancy qubits,we study the spin-1ground state of each of four inequivalent forms of the neutral carbon–silicon divacancy,as well as a pair of defect spin states of unidentified origin.These defects are optically active near telecommunication wavelengths11,and are found in a host material for which there already exist industrial-scale crystal growth12and advanced microfabrication techniques13.In addition,they possess desirable spin coherence properties that are comparable to those of the diamond nitrogen–vacancy centre.This makes them promising candidates for various photonic,spintronic and quantum informa-tion applications that merge quantum degrees of freedom with classical electronic and optical technologies2,14–17.

SiC is a wide-bandgap,group IV semiconductor with well-established growth and device engineering protocols.Inch-scale,high-quality bulk and epitaxial single crystals of SiC are commercially available12,and a wide variety of advanced electronic13,18,19,optoelectronic13,20and electro-mechanical20devices have been successfully fabricated from SiC.Other notable features of SiC are the existence of many polytypes,each with a different bandgap18;a native oxide that allows for sophisticated comple-mentary metal-oxide-semiconductor circuitry18,19;and its common use as a growth substrate for other technologically relevant materials,such as gallium nitride and graphene21,22.Because of this versatility,the existence of SiC-based analogues to the diamond nitrogen–vacancy centre could lead to exciting developments in quantum engineering and the study of quantum phenomena in the solid state.

Here we are interested in defects that possess a tightly bound elec-tronic spin that can be polarized and measured through the absorption and luminescence of light.In all experiments,samples diced from a 2-inch wafer of high-purity semi-insulating(HPSI)4H-SiC are optic-ally excited with below-bandgap light from an853nm(1.45eV)diode laser.Photoluminescence spectra taken at sample temperatures ranging from20to300K are shown in Fig.1a.At20K,several sharp lines with energies ranging from1.09to1.20eV are apparent,along with a series of broader features found from0.9to1.20eV.At low temperatures, luminescence from a single species of optically active defect commonly consists of a sharp zero-phonon line(ZPL)and a broad sideband composed of lower-energy phonon replicas of the ZPL.If several dis-tinct species are probed simultaneously,the total photoluminescence signal will be the sum of its parts,so that the ZPL of one defect species may lie on top of the phonon sideband of another.This is what is observed in Fig.1a.An expanded view of the20K photoluminescence from1.09to1.20eV can be seen in Fig.1b,where six sharp lines have been given the labels PL1–PL6.Four of these,PL1–PL4,form a group of lines known in previous literature by the singular label,UD-2 (ref.23).The other two,PL5and PL6,are close to one another in energy and share several other features that are described in the Sup-plementary Information.This suggests that PL5and PL6are related, but their origins are currently unidentified.At higher temperatures,all six lines simultaneously broaden and decrease in height,so that they are almost completely indistinguishable from the phonon sidebands by 200K.However,luminescence through these phonon sidebands is still clearly visible,even at300K.

Previous results from photo-enhanced electron spin resonance and annealing experiments have indicated that the four UD-2lumin-escence lines(PL1–PL4)originate from four distinct forms of the neutral divacancy,which is an uncharged defect complex consisting of a carbon vacancy adjacent to a silicon vacancy24,25,[V Si–V C]0.Two forms of the divacancy,which are often given the labels(hh)and(kk), are oriented along the c axis of the crystal.The other two,(hk)and(kh), are oriented along the basal bond directions.These four defects give rise to the P6b/P69b(c-axis)and P7b/P79b(basal)spin-resonance signals that are often observed in electron spin resonance studies of 4H-SiC,and that have been shown to correspond to spin-1ground states that can be spin-polarized with incident light6,7,26.As discussed in the Supplementary Information,we use angle-resolved magneto-luminescence and continuous-wave optically detected magnetic res-onance techniques to confirm that each of the four UD-2luminescence lines corresponds to a different form of the neutral divacancy.These experiments also show that the photoluminescence intensity of each divacancy is modulated by the dynamics of its ground state spin.

An abridged version of these data can be seen in Fig.1c–h.In each panel,the normalized change in photoluminescence(D PL/PL)from one of the six lines,PL1–PL6,is seen as a function of applied micro-wave frequency at20K and zero magnetic field.The direction of the microwave driving field varied across the observed spin ensemble,so that spins oriented in any direction could be driven.Spin resonances are observed in all six lines.In Fig.1c we see a sharp decrease in PL1 luminescence resulting from microwave-induced transitions between sublevels of the(hh)c-axis divacancy ground state spin.The central frequency of this resonance corresponds to the axially symmetric spin splitting(D)of this defect spin state.In Fig.1d,there is a similarly shaped increase in PL2luminescence centred at a frequency corres-ponding to D for the other form of the c-axis divacancy,(kk).A pair of resonances is observed in both Fig.1e and f,which show D PL/PL for

1Center for Spintronics and Quantum Computation,University of California,Santa Barbara,California93106,USA. 84|N A T U R E|V O L479|3N O V E M B E R2011

PL3and PL4,respectively.Each figure corresponds to one of the two basal forms of the divacancy.Owing to the hexagonal crystal structure of 4H-SiC,these basal defects possess a lower symmetry than their c -axis counterparts.Their ground state spins therefore exhibit a trans-verse anisotropy spin splitting (E )in addition to D .This results in two zero-field resonances at frequencies defined by (D 6E ),as seen in the data 7.Figure 1g and h shows spin resonances observed in PL5and PL6,which are emitted by the basal and c -axis forms of the unidentified defects,respectively.

As shown in the Supplementary Information,the resonances in Fig.1c–h do not respond uniformly to elevated temperatures.The basal divacancy resonances are no longer detectable at 100K,whereas the (kk )and (hh )c -axis divacancy resonances are observed up to temperatures of 200and 250K,respectively.The resonances of the unidentified defects persist to room temperature however,and decrease in magnitude by only about 30%between 20and 300K.We now demonstrate coherent control and direct optical measure-ment of each of these six defect spins by extending our measurements to the time domain.The time-resolved measurements that we describe include three steps.First,we polarize the defect spin ensemble with a pulse of light.Then,we coherently manipulate the ensemble with pulsed microwaves.Finally,we excite the ensemble with a second pulse of light and measure its photoluminescence intensity,which is spin-dependent.For instance,the results of such an experiment demo-nstrating coherent control over the PL4basal divacancy spins at 20K are shown in Fig.2a.We coherently rotate these spins by applying a pulse of 1.3526GHz microwaves resonant with the high-frequency transition seen in Fig.1f.By varying the duration of the microwave pulse,we observe Rabi oscillations.The magnetic field component of the microwave driving field was directed only along the c axis of the material,and no static magnetic field was applied.This measurement was made at several different microwave powers,and the resulting spin dynamics were fitted to an exponentially decaying cosine to determine the Rabi frequency,v R .As can be seen from the data in Fig.2b,the Rabi frequency increases linearly with the square root of microwave power,as expected from the Rabi formula 27.

A Ramsey pulse sequence 28is used to observe free induction decay of the same defect ensemble at 20K (Fig.2c),and the resulting dynamics are fitted to reveal an inhomogeneous spin coherence time

ΔP L /P L (%)

Frequency (GHz)

Frequency (GHz)

Frequency (GHz)

ΔP L /P L (%)

PL1

PL2

PL3

Room temperature coherent control of defect spin

PL4

PL5

PL6

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d e f g h ΔP L /P L (%)

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0+0.51.28

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0–2–41.28 1.32 1.360

+2+41.1

1.2 1.3–40+4T = 20 K T = 100 K T = 200 K T = 300 K Photon energy (eV)

P h o t o l u m i n e s c e n c e , P L (103 c o u n t s )

0.9

1.0 1.1 1.2

5

10

15Photon energy (eV)

–30+3P h o t o l u m i n e s c e n c e , P L (103 c o u n t s )

Figure 1|Optical detection of defect spins in 4H-SiC.a ,Photoluminescence spectra of HPSI 4H-SiC at sample temperatures ranging from 20to 300K.b ,An expanded view of low-temperature (20K)photoluminescence showing the six defect lines (PL1–PL6)discussed in the text.PL1–PL4are the four distinct forms of the neutral divacancy,whereas PL5and PL6remain unidentified.c –h ,The normalized change in luminescence (D PL/PL)collected from PL1(c ),PL2(d ),PL3(e ),PL4(f ),PL5(g )or PL6(h )as a function of applied microwave frequency at 20K.Solid red lines in c –h are fits.

a

b

c

d Power increas

e (dB)

ωR (M H z )

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20

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25102050ΔP L /P L (%)

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400600

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–2

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τ (μs)

T = 20 K B = 0 G

f = 1.3526 GHz

Δf = 3.33 MHz

T 2* = 1.44 ± 0.02 μs

T 2 = 184 ± 1 μs T CPMG = 357 ± 3 μs

Figure 2|Time-resolved dynamics of basal divacancy spins at 20K.a ,Rabi oscillations observed in basal divacancy spins at 20K and 0G.b ,Rabi frequency (v R )measured as a function of relative microwave power.In both a and b ,the driving frequency (f 51.3526GHz)was resonant with the high-frequency feature seen in Fig.1f.c ,Ramsey decay observed in the same population of basal divacancy spins,revealing that T 2*51.44m s.Oscillations are due to a

microwave detuning of D f 53.33MHz.d ,Optically detected Hahn echo and CPMG decays,with T 25184m s and T CPMG 5357m s.Solid lines are fits;error bars indicate 61s.d.

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of T 2*51.4460.02m s for the ground state spins.The Ramsey decay oscillates because the driving field was detuned from resonance by 3.33MHz.Data from Hahn echo and 3-p pulse Carr-Purcell-Meiboom-Gill (CPMG)pulse sequences 28are shown in Fig.2d,reveal-ing homogenous spin coherence times of T 2518461m s and T CPMG 535763m s at 20K in our samples.This is the same order of magnitude as T 2for diamond nitrogen–vacancy centre ensembles surrounded by a spin bath composed of 13C nuclear spins and back-ground paramagnetic impurities 29.

Using the same c -axis driving field geometry,Rabi oscillations were also observed at the high-frequency resonance of PL3.However,to efficiently couple to the low-frequency resonances of PL3or PL4,a driving field with a magnetic field component oriented perpendicular to the c axis needed to be used.The reduced symmetry of a basal divacancy leads to different microwave coupling geometries for the two observed spin transitions.The data therefore suggest that the low-frequency dipole transitions of the basal divacancies are perpendicular to the c axis whereas the high-frequency dipole transitions are not.The c -axis forms of the neutral divacancy offer a more direct com-parison to the diamond nitrogen–vacancy centre because they share the same symmetry and are predicted to have a similar electronic structure 5.Rabi and Ramsey oscillations induced by an in-plane driv-ing field are observed for the (hh )divacancy at 200K and 52G (Fig.3a and b),illustrating coherent control over this defect.The 52G field was applied along the defect axis in order to split the m S 561spin sub-levels of the ground state,which are roughly degenerate at zero mag-netic field.Similar results were also observed for the (kk )c -axis divacancy at 200K (see Supplementary Information).While we find that T 2*518266ns,a Hahn echo measurement taken at 113G (Fig.3c)shows that T 2526364m s.Additionally,periodic modula-tions of the Hahn echo envelope are observed in Fig.3c that appear when a magnetic field is applied along the c axis of the crystal.These modulations increase in frequency as the magnetic field is increased,

and fits to the data at a given field reveal that they contain two fre-quency components equal to the Larmor frequencies of 29Si and 13C nuclei.These modulations therefore represent coherent interactions between the (hh )divacancy spins and the surrounding nuclear spin bath 30.

Lastly,we demonstrate room temperature coherent control of the unidentified defects corresponding to PL5and PL6.In Fig.4a and b,we show Rabi measurements of the c -axis (PL6)and basal (PL5)orienta-tions of this defect,respectively.These measurements were made at 300K and 0G,with an in-plane driving field along the h 1 100i crystal direction.Although the c -axis defect spins oscillate at one frequency,the basal defect spins do not.This beating effect is observed because the basal defect spins exist in three orientations that couple unequally to the in-plane driving field.Ramsey measurements on both the c -axis and basal orientations of this defect are shown in the Supplementary Information,and exhibit maximum T 2*times of 21463ns and 1,248645ns respectively.Previous work using conventional electron spin resonance techniques has shown that silicon vacancies in SiC also exhibit room temperature Rabi oscillations 8.

Hahn spin echo measurements at zero magnetic field reveal that the c -axis and basal orientations of the unidentified defect decay

b

a

ΔP L /P L (%)

T = 200 K B = 52 G

1

23

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–0.2

Δf = 5.0 MHz

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τ (μs)

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T 2 = 263 ± 4 μs

B = 113 G

100

200300

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–0.02

τ (μs)

ΔP L /P L (%)

T 2* = 182 ± 6 ns B = 52 G 0.5 1.0

–0.02

f = 1.3000 GHz

τ (μs)

Figure 3|Time-resolved dynamics of c -axis divacancy spins at 200K.

a ,Rabi oscillations observed in c -axis (hh )divacancy spins at 200K and 52G.The magnetic field was oriented along the c axis.The driving frequency

(f 51.3000GHz)was resonant with the central frequency of the feature seen in Fig.1c,once Zeeman shifted by 52G.b ,Ramsey decay observed in the same population of (hh )divacancy spins,revealing that T 2*5182ns.Oscillations are due to a microwave detuning of D f 55.0MHz.c ,Hahn echo at 113G,showing oscillations induced by the nuclear spin bath;here T 25263m s.Solid lines are fits;error bars indicate 61s.d.

ΔP L /P L (%)

e d

B = 22 G

B = 187 G

B = 250 G

B = 345 G

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T 1 = 185 ± 6 μs c -axis:

T 1 = 183 ± 5 μs B = 0 G

2004000

–0.02

–0.04

τ (μs)

ΔP L /P L (%)

c -axis:

T 2 = 40.6 ± 0.7 μs Basal:

T 2 = 39.0 ± 0.5 μs 0

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f = 1.3434 GHz

T = 300 K B = 0 G

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a b

Figure 4|Coherent control of defect spins in SiC at room temperature.a ,b ,Rabi oscillations observed at 300K and 0G in the c -axis (a )and basal (b )orientations of the unidentified defects,which emit PL6and PL5,respectively.c ,Hahn echo decays at 0G for the same unidentified defects,revealing T 2times of ,40m s.d ,Magnetic field dependence of the c -axis Hahn echo,showing oscillations induced by the nuclear spin bath.e ,T 1

measurements for the c -axis and basal orientations,revealing long longitudinal spin relaxation times of T 15183m s and T 15185m s respectively.Solid lines are fits;error bars indicate 61s.d.

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exponentially with T2times of40.660.7m s and39.060.5m s,respec-tively(Fig.4c).As with the(hh)divacancy,the spin echo envelope of the c-axis unidentified defect becomes modulated when a non-zero magnetic field is applied along the c-axis of the crystal.At each field (Fig.4d,bottom three panels),fits to the data again reveal two fre-quency components equal to the Larmor frequencies of29Si and13C nuclei.In Fig.4e we measure the longitudinal spin relaxation time,T1, and find values of18365m s and18566m s for the c-axis and basal spins,respectively.These are relatively long T1times,suggesting that we are probing spins in a ground or metastable electronic state of the defect,rather than those of an orbital excited state with a short optical lifetime.

These experiments demonstrate that several highly controllable defect-based quantum states exist in SiC,and that they can be manipu-lated with the same techniques developed and optimized for use with diamond nitrogen–vacancy qubits.Notably,we have shown that two of these defects are capable of room temperature operation,and that differences in defect composition or orientation made possible by the binary nature of SiC lead to a rich assortment of electronic and spin properties.Because well-established growth and processing protocols already exist for SiC,these defects could be the basis for a previously unachievable degree of integration between defect qubits and existing device technologies.

METHODS SUMMARY

Samples were mounted in a liquid helium flow cryostat with optical and micro-wave access.A closed-loop sample heater was used to hold sample temperatures constant between20and300K.853nm diode laser light was used for sample excitation,and was pulsed using an acousto-optic modulator(AOM).A14mm focal length lens(Figs1,3and4)or a603microscope objective(Fig.2)focused the light on the sample surface with spot diameters of approximately15or1m m, respectively.The laser power was,20mW at the sample surface.Two infrared detectors were used to measure photoluminescence:a liquid-nitrogen-cooled spectrometer(Fig.1),or a femtowatt photoreceiver with an analogue voltage output(Figs2–4).Analogue voltages were measured and processed digitally using a data acquisition system(DAQ).Both detectors had an800–1,700nm operating range.Microwaves were supplied to the cryostat by a signal generator and were modulated using a selection of microwave switches and mixers.A permanent magnet was used to apply a magnetic field along the c axis of the material in Figs3and4d.Otherwise,no magnet was present.

Samples were diced from a365-m m-thick wafer of HPSI4H-SiC purchased from CREE(part number:W4TRD0R-0200),and had dimensions of roughly 2mm33mm.Ring-shaped microwave sources34m m(Fig.1)and1mm (Fig.2)in diameter were patterned on the surfaces of two samples using standard photolithographic techniques.In both cases,a10/90nm Ti/Pt metallization was used.A third sample was mounted on top of a1.8mm wide by9mm long microwave stripline(Figs3and4)made from RT/duroid6002(Rogers Corporation)plated with1.8m m of Au.All microwave devices were connected via wire bonds to the microwave line in the cryostat.

Full Methods and any associated references are available in the online version of the paper at http://www.sodocs.net/doc/03bad489e53a580216fcfeb5.html/nature.

Received3July;accepted19September2011.

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Supplementary Information is linked to the online version of the paper at

http://www.sodocs.net/doc/03bad489e53a580216fcfeb5.html/nature.

Acknowledgements We are grateful to G.D.Fuchs,A.Janotti,D.M.Toyli,C.G.Van de Walle,J.B.Varley and J.R.Weber for discussions.We thank M.E.Nowakowski for help with sample preparation.This work was supported by the Air Force Office of Scientific Research(AFOSR)and the Defense Advanced Research Projects Agency(DARPA). Author Contributions All authors helped to design the research,perform the research and write the paper.

Author Information Reprints and permissions information is available at

http://www.sodocs.net/doc/03bad489e53a580216fcfeb5.html/reprints.The authors declare no competing financial interests. Readers are welcome to comment on the online version of this article at

http://www.sodocs.net/doc/03bad489e53a580216fcfeb5.html/nature.Correspondence and requests for materials should be addressed to D.D.A.(awsch@http://www.sodocs.net/doc/03bad489e53a580216fcfeb5.html).

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METHODS

Experimental set-up.Inall experiments,samples were held at temperatures ranging from20to300K by mounting them in a liquid helium flow cryostat outfitted with a closed-loop sample heater.A window and a microwave feedthrough provided optical and microwave access to the sample.Light used for sample excitation came from an 853nm diode laser that was first passed through an acousto-optic modulator(AOM) and then through a series of polarization optics before being reflected off a dichroic mirror designed to transmit wavelengths in the932–1,300nm range.The reflected laser beam was then focused by either a14mm focal length lens(Figs1,3and4)or a 603microscope objective(Fig.2)onto the sample surface with a spot diameter of roughly15or1m m,respectively.The polarization optics were tuned to ensure that incident light at the sample surface was linearly polarized parallel to the table surface.

A laser power of,20mW at the sample surface was used.Photoluminescence was collected through the same focusing optic and then transmitted through the dichroic and a900nm longpass filter to one of two infrared detectors,depending on the data type being collected.The first detector was a liquid-nitrogen-cooled spectrometer (Fig.1);the second was a femtowatt photoreceiver with a20Hz bandwidth and an analogue voltage output(Figs2–4).Analogue voltages were measured and processed digitally using a data acquisition system(DAQ).

For continuous-wave measurements,microwaves supplied by a signal generator were passed through a microwave switch and directional coupler before reaching the cryostat microwave feedthrough and then ultimately the sample.The switch was controlled using the DAQ,and the‘couple’port of the directional coupler was fed to a detector diode so that microwave power at the directional coupler could be measured directly.These measurements were then used to compensate for frequency-dependent variations in microwave transmission to the cryostat.For pulsed measurements,a microwave mixer,switch and amplifier were placed in series between the signal generator and directional coupler.Measurements using pulsed light and microwaves were timed using a digital delay generator and an arbitrary waveform generator that operated the mixer,switch and AOM.

A permanent magnet in a motorized goniometric mount was used to apply a magnetic field along the c axis of the material in experiments where a magnetic field was required(Figs3and4d).Otherwise,no magnet was present. Sample fabrication.Samples were diced from a365-m m-thick wafer of HPSI4H-SiC purchased from CREE(part number:W4TRD0R-0200),and had dimensions of roughly2mm33mm.Ring-shaped microwave sources34m m(Fig.1)and 1mm(Fig.2)in diameter were patterned on the surfaces of two samples using standard photolithographic techniques.In both cases,a10/90nm Ti/Pt metalliza-tion was used.A third sample was mounted on top of a1.8mm wide by9mm long microwave stripline(Figs3and4)made from Rogers Corporation RT/duroid 6002plated with1.8m m of Au.All microwave devices were connected via wire bonds to the microwave line in the cryostat.Measurement techniques.A5s exposure time was used to collect the data shown in Fig.1a and b.Spectrally filtered optically detected magnetic resonance data (Fig.1c–h)were measured by first collecting photoluminescence spectra at each frequency,both with and without microwave power applied to the sample.The latter was subtracted from the former,and a software binning algorithm was used to sum the number of detector counts collected under each ZPL feature(D PL).The binning algorithm was designed to ignore counts resulting from phonon sideband emission,and did this by subtracting out any broad background located underneath a sharp ZPL in a spectrum.The exposure time for each spectrum was19s,and the final signal(D PL/PL)was normalized by the total number of ZPL detector counts measured when no microwaves were applied(PL).Lorentzian fits to the data were used to determine the frequencies of the observed resonances,as discussed in the Supplementary Information.

Time-resolved spin dynamics were measured optically using the femtowatt photoreceiver,which captured all light in the900–1,700nm range.Selective manipulation of one defect species over the others was possible because the micro-wave resonances of each species were at different frequencies,or could be tuned using a magnetic field.In Figs2–4,D PL/PL5V Mod/V Tot,where V Mod is the magnitude of the,20Hz modulated component of the output voltage,and V Tot is the total time-averaged output voltage.Because collected light was not spectrally filtered within the900–1,700nm range,the time-resolved signals in Figs2–4were normalized by the total infrared luminescence collected from the sample.The data points shown in the time-resolved plots are the mean of multiple consecutive quick scans taken at identical conditions.The error bars are the standard deviation of this mean,calculated using the variance of these quick measurements.

Pulse sequences and additional information.All pulse sequences consisted of an initial laser pulse to polarize the defect spins,followed by microwave pulses for spin manipulation,and then a final laser pulse to measure the spins.For T1 measurements,an additional laser pulse was added between the microwave and final laser pulses in order to keep the optical duty cycle constant during the measurement(see Supplementary Information).For the Rabi,Fig.2b Ramsey, and T1measurements,the relevant pulse sequence was repeated continuously while the microwave driving field was modulated on and off at,20Hz.For the Fig.3b Ramsey,Hahn and CPMG measurements,the appropriate sequence was repeated continuously while the final microwave pulse was modulated between positive and negative phases at,20Hz.The modulated and average photoluminescence components that resulted were measured using the femtowatt photoreceiver via the DAQ.

Additional data,details of the experimental set-up,sample structures,pulse sequences,and fits to data in Figs3c and4d are given in the Supplementary Information.

RESEARCH LETTER

自旋晶体管
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