Electrical Tuning of Single Nitrogen-Vacancy Center Optical Transitions Enhanced by Photoinduced Fields

1.4 MB·English

by  L. C. Bassett

ElectricalTuningofSingleNitrogen-VacancyCenter
OpticalTransitionsEnhancedbyPhotoinducedFields
L. C. Bassett, F. J. Heremans, C. G. Yale, B. B. Buckley, and D. D. Awschalom
∗ ∗ ∗ ∗ †
Center for Spintronics and Quantum Computation,
University of California, Santa Barbara, California 93106, USA
(Dated:January20,2013)
We demonstrate precise control over the zero-phonon optical transition energies of individual nitrogen-
vacancy(NV)centersindiamondbyapplyingmultiaxiselectricfields,viathedcStarkeffect. TheStarkshifts
displaysurprisingasymmetriesthatweattributetoanenhancementandrectificationofthelocalelectricfield
byphotoionizedchargetrapsinthediamond.Usingthiseffect,wetunetheexcited-stateorbitalsofstrainedNV
2
centerstodegeneracyandvarytheresultingdegenerateopticaltransitionfrequencyby>10GHz,ascalecom-
1
parabletotheinhomogeneousfrequencydistribution.ThistechniquewillfacilitatetheintegrationofNV-center
0
spinswithinphotonicnetworks.
2

n PACSnumbers:71.55.Cn,71.70.Ej,78.56.-a,81.05.ug
a
J

0 Nitrogen-vacancy (NV) centers in diamond are promising [11,14]. Thespin-tripletground(GS,symmetry3A )andex-
2
1 solid-statequbitsforemergingquantumtechnologies, dueto cited states (ES, symmetry 3E) are connected by ZPL tran-

theirlongspincoherencetimes[1]andfastmanipulationrates sitions around 637.2nm (1.946eV). Our experiments are
]
l [2], together with a level structure that allows for straight- performedatzeromagneticfield,wherethespin-tripletbasis
l
a forward optical initialization and readout of the electronic states are S , S , S . A 532nm (2.3eV) “repump”
x y z
h {| i | i | i}
spinstate[3]. Furthermore, inhigh-qualitysingle-crystaldi- beam pulsed at 300kHz in a confocal geometry maintains
- ≈
s amondattemperaturesbelow 25K[4],sharpzero-phonon- aspin-polarizedpopulationin Sz . Betweenrepumpcycles,
e ≈ | i
line (ZPL) optical transitions facilitate the coherent coupling we count photoluminescence excitation (PLE) photons emit-
m
betweenNV-centerspinsandphotons[5,6]. Theintegration tedbytheNVcenterintotheredshiftedphononsideband[see
t. of NV centers within photonic structures [7] to route single Fig. 1(a)] after absorption from a narrow-line red laser tun-
a
photonsandenhancethespin-photoninteractioncouldthere- ableacrosstheZPLtransitions. Aswescantheredlaserfre-
m
fore lead to scalable applications for quantum information quency,wetypicallymeasuretwopeaksinthePLEspectrum
-
processingandsecurecommunication[8]. as shown in Fig. 1(b); these correspond to spin-conserving
d
n Assolid-state“trappedatoms,”NVcentersaresensitiveto transitionsfromtheGSorbitalsinglet A2,Sz tothetwoES
| i
o their local environment. While this sensitivity has enabled orbitaleigenstates E1,Sz , E2,Sz . Inacrystalenviron-
[c nanoscalemagnetic[9]andelectric[10]metrology,italsoex- ment with perfect C{|3v symime|try andi}zero electric and mag-
posesindividualNVcenterstosampleinhomogeneities,lead- netic fields, these ES orbital states would be degenerate, but

2 ing to a distribution of ZPL frequencies within a diamond the symmetry is generally broken by local crystal strain and
v
[11]. Theabilitytotunethesefrequenciesiscrucialforpho- bynonuniformelectrostaticchargedistributionsthatgenerate
8
tonicapplications,forinstancetoutilizetheselectionrulesat localelectricfields.
7
8 theC3v symmetrypoint forspin-photonentanglement [6]or The dc Stark perturbation to the Hamiltonian, HˆStark =
3 to coherently couple distant NV centers to indistinguishable µˆ F, describes the interaction between the local electric
− ·
4. photons. Through the dc Stark effect, applied electric fields field F and the electric dipole operator µˆ. For fixed stress,
0 perturb both the ground-state spin [10, 12] and excited-state thestrainperturbationcanbecastintothesameformbyiso-
1 orbitals[13],providingthemeanstocontroltheopticaltran- lating components which transform as the irreducible repre-
1 sitions. sentations of C3v [14]. The combined perturbation has the
v: Here we use micron-scale devices to manipulate electric formVA1OˆA1+VExOˆEx+VEyOˆEy,whereOˆΓa isanorbital
i operatortransformingasthebasisstate Γ and
X fields in three dimensions, to compensate the intrinsic local | ai
strain and electrostatic fields of individual NV centers and
r V =S µ F
a achievefullcontroloftheorbitalHamiltonian. Furthermore, A1 A1 − k z
V =S µ F (1)
by analyzing the Stark shifts as a function of applied volt-  Ex Ex − ⊥ x
V =S µ F
ages, we infer a surprising amplification and rectification of  Ey Ey − ⊥ y
the local electric field, consistent with electrostatic contribu- are the symmetrized field strengths, in terms of fixed strain
tionsfromphotoionizedchargetrapswithinthediamondhost. components S , projections of the local electric field F ,
Γa i
By harnessing this reproducible effect, we can tune the NV- and the reduced matrix elements of the electric dipole oper-
centerHamiltoniantoarbitrarypointsacrossarangecompa- ator µ ,µ . We choose orbital basis states E , E
x y
rabletotheinhomogeneousZPLdistribution. for thekES⊥which transform like vectors x,y{|in ithe| NVi}-
(cid:8) (cid:9) { }
TheelectronicstructureofthenegativelychargedNVcen- center coordinate system [15], and we ignore the small
ter is determined by symmetry, through its point group C ( 100MHz)spin-spincouplingbetweenESspinstates S
3v z
≈ | i
2
diamondsurface.Thesampleisa0.5-mm-thicksingle-crystal
diamondgrownbychemicalvapordepositionwith<5ppbni-
trogencontent(ElementSix),irradiatedwith2MeVelectrons
(1.2 1014cm 2)andthenannealedat800 CtocreateNV
− ◦
×
centers. Measurements are performed in a continuous-flow
cryostat operating at 20K. Symmetric biases V and V
X Y
≈
applied as shown in Fig. 1(c) produce lateral electric fields
F and F in the [110] and [¯110] crystal directions, respec-
X Y
tively, while a common dc bias generates fields in the [001]
out-of-plane (Z) direction. The sample (X,Y,Z) and NV-
center (x,y,z) coordinate systems are uniquely related for a
givenNV-centerprojectionfromthe 111 family[17].
h i
Figure1dcontainsaseriesofPLEspectrashowingtheopti-
calresonancesoftheNVcentermarkedinFig.1(c),asafunc-
tionofseparatebiasesV andV withV =0V.Thelateral
X Y dc
biases are applied as symmetrically pulsed square waves at
1kHz,withPLEphotonsbinnedaccordingtopolarity. While
the response to static lateral bias is qualitatively similar, this
techniqueseparatesslowphotoinducedchargingeffectsfrom
the dielectric response as discussed below. Two features are
evident in the data: first, we observe an unexpected “kink”
at zero bias, and second, the resonances cross at V 7V,
FIG.1. (a)Simplifiedenergy-leveldiagram(nottoscale)showing X
≈
onlythe Sz levelsoftheNV-centergroundandexcitedstates,with demonstrating that we can indeed restore C3v symmetry to
| i
resonantexcitation(redarrows)andredshiftedemission(grayarrow) thesystem. Weexplorebothofthesefeaturesbelowwithad-
marked. (b) PLE spectrum (points) with no applied bias, marked ditionalexperiments.
by dashed line in (d), with a two-Lorentzian fit (solid curve). (c)
The kink at zero bias reflects an asymmetry in the local
Micrographandphotoluminescenceimage(center)ofdeviceA,with
electric field vector as a function of polarity, i.e., F(+V) =
electricalconnectionsmarked.(d)PLEspectraofthe6-µm-deepNV 6
F( V).Wearguethatthisasymmetryresultsfromthepho-
centermarkedbyanarrowin(c)asafunctionoflateralbiasapplied − −
symmetricallytotheX(leftpanel)orY (rightpanel)gatepairs,with toionization of charge traps in the diamond host. Even in
V = 0V. InallPLEspectra,theoriginoftherelativefrequency high-quality single-crystal synthetic diamonds, deep defects
dc
axisisarbitrary. such as vacancy complexes and substitutional nitrogen have
importanteffectsonthematerial’selectronicproperties[18].
Inparticular, substitutionalnitrogenatomsformdonorlevels
and S , S [16]. By defining Hˆ A ,S 0, the
{| xi | yi} | 2 zi ≡ 1.7–2.2eV below the conduction band edge [19], and the
Hamiltonian in the E ,S , E ,S basis can be written ≈
{| x zi | y zi} timescaleforchargetransportthroughtheselevelsisverylong
as
(hours) even in nitrogen-rich diamond at room temperature
1 V V [20]. These traps are easily ionized by the 532nm repump
H =(~ω0+∆µkFz)I+ √2(cid:18)−VEExy −−VEExy (cid:19), (2) beam(≈100µW)whichis4–5ordersofmagnitudestronger
than the red laser ( 1nW). When voltages are applied, this
where~ω0isthenaturaltransitionenergyincludingfixedper- leadstoalong-lived≈nonequilibriumchargedistributioninthe
turbationsofA symmetry,and∆µ = µGS µES ,defined
suchthatboth∆1µ andµ arepositkive.Thketr−anskitionenergy illuminated volume of the sample, which can either amplify
eigenvaluestakethkeform⊥E =hν¯ 1(cid:0)hδ,where (cid:1) orscreenthelocalelectricfield.
± ± 2 Asasimplifiedone-dimensionaldemonstration,wepresent
in Fig. 2(a) the Stark-shift response of an NV center 13µm
hν¯=~ω0+∆µ Fz, (3a)
k belowthesurfaceofaseconddiamondsampleirradiatedand
1/2
hδ =√2 V2 +V2 (3b) annealedundersimilarconditions,butpatternedwithaglobal
Ex Ey
topgateofthetransparentconductorindium-tin-oxide(device
(cid:16) (cid:17)
are the longitudinal and transverse components due to fields B).Asthetop-gatebiasissteppedinaloopover 160min,
≈
ofA andEsymmetry,respectively. FromEq.(1),itisclear we observe hysteresis in the response characteristic of 1h
1
≈
thatalocalelectricfieldcancancelthetransversecomponents charge-relaxationtimescales. Furthermore,bycomparingthe
ofintrinsicstraintorestoreC symmetrytothesystem,and magnitudes of the Stark shifts due to biases applied later-
3v
fromEq.(3a)weseethatanelectricfieldF appliedalongthe ally across an 8µm gap [Fig. 1(d)] and vertically across the
z
NV-centersymmetryaxisshiftstheenergyofbothtransitions 0.5mm sample thickness [Fig. 2(a)], we find that, when the
bythesameamount. top-gatebiasisnegative,thelocalelectricfieldbelowthetop
WefirstinvestigatetheseeffectsusingdeviceA,shownin gateappearstobeamplifiedbyroughlyanorderofmagnitude
Fig. 1(c), consisting of four Ti-Pt-Au gates fabricated on the over dielectric predictions [17]; conversely, the field appears
3
an applied voltage V, and ξ is a dimensionless vector giv-
ing the relative strength and direction of the rectified field,
assumed to scale linearly with V . Because of the long
| |
chargingtimescale,therectifiedfieldβ V ξdoesnotchange
| |
when we switch the bias polarity on millisecond time scales
while the dielectric component βVvˆ changes sign, produc-
ingapolarity-asymmetricresponse. Theassumptionofalin-
earrelationshipbetweentherectifiedfieldstrengthand V is
| |
motivatedbytheempiricalobservationthatν¯,proportionalto
F ,varieslinearlywithappliedbiasinallourmeasurements.
z
Thisamountstoanapproximationthatthespatialdistribution
of photoionized charge remains fixed, while the charge den-
sityvarieslinearlywith V .
| |
Figure 2(c) shows the mean (ν¯) and difference (δ) of the
transitionfrequenciesextractedfromfitstothePLEspectrain
Fig. 1(d). The NV-center symmetry axis ([11¯1] in this case)
is uniquely determined by the sign of ν¯ in response to elec-
tricfieldsindifferentdirections. BysubstitutingEq.(4)into
Eqs.(3)andapplyingtheappropriatecoordinatetransforma-
tion, we obtain a model that quantitatively agrees with our
observations[17],asshownbythefitstothedatainFig.2(c).
Giventhatthisisonlyasimplifiedphenomenologicaldescrip-
FIG.2. (a)Stark-shifthysteresisloopforanNVcenter13µmbe- tion of a complicated three-dimensional system, it matches
lowatransparenttopgate,asafunctionoftop-gatevoltage. Points ourobservationssurprisinglywell.
markthetransitionfrequenciesfromatwo-LorentzianfittoaPLE
Finally,wepresentacontrolexperimentinwhichwemiti-
spectrumatthecorrespondingvoltageandcolor-codedarrowsindi-
gateeffectsduetothe532nmrepumpcycle. Occasionalre-
catethesweepdirection. (b)Schematicofthelocalelectricfieldsin
pumppulsesarestillrequiredtocompensateforphotoioniza-
alateralgeometry. Photoionizedchargetrapsintheilluminatedvol-
umecontributearectifiedfieldRpredominantlyinthe+Zdirection, tionoftheNV−chargestateduetosequentialtwo-photonab-
whichaddstothedielectricfieldEtoshiftthedirectionofthelocal sorption,butwithweak(<1nW)resonantlight,therequired
fieldF.(c)dcStarkcomponentsν¯andδ(points)extractedfromfits repumpperiodcanbeincreasedtoseveralseconds[4],allow-
ofthePLEspectrainFig.1(d),withacombinedfitaccordingtothe ingtimetoapplybias,recordacompletePLEspectrum,and
modeldescribedinthetext(solidcurves). (d)dcStarkcomponents
rezerothebias,allbetweenrepumppulses. Sinceweakspin-
(points) and fits (solid curves) measured both with (green squares)
nonconserving optical transitions quickly polarize the NV-
and without (orange circles) the 532nm repump excitation. Inset:
centerspinawayfromresonanceintheabsenceoftherepump
MicrographandphotoluminescenceimageofdeviceC,withelectri-
calconnectionsmarked.The7-µm-deepNVcentermeasuredin(d) cycle, we mix the spin population by applying a microwave
is circled. In all cases, marker sizes slightly exceed measurement magnetic field resonant with the GS spin transition. We use
uncertainties. anotherdeviceforthispurpose(deviceC),showninFig.2(d),
whichisfabricatedonthesamediamondasourfour-gatelat-
eral device. It consists of a short-terminated waveguide to
to be completely screened above a threshold bias, where the
generatemicrowavefieldsandserveasground,andagatethat
response is flat. The response of an NV center in device A
when biased produces lateral electric fields across an 8µm
tovariationsofV isqualitativelysimilar[17],andbothare
dc gap.
consistentwithapictureinwhichpositivechargesintheillu-
Figure 2(d) shows ν¯ and δ as a function of gate voltage
minatedvolumebelowtheNVcenterrectifytheZcomponent
for the NV center circled in the inset. Once again the bias
oftheelectricfield.
polarityisswitchedat1kHzandthePLEphotonsarebinned
We can incorporate these charging effects into a phe-
accordingly. A polarityasymmetry is clearly observed when
nomenological model capturing the essential features of our
the repump beam is present, particularly as a kink in ν¯, and
observations. AsdepictedinFig.2(b),thelocalelectricfield
it is significantly reduced when the biases are applied in the
for an NV center between two surface gates is composed of
absenceoftherepumpcycle. Fitstothedatausingourmodel
adielectriccomponentroughlyparalleltothesamplesurface
[17] are shown as solid curves, from which we find that ξ
and a rectified component due to photoionized charge that is | |
isreducedfrom0.71 0.02withthestandardrepumpcycleto
mainlyoutofplane. Wemodelthisfieldas ±
0.33 0.03whenthe532nmbeamisomitted.
±
F=βVvˆ+β V ξ, (4) Based on this understanding, we can exploit the photoin-
| | ducedchargetoobtaingreatlyenhancedtunabilityinourfour-
whereβaccountsforgeometricanddielectricfactorsthatpre- gategeometry(deviceA).Sincetherectifiedfieldpointspre-
dict a local electric field in the direction vˆ in response to dominantly out of plane and has strength comparable to the
4
In conclusion, we have used electric fields to tune the
ZPLtransitionsofindividualNVcentersinmicron-scalede-
vicessizecompatiblewithphotonicstructures. Throughtheir
dc Stark shifts, NV centers serve as nanoscale probes of
theirelectrostaticenvironment,revealingstrongsignaturesof
charge accumulation due to photoionization of deep donor
levels in the diamond. We have analyzed these effects with
aphenomenologicalmodelandusedtheadditionalfieldspro-
videdbyphotoionizationtoobtainthree-dimensionalcontrol
ofthelocalelectricfield,inordertotuneboththeoverallen-
ergyandorbitalsplittingoftheexcited-stateHamiltonian. In
particular, wehavedemonstratedhowtoreachtheC sym-
3v
metrypointandthenapplylongitudinalperturbationstoshift
thedegeneratephotonenergy. BycouplingmultipleNVcen-
terstoindistinguishablephotonswiththistechnique,photonic
networks could provide a quantum bus to coherently couple
distantNVcenters,andentanglementswappingprotocols[8]
couldenablelong-distancequantumkeydistribution.
WeacknowledgefinancialsupportfromtheAFOSR,ARO,
andDARPA,andthankR.Hanson,C.G.VandeWalle,U.K.
FIG. 3. Tuning diagram for the NV center marked in Fig. 1(c). Mishra,K.Ohno,andD.J.Christleforusefuldiscussions.
Degeneracy is achieved at different frequencies by setting the ap-
pliedbiases(Vdc,VX,VY)asmarkedintheupperpanel;inthelower
panelweshowPLEspectraasafunctionofVX aroundeachofthese
pointsforfixedVdc(VY isalsovariedtokeeptheratioVX/VY con-
stant).WecanshiftasecondNVcentertodegeneracywithinthetun- ∗ Theseauthorscontributedequallytothiswork
ingrangeofthefirst,asshownbythePLEspectraoutlinedinblue † Correspondingauthor.
(lowerpanel)andthecorrespondingblueline(upperpanel)marking Emailaddress:[email protected]
thedegeneratefrequency. [1] G.Balasubramanianetal.,Nat.Mater.8,383(2009).
[2] G.D.Fuchsetal.,Science326,1520(2009).
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dielectriccomponent,weeffectivelyobtainthree-dimensional 74,104303(2006).
[4] K.-M.C.Fuetal.,Phys.Rev.Lett.103,256404(2009).
controlofthelocalelectricfieldvector. Theapplicationofa
[5] B. B. Buckley, G. D. Fuchs, L. C. Bassett, and D. D.
negative reference bias V as shown in Fig. 1(c) increases
dc Awschalom,Science330,1212(2010).
therectifiedcomponentFZ independentlyof(FX,FY). Asa [6] E.Toganetal.,Nature466,730(2010).
demonstration of the flexibility of this technique, we present [7] A.Faraonetal.,Nat.Photon.5,301(2011); C.Santorietal.,
atuningdiagraminFig.3inwhichweuse(V ,V )toscan Nanotechnology21,274008(2010).
X Y
throughtheC degeneracypointatdifferentsettingsofV . [8] S. D. Barrett and P. Kok, Phys. Rev. A 71, 060310 (2005);
3v dc
L.Childress, J.M.Taylor, A.S.Sørensen, andM.D.Lukin,
Eachcrossingoccursatadifferentfrequency,withthecorre-
Phys.Rev.A72,052330(2005).
spondingbiaspoint(V ,V ,V )markedintheupperpanel.
X Y dc [9] J.R.Mazeetal.,Nature455,644(2008);G.Balasubramanian
Essentially, we are compensating the transverse components
etal.,Nature455,648(2008); B.J.Maertzetal.,Appl.Phys.
(SEx,SEy) of the intrinsic fields and tuning the longitudinal Lett.96,092504(2010).
component of F to shift the frequency. Since the rectified [10] F.Doldeetal.,Nat.Phys.7,459(2011).
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NV center in the same device at V = 0V and display [15] TheNV-centercoordinatesystemischosensuchthatzˆpoints
dc
alongtheN-Vsymmetryaxisandxˆliesinareflectionplane.
C degeneracyatafrequencywithinthetuningrangeofthe
3v
[16] Note that while spin-spin coupling leads to mixed ES spin
first. If these two NV centers were in separately controlled
eigenstatesinsomeregimes,itdoesnotsignificantlyaffectthe
devices and tuned simultaneously to degeneracy at the same
opticalpumpingmechanismwhichpolarizesthespininto Sz
frequency,theywouldcoupleidenticallytoindistinguishable inourexperiments. | i
photons. [17] Seesupportingonlinematerial.
5
[18] J. Isberg, A. Tajani, and D. J. Twitchen, Phys. Rev. B 73, 8,721(1999).
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SupplementalMaterialfor
“ElectricalTuningofSingleNitrogen-VacancyCenter
OpticalTransitionsEnhancedbyPhotoinducedFields”
L. C. Bassett, F. J. Heremans, C. G. Yale, B. B. Buckley, and D. D. Awschalom
Center for Spintronics and Quantum Computation,
University of California, Santa Barbara, CA 93106, USA
(Dated:January20,2013)
2 METHODSANDSUPPLEMENTARYDATA
1
0
Opticalmethods
2

n
a Measurements were performed using two home-built con-
J focal microscopes designed to excite single NV centers both

0 resonantly at 637.2nm and in the blue-shifted phonon side-
1 bandat532nm,whilecollectingphotoluminescencephotons

from the red-shifted photoluminescence sideband between
]
l 650–830nm. Details and a schematic are available else-
l ≈
a where [1]. The 532nm laser serves both as the excitation
h
forstandardphotoluminescencespatialimagingandasa‘re-
-
s pump’cycletomaintaintheNV− chargestatewhichispho-
e toionizedbyresonantexcitationalone.
m
Resonant excitation is provided by tunable diode lasers
.
at from the New Focus VelocityTM series, which are tuned by FIG. S1. Stark shift hysteresis loop for the NV center marked in
m meansofapiezoelectricactuatorthatmakesfineadjustments Fig. 1c of the main text as a function of Vdc (with VX,VY = 0).
tothelasercavity. Animportanttechnicalaspectoftheseex- Points mark the optical resonance frequencies extracted from two-
-
d periments is the calibration of the laser frequency response Lorentzian fits to PLE spectra at the corresponding voltage, and
n to variations in the voltage applied to the piezo, since this is color-coded arrows mark the sweep direction. Errorbars represent
o thefrequencyuncertaintiesfromthefits.
typically nonlinear and hysteretic. In one of our microscope
c
setupswehavepre-calibratedthelaserfrequencyresponseto
[
particularpiezomodulationsequencesusingaMach-Zehnder

2 cies( 10satopticalpower 10µW),whilefullrelaxationin
interferometer. In the other setup, unpredictable mode hops ≈ ≈
v thepresenceofthe532nmlightalonerequiredseveralhours.
of the laser make such calibrations unreliable, so we con-
8
7 tinuously monitor the laser frequency interferometrically: a
8 Fabry-Perotcavitywithafreespectralrangeof1.5GHzpro-
3 videsfinefrequencyresolution,whileaMach-Zehnderinter- ChargingbehaviorindeviceA
.
4 ferometer with free spectral range 7GHz is used to detect
≈
0 mode hops. In both cases, our calibrations provide relative The interpretation of the hysteresis measurements pre-
1 frequencydeterminationswith 100MHzuncertaintyacross sented in the main text (Fig. 2a) is simplified by the one-
1 ≈
: the ≈90GHz piezo modulation range. The resonant light is dimensional geometry of the top-gate device, but we mea-
v prepared with circular polarization, so that the (linear) opti- sured a qualitatively similar response in our four-gate lateral
Xi calselectionrulesfor Sz opticaltransitionsdonotcausethe device(deviceA,seeFig.1cinthemaintext)tovariationsof
| i
r resonancestodisappearincertainregimes. the reference voltage Vdc common to all four gates. Figure
a Inbothsetups,wealsohavetheabilitytoaddconfocalexci- S1 shows a hysteresis loop as a function of V for the NV
dc
tationat405nm(3.1eV)totheopticalpath. Unsurprisingly, centermarkedinFig.1c,whichis 7µmbelowthediamond
≈
this higher-energy excitation significantly alters the charging surface. Althoughtheresponseissimilartothetop-gatemea-
dynamics of the system. Generally it causes the NV center surementswedonoticeafewdifferences:First,thehysteresis
opticaltransitionstobecomelessstableandsoitwasnotused ‘direction’ is reversed, in the sense that the Stark response
duringanyofthemeasurementspresentedinthemaintext,but lagsV inFig.S1,whileitleadsthetop-gatebiasinFig.2a.
dc
wediduseitasacontrolto‘reset’theequilibriumchargedis- Second,the‘thresholdbias’isclosertozerointhelateralde-
tribution with no applied bias between experiments. A short vice than in our top-gate measurements. These differences
burstof405nmlightappliedinthisconfigurationwasgener- areprobablyduetoavarietyoffactors,including(a)geomet-
allyenoughtorestoretheinitialNVcentertransitionfrequen- ricdifferencesduetothegategeometryandthedepthsofthe
2
respectiveNVcenters,(b)variationsinthediamondsamples,
(c) details of the diamond-metal interfaces for different met-
als(Ti/Pt/Auonthelateraldeviceandindium-tin-oxideasthe
top gate), and perhaps most importantly (d) the electrostatic
boundary conditions at the back of the device – the top-gate
device B is indium-bonded to ground on the backside, while
deviceAisgluedtothegroundplanewithaninsulatingadhe-
sive.
Wenotethatpolarity-dependentStarkshiftshavebeenre-
cently observed for Chromium centers in diamond [2], and
suggestthataone-dimensionalexperimentwithatransparent
topgatecoulddeterminewhetherthesedevicesdisplaysimi-
larchargingbehavior.
Photoconductivity
When voltages are applied between surface gates in the
presence of optical excitation, we expect the photoexcitation
of defect levels to lead to a photocurrent near the surface.
Fig. S2 shows the photoconductivity response of device A
whentheexcitationbeamisfocusedontheNVcentermarked
inFig.1cofthemaintext,6µmbelowthediamondsurface.
Thetoppanelshowsanexampleofatypicaldcphotoconduc-
tivityresponseforthisandsimilardeviceswehavemeasured,
withalmostnomeasurablecurrentflowinginthedarkandtyp-
icalphotocurrentsofafewnanoampereswhentheexcitation
beam is applied. On this particular device, a larger current FIG.S2. Toppanel: I-V curvesshowingconductivitybetweengate
‘leak’ existed between the left and lower gates, as shown in theright-handgateofdeviceA(seeFig.1cinthemaintext)andthe
the lower panel of Fig. S2. When VLower VLeft & 20V, a remainingthreesurfacegates,bothwith(greencircles)andwithout
currentofseveralmicroamperesflowsbetw−eenthem. (purplesquares)532nmexcitation.Lowerpanel:Similarphotocon-
ductivitymeasurements(excitationapplied)withthebiasconnected
It is important to note, however, that the presence of a
to the left-hand gate (red circles) and lower gate (blue squares),
photocurrent between gates near the diamond surface does
showingalargerleakagecurrentbetweenthesetwogates.
not preclude the accumulation of a space charge deeper in
the sample, especially since photoexcited charge transport
throughdiamondisaninefficientprocess,andthetimescales
from the 111 family; note that antiparallel (i.e., N-V com-
forchargestorageareverylong[3]. Asillustratedschemati- h i
paredtoV-N)orientationsaredistinguishableduetotheper-
callyinFig.2bofthemaintext,theout-of-planecomponent
manentdipoleinthezdirection.Usingthecoordinatesystems
of the photoinduced field is primarily due to positive charge
described in the text, we note that N-V axis projects either
fromphotoionizeddonorsbelowtheNVcenter,whichresults
in the X or Y sample directions, and also has a compo-
from the effective voltage applied across the sample rather ± ±
nent along Z. We can therefore label a given orientation
than between two lateral gates. Thus even with a substantial ±
by (p ,p ,p ), where p = 0, 1 give the sign of the
leakbetweentwogates,boththedielectricandphotoinduced X Y Z X,Y ±
N-V projection in the (X,Y) axes (note p2 +p2 = 1) and
components of the dc Stark shift are always present. Practi- X Y
p = 1givesthesignoftheZ-projection. ForagivenNV
cally,however,photocurrentsmayleadtolocalheatingofthe Z ±
center,wecandeterminewhetherp orp equalszerofrom
sample, and we attribute the leak between the left and lower X Y
thedependenceofthephotoluminescenceonthelinearpolar-
gates to the broadening of the PLE resonances observed in
ization of the 532nm repump beam (the photoluminescence
Fig.3ofthemaintextwhenlargerlateralvoltagesareapplied.
is a maximized when the light is polarized perpendicular to
theN-Vaxis). Itisthenusuallystraightforwardtodetermine
theexactprojectionfromtheslopeofthelongitudinaldcStark
ANALYSISOFDCSTARKSHIFTS componentν¯inresponsetoappliedvoltages,keepinginmind
that the rectified field points mainly out of plane. For exam-
The first step in the analysis of dc Stark shifts in our de- ple, we know from polarization measurements that the NV
vicesisadeterminationoftheNVcenter’sorientationinthe center of Fig. 1 projects in the X direction, and from the
±
diamond crystal. This may be any of the eight projections sign of ν¯ in response to V (Fig. 2c) we see that p = +1
X X
3
andp = 1,correspondingtothecrystaldirection[11¯1]as tweensampleandNV-centercoordinatesystemsisgivenby
Z
−
depictedintheschematicofFig.2b.
F =MF , (S1)
NV Sample
GiventheNV-centersymmetryaxis,thetransformationbe- whereMistherotationmatrix
p p √2p
1 X Y − Z
M= √3p p √3p p 0 . (S2)
√3− Y Z X Z 
√2p √2p p
X Y Z
 
ApplyingthistransformationfortheNVcenterinourlateraldevice,weobtainexpressionsforthedcStarkcomponentsν¯andδ
intermsofthelocalfieldinsamplecoordinates:
∆µ
hν¯=~ω0+ k √2FX FZ , (S3a)
√3 −
(cid:16) (cid:17)
hδ =√2 SEx − √µ⊥3 FX +√2FZ 2+ SEy −µ⊥FY 2 1/2. (S3b)
(cid:26)h (cid:16) (cid:17)i (cid:2) (cid:3) (cid:27)
ByexpressingthelocalfieldaccordingtoourmodelasF = portdynamicsofphotoexcitedcharges,andpotentiallyspatial
βVvˆ +β V ξ, we obtain a dependence on applied bias that inhomogeneities in the distribution of deep donors. Further-
| |
wecanquantitativelycomparetoourmeasurements. more, although we expect that substitutional nitrogen atoms
To reduce the number of free parameters, we fix the dominatetheelectrostatics,otherdefectcentersmayalsoplay
components of the dielectric unit vector vˆ based on elec- animportantrole,suchasvacancycomplexesunintentionally
trostatic simulations of our device using the COMSOL createdduringtheirradiationandannealingprocess.Basedon
MULTIPHYSICSr software. For a single set of mea- the electron irradiation dose used, we expect a vacancy con-
surements (e.g., ν¯ and δ as a function of bias along centration (before annealing) of 6 1013cm 3 [4], which
−
≈ ×
a single direction), this leaves eight free parameters: is roughly an order of magnitude less than the nitrogen con-
ω ,S ,S ,β∆µ ,µ /∆µ ,ξ ,ξ ,ξ . This equals centrationinthesesamples, andtheseacceptordefectsprob-
0 Ex Ey k ⊥ k X Y Z
thecombinednumberoffreeparametersexpectedfortheform ably have an effect on the transport of photoionized charge
(cid:8) (cid:9)
ofbothν¯andδ(i.e.,twolinesandtwohyperbolaeconstrained through the sample. Still, we can gather some quantitative
tomeetatV = 0)andsoresultsinawell-conditionedmini- informationaboutthephotoinducedchargedistributionsfrom
mizationproblem. Whenwehavemultiplemeasurementsof theNV-centerStarkresponse,whichwecancomparetoasim-
the same NV center, e.g., for the repump/no repump mea- plified‘band-bending’modeltreatingthedeviceasaSchottky
surements in Fig. 2d, we can constrain the parameters even diode.
further,andrequirethat ω ,S ,S ,β∆µ ,µ /∆µ are The top-gate geometry of device B is the simplest to ana-
0 Ex Ey k ⊥ k
commonforeachNVcenter,whileonlytherectificationvec- lyze, and as mentioned in the text we can compare the mag-
(cid:8) (cid:9)
tor ξ varies independently for each set. In the case of the nitudesofthedcStarkshiftsobservedinthatdevice(Fig.2a)
lateral measurements of Fig. 2c, we also allow the dielectric withthoseofdeviceA(Fig.2c)toestimatethelocalelectric
coefficientβ tovarybetweentheV andV measurements, fieldstrength. Assumingthatinthetop-gatedevicethelocal
X Y
andtheresultingbest-fitparametersforacombinedfitasde- electric field points only in the +Z direction, we relate the
scribedabovearelistedinTableI. Asexpected,therectified slope of ν¯ to the local electric field F = β V through the
Z Z
fieldpointsmainlyinthe+Z direction. relation
dν¯ β ∆µ
Z
= k, (S4)
dV √3h
Electrostaticsofthephotoinducedfields
where the factor 1/√3 appears due to the projection of the
Afulldescriptionofthephotoinducedfieldsinourdevices NV-centersymmetryaxisinthesample. Belowthethreshold
is beyond the scope of this work, especially since our phe- biasinFig.2a,dν¯/dV 0.06GHz/V. Incomparison,from
≈
nomenological model seems to capture the behavior impor- the fits to the lateral data in Fig. 2c described in the previ-
tant for controlling NV-center Stark shifts in these geome- ous section, we find that the dielectric response of device A
tries. Such a description would presumably need to account is β ∆µ /h 0.2GHz/V. Therefore the ratio of the
Lateral
k ≈
forthegategeometriesofourdevices,thevariationofoptical dielectricfieldindeviceAtotherectifiedfieldindeviceBis
intensity through the sample in a confocal geometry, trans- β /β 2,whilefromdielectricresponsealonethisra-
Lateral Z
≈
4
TABLEI.Best-fitparametervaluesfromfitsofourmodeltothedatainFig.2cinthemaintext,forStarkshiftsasafunctionofappliedbias
(VX,VY)inorthogonaldirections. Uncertaintiesareat95%confidencefromthefitalone, anddonotincludesystematicerrorsduetothe
somewhatstrongcovariancebetweenmanyoftheseparametersandtheuncertaintyinthefixeddirectionvˆ ofthedielectricfield. Basedon
electrostaticmodeling,weusevˆ =(0.998,0.04,0.07)and( 0.002,0.9998,0.02)fortheVX andVY dependence,respectively.
−
Common Direction-dependent Biasdirection
parameters parameters VX VY
ω /2π 0.66 0.03GHz β∆µ /h 0.334 0.002GHz/V 0.175 0.003GHz/V
0
S /h 5.06±0.03GHz ξ k 0±.15 0.01 0±.19 0.02
Ex ± X ± ±
S /h 0.78 0.06GHz ξ 0.43 0.02 0.30 0.02
Ey ± Y − ± − ±
µ /∆µ 1.41 0.02 ξ 1.01 0.01 1.60 0.02
Z
⊥ k ± ± ±
tioshouldbe 100, correspondingtoanenhancementofthe
≈
verticalelectricfieldbelowthetopgatebyafactorof 50.
≈
If we picture the top-gate device as a Schottky diode, this
comparison suggests that when negative (reverse) bias is ap-
plied, the potential drops across a distance of only 10µm
≈
ratherthanthefull0.5mmthicknessofthesample. Assum-
ing uniform ionization of deep donors with density N , the
d
equivalentSchottky‘depletionwidth’obtainedfromthesolu-
tiontoPoisson’sequationisgivenby[5]
2(cid:15)(cid:15) ϕ
0
w = | |, (S5)
d
s eNd
in terms of the Schottky barrier height ϕ and diamond’s di-
electric constant (cid:15) 5.7. For w 10µm and ϕ
d
≈ ≈ ≈
10V,thisestimateyieldsanionizedchargedensityofN
d
≈
6 1013cm−3, which is in agreement with a 10% ioniza- FIG.S3.PLEspectraasafunctionofgatevoltage,fortheNVcenter
× ≈
tionoftheanticipatedsubstitutionalnitrogenconcentrationof circledinFig.2d,bothwiththestandard532nmrepumpcycle(left)
afewpartsperbillion( 1 1015cm 3).Thisroughcalcula- andwithonlyintermittentrepumppulsesappliedatzerobias(right).
−
tionshowsthatthephot≈oin×ducedfieldsweobserveareconsis- The|Szitransitionfrequenciesreconstructedfromthefitsshownin
Fig. 2d are overlaid (dashed curves). Other resonances visible in
tentwiththeexpectedconcentrationofdeepdefects,although
these spectra correspond to spin-conserving optical transitions for
itdoesnotaccountfornonlinearitiesinthedistributionofpho- the Sx , Sy spinstates,asdescribedinthetext.
toionized charge. For example, we observe a qualitatively {| i | i}
similar enhancement of the Z-direction field when focussed
onNVcentersupto 50µmbelowthetopgate, suggesting
≈ resonancefrequenciesfromfitstothesePLEspectratocom-
thatthechargedistributionisnotconfinedtoalayernearthe
pute the dc Stark components ν¯ and δ plotted in Fig. 2d of
surfacegatebutratherfollowstheregionofhigheropticalin-
themaintext. ThesearemarkedbydashedcurvesinFig.S3,
tensity.
which are the resonance frequencies reconstructed from the
best-fit results of our model plotted in Fig. 2d. The analysis
leading to the fits is similar to that described above (in this
Theroleoftherepumpcycleonphotoinducedfields
case the NV-center projection is [1¯11]), and the best-fit pa-
rametersarelistedinTableII.
As described in the main text, we performed a control
experiment to investigate the influence of the 532nm re-
pump cycle on the rectified component of the local electric
field. Using the device shown in Fig. 2d, we apply a mi-
crowave current through a short-terminated waveguide reso- [1] B.B.Buckley,G.D.Fuchs,L.C.Bassett, andD.D.Awschalom,
nantwiththeground-state S S , S transitionat Science330,1212(2010).
z x y
2.878GHz.Thismaintains|amiix⇔ed{sp|insita|tediu}ringourmea- [2] T. Mu¨ller, I. Aharonovich, L. Lombez, Y. Alaverdyan, A. N.
Vamivakas, S. Castelletto, F. Jelezko, J. Wrachtrup, S. Prawer,
surements since, in the absence of the repump cycle, weak
andM.Atatu¨re,NewJ.Phys.13,075001(2011).
spin-nonconserving transitions would otherwise polarize the
[3] C.E.Nebel,M.Stutzmann,F.Lacher,P.Koidl, andR.Zachai,
spinawayfromresonancewiththeredlaser. InthePLEspec-
Diam.Relat.Mater.7,556(1998);F.J.Heremans,G.D.Fuchs,
tra(Fig.S3),wethereforeobservethespin-conservingoptical C.F.Wang,R.Hanson, andD.D.Awschalom,Appl.Phys.Lett.
transitionsforallthreetripletspinstates. Weisolatethe Sz 94,152102(2009).
| i
5
TABLEII.Best-fitparametervaluesfromfitsofourmodeltothedatainFig.2dinthemaintext,investigatingtheroleofthe532nmrepump
laser on the photoinduced field. As in Table I, uncertainties are quoted at 95% confidence from the fit, but do not account for covariance
betweenthefitparametersandthedirectionofthedielectricfield,fixedtovˆ =(0.97,0.04, 0.24)basedonelectrostaticmodeling.
−
Common Repump-dependent
parameters parameters Withrepump Withoutrepump
ω /2π 0.17 0.02GHz ξ 0.239 0.009 0.06 0.01
0 X
− ± − ± ±
S /h 2.34 0.09GHz ξ 0.12 0.01 0.13 0.02
Ex − ± Y ± ±
S /h 3.08 0.05GHz ξ 0.66 0.02 0.30 0.03
Ey ± Z ± ±
µ /∆µ 0.91 0.01
β⊥∆µ /hk 0.99 0.±01GHz/V
k ±
[4] D.J.Twitchen,D.C.Hunt,V.Smart,M.E.Newton, andJ.M. [5] C.Kittel,IntroductiontoSolidStatePhysics,7thed.(JohnWiley
Baker,Diam.Relat.Mater.8,1572 (1999). &Sons,Inc.,1996)p.574.