Mapping spin coherence of a single rare-earth ion in a crystal onto a single photon polarization state

0.44 MB·English

by  Roman Kolesov

Mapping spin coherence of a single rare-earth ion in a crystal onto a single photon
polarization state
Roman Kolesov, Kangwei Xia, Rolf Reuter, Rainer St¨ohr, Tugrul Inal, Petr Siyushev, and J¨org Wrachtrup
3. Physikalisches Institut, Universita¨t Stuttgart and Stuttgart Research Center of Photonic Engineering (SCoPE),
Pfaffenwaldring 57, Stuttgart, D-70569, Germany
We report on optical detection of a single photostable Ce3+ ion in an yttrium aluminium garnet
(YAG) crystal and on its magneto-optical properties at room temperature. The quantum state of
anelectronspinoftheemittinglevelofceriumioninYAGcanbeinitialized bycircularlypolarized
3
laser pulse. Furthermore, its quantum state can be read out by observing temporal behaviour of
1
circularly polarized fluorescence of the ion. This implies direct mapping of the spin quantum state
0
of Ce3+ ion onto the polarization state of the emitted photon and represents one-way quantum
2
interface between a single spin and a single photon.

n
a
J
Rare-earthdoped optical materials are known to have level with the peak absorption around 460 nm. Taking

2 outstanding properties for optical information storage into account 60 ns lifetime of the fluorescence and al-
2
and processing, both classical [1] and quantum [2–4]. In most unity quantum efficiency [6], a single Ce3+ ion is

thatrespect,the mostvaluablefeature ofrare-earthions expected to emit 1.6 × 107 photons per second. This
]
i is that the quantum transitions between their electronic amount of light can be easily detected by means of con-
c
s states and nuclear hyperfine levels have extremely high focal microscopy. In order to distinguish individual ions
-
l quality factor due to efficient screening of their optically inacrystal,thedistancebetweenthemshouldbegreater
r
active 4f electrons from the surrounding crystalline en- thantheresolutionofthemicroscoperesultinginamaxi-
t
m
vironment by outer lying 5s and 5p electronic shells. As mumconcentrationofceriumof36ppb(partsperbillion)
. a result, rare-earth ions in optical crystals have demon- relative to yttrium. This value sets the absolute upper
t
a strated benchmark performance in storing quantum in- limit on the concentration of cerium impurity. In turn,
m
formation for over a second [2], storing and retrieving any yttrium-based crystal contains trace amounts of all
- quantum state of a single photon [3], and quantum en- rare-earth elements including cerium, so that only the
d
tanglement [4], etc. In these applications, the quantum YAG crystals of highest purity can be used for isolation
n
o state of a single flying qubit (a single photon) or of a of a single emitting ion.
c pair of entangled flying qubits (a pair of entangled pho-
[ tons) is mapped onto an ensamble of rare-earth ions. Inthepresentstudy,weusedthesamecrystalinwhich

1 However, another challenging task of interfacing a sin- we detected single praseodymium ions in our previous
v gle flying qubit with a single stationary qubit is very publication[5](ultra-pureYAGcrystalproducedbySci-
5 hard to address. The reason is that the high Q-factor entific Materials Corp., boule 14-12). Optical detection
1 of electronic transitions of rare-earth ions inevitably re- of a single cerium center was performed in a home-built
2
sults in very low photon flux emitted by an individual confocalmicroscope operating at roomtemperature (see
5
. ion. This, in turn, makes single rare-earth ions in crys- Supplementary Fig. S1). We used frequency-doubled
1 tals very hard to detect. A solution to this problem [5] output of a femtosecond Ti:Sapphire laser operating at
0
is to detect the emission originating from strong parity- ≈920nmasanexcitationsource. Therepetitionrateof
3
1 allowed4f(n−1)5d→4fntransitionyieldinghighphoton frequency-doubled pulses was reduced from the original
: flux. 76MHz to a few MHz rate by a pulse-picker. The flu-
v
orescenceofceriumionswassplitintotwopaths andde-
i In the present work, we optically address for the first
X tectedby twosingle-photon-countingavalanchephotodi-
time single electron spins of Ce3+ ions in a crystal. We
r odes. Inthisway,aHanbury-BrownandTwisssetupwas
a show that the electron spin of an ion can be prepared in
arranged in order to allow photon correlation measure-
a coherent state by circularly polarized laser excitation.
ments. The detection wavelength range was restricted
Furthermore, it is shown that spin coherence can be ef-
between 485 nm and 630 nm. While the short wave-
ficiently mapped onto the polarization state of a photon
length boundary is needed to reject the excitation light,
emitted by a Ce3+ ion. Thus, we demonstrate a one-
the long wavelength cut-off was introduced in order to
waycoherentinterfacebetweenasinglespinandasingle
block fluorescence of Cr3+ impurity ions present in the
photon.
crystal. The resulting scanning image of the crystal is
Ce3+ : YAG is a very efficient scintillator emitting in showninFig.1a. Eachindividualbrightspotcorresponds
green-yellowspectralrange(peakemissionisat550nm) to a single cerium ion. Several tests were performed to
with quite short lifetime (∼ 60 ns). The fluorescence confirm that: 1) photon corellation measurements per-
of Ce3+ can be efficiently excited by optical pumping formed on these spots show pronounced antibunching at
into the phonon absorption sideband of the lowest 5d zero delay time between the count on two detectors in-
2
a) the contratry, the structure of the excited 5d electronic
1mm
b) levels is dominated by crystal field splitting slightly per-
60
turbed by spin-orbit interaction. For the 5d levels the
stnuoC 4500 electron spin thus is a good quantum number while in
ecnedicnioC 1230000 tmshitoeiom4nefsntbsutematwt.eesTenthhitseh,esinpgitnruoruinsn,dhsiug4ghfglyeasntmdsitxthheadetewtxhicetihtoeptdhtie5cdaolrltebrviatenals-l
0 500 1000
Time Delay (ns) shouldbe accompaniedby aflip ofa Ce3+ electronspin.
c) d) Owing to its spin-flip optical transitions, Ce3+ : YAG
)stinU .brA( ytisnetnI ecnecseroulF1110002340 100 2TT0i1m=06e3 (.n83s 0n)0s 400 500 )stinU .brA( ytisnetnI ecnesceroulF00112.....05050450 50W0avele5n5 g0th (nm6)00 650 cpcippmnrrrooveyyellneaassvrtttrrisaaoiizzeollusaefwsedtlffeCiyioxtoehenchpbtityot:,bihcfiiYdta.eteilhA.resfieetxGmcretootleadpncrgm,tnrgniywaceesFlaaattlasmisazurfilidaarneieegdlgnmmdnadteyoeuphtnnicreectseofftmdpfioreaaecfabgltttdty,eaehdrtaieaii.anpeemlxg.pcipblartiyeecrhgrodurncitolmeiaa[ru7trtceig]licun.yohltnTamaptrlhhooollyyee--f
larized laser pulse [8]. In this work, the magnetization
FIG. 1: Detection of a single Ce3+ ion in a YAG crystal.
a) Scanning confocal image of Ce3+ centers in a nominally was attributed to non-equilibrium population of the two
pureYAGcrystal. b) Photon correlation signal taken on the spin levels of Ce3+ ion in its lowest 5d state. Further-
markedspotonFigurea)withapulsedlaserexcitation. The more, it was shown that the non-equilibrium spins ex-
peak at zero time delay is much weaker than the other two periences coherent Larmor precession in the externally
indicatingthattheemitterisindeedasinglequantumobject. applied magnetic field. However, direct detection of the
c) Fluorescence decay signal taken on the same spot reveals
magnetization can only be used to study the coherent
thelifetime of 64ns in agreement with theknown lifetime of
spin behaviour of an ensamble of spins, but inapplicable
lowest5dstateofCe3+ inYAG.d)Thespectrumoftheemis-
to study an individual cerium ion since its magnetic sig-
sion of thesame spot (lower curve,black line) well correlates
with the fluorescence spectrum of a bulk Ce : YAG crystal nalistooweaktobedetectable. Ontheotherhand,since
(upper curve, red line). The arrows indicate the excitation theCe3+ spincanbeorientedbychosingtheappropriate
wavelength. polarizationoftheexcitationlight,thepolarizationofthe
ceriumion fluorescencealso depends onthe spin state of
the emitting 5d level. A quantitative understanding of
dicating asingle quantumemitter givingrise tothe fluo- this dependence requires the knowledge of the orienta-
rescence (see Fig.1b); 2) the fluorescence lifetime of each tionsofthedipolesassociatedwiththeopticaltransitions
spotiscloseto60nsinagreementwiththe lifetime data betweenthe4f andthelowest5dKramer’sdoublets.The
takenonhighlydopedCe:YAGcrystals(seeFig.1c);2) result of a detailed calculation (see Supplementary Ma-
the emission spectrum is the same as that of the highly terial) is depicted in Fig.2b and in Supplementary Fig.
doped Ce:YAG crystals (see Fig.1d). The typical pho- S2. Sincetheratiooftheoscillatorstrengthsofthetran-
toncountrateonthe two detectorsproducedbya single sitions |4f(1)↓i↔|5d(1)↑i and |4f(1)↑i↔|5d(1)↓i is
Ce3+ ionwas40−50kcounts/swiththepulserepetition 0.284/0.0007 ≈ 400 for σ+/σ− polarizations, circularly
rate 7.6MHz. The ions are photostable for many hours polarized light can excites Ce3+ ion from its lowest 4f
of continuous illumination and show no blinking. doubletintooneofthe5dspinstates400timesmoreeffi-
In order to get insight into the optically excited spin ciently than into the other spin state resulting in almost
dynamics of cerium in YAG, we consider the electronic perfect spin polarization in the excited state. In turn,
energylevelstructureofCe3+ :YAGindetail. Ce3+ ion the emissionoriginatingfromoneofthe spinsublevelsof
hasonlyoneunparedelectronwhosegroundstateis4f1. thelowest5dstateandterminatingatthelowest4f dou-
The 14-fold degeneracy of that state (7-fold degeneracy blet should be circularly polarized. This transition cor-
due to the orbital momentum times doubly degenerate responds to the zero-phonon line (ZPL) of Ce3+ : YAG
spin) is lifted by the combined action of spin-orbit cou- at489nm[9]. Anyrelaxationprocessleadingtospinflip
pling and the crystal field (see Fig.2a). Overall, the 14- of the 5d emitting state should give rise to the opposite
folddegenerate4f1 manifold issplit into 7spindoublets circularpolarizationoftheemittedfluorescenceasshown
(socalledKramer’sdoublets)whicharegroupedintotwo inFig.2c. Ifanexternalmagneticfieldisappliedperpen-
sub-manifolds, 2F and 2F , containing 3 and 4 dou- diculartothesystemquantizationaxis,theexcitedstate
5/2 7/2
blets respectively. The energy difference between 2F spinstartsprecessingatLarmorfrequencydefinedbythe
5/2
and 2F is mostly defined by spin-orbit coupling while magnitudeofthefieldandtheg-factorofthe5d(1)state:
7/2
the splitting within the manifolds is determined by the ω = µBg⊥B⊥/¯h. This leads to oscillatory behaviour of
crystal field. The degeneracy of the Kramer’s doublets the σ+ and σ− components of the fluorescence (see blue
can only be lifted by an external magnetic field. On curve on Fig.2c). Any decoherence process shortens the
3
lifetime of oscillations (see Fig.2d). In case of Ce3+ ion a ) 2D b)
5/2
in YAG the dephasing arises from the hyperfine interac- 5d(1)↓ 5d(1)↑
tion with the surrounding27Al nucleiproducing random 5d1 2D3/2
mmaaUggnnnfeeottriicctufifineealltddeliyas,tetsththieemZalotPceLadtitooofnbCoefe≈3t+h4e0:cGYerA[i8uG]m. iisonn.otTohbis- 489 nm σ+=0.00σ0- =70 .286 σ=+0.2σ86=- 0.0007
2F
7/2
servable at room temperature, i.e. the emission into the
lowest 4f Kramer’s doublet (see Fig.2b) cannot by dis- 4f1 Free ion 2F5/2 4f(1)↓ 4f(1)↑
SO Coupling
criminated from the emission terminating at other 4f CF Spli!ng
states. Indeed, the presence of the other 4f states de- c)
teriorates the contrast of the spin-dependent fluorescent 5d(1)↓ 5d(1)↑ 5d(1)↓ 5d(1)↑ 5d(1)↓ 5d(1)↑
signal. This can be seen from the fact that the sum of s- s+
s+ s+
thedipolestrengthscorrespondingtothe emissionofthe
two circularly polarized components are equal for both 4f(1)↓ 4f(1)↑ 4f(1)↓ 4f(1)↑ 4f(1)↓ 4f(1)↑
5d spin states (see Supplementary Table S1). Thus, by 0.20
s)
detecting the full fluorescence signal it is impossible to nit
U
reveal the emitting spin state of the 5d level. However, b. 0.15
sInpepcatrratilcfiulltaerr,inthgeoefmthisesieomnistseiromninimatpinrogvaest tthhee sleitvuealstibone-. nsity (Ar 0.10 σ+
lionnggoinnglytoththeew2aFv5e/l2enmgatnhisfoslhdocratenrbtehsaenpa5r5a0tendmby. dUetnedcetr- nce Inte 0.05
these circumstances,the contrastofthe spindependence sce σ−
e
of the circularly polarized fluorescence signal can be re- or
u 0.00
stored. The calculated time traces corresponding to the Fl 0 10 20 30 40 50
Time (ns)
experimentalsituationareindicatedinFigs.3a-c. Hereit
d)
isassumedthattheexcitationofceriumionsandthe de- 0.20 cos(ωt)|5d(1)↓〉- cos(ωt)|5d(1)↑〉+
tectionoftheir fluorescencearearrangedalongthe (111) nits) sin(ωt) |5d(1)↑〉 sin(ωt) |5d(1)↓〉
crystallographic axis of YAG ((111) was the orientation b. U 0.15 s- s+
of the crystalused in the experiment) while the external Ar
y (
mtoatghniestiacxfiise.ldTihseapsppilniedreelaitxhaetriopnaraatlltehleorrapteerp1e/n2d8icnusl−a1r ntensit 0.10 4f(1)↓ 4f(1)↑
[8]andspindephasingintherandomhyperfinemagnetic nce I 0.05 σ+
field are taken into account. sce σ
Experimental observation of the excited state dynam- ore −
u 0.00
icsofceriumionsisnowstraightforward. Individualions Fl 0 5 10 15 20
Time (ns)
identifiedintheconfocalmicroscopearenowexcitedwith
acircularlypolarizedlaserpulses. Thepolarizationofthe FIG.2: ElectroniclevelstructureofCe3+ ioninaYAGcrys-
fluorescencedetectedwithinthewindow485nmthrough tal. a) Electronic 4f1 and 5d1 shells are split by a combined
550nmisalsochosentobeeitherσ+ orσ−. Anexternal action of spin-orbit coupling and the crystal field. While in
magnetic field is applied either parallel or perpendicular thelower 4f1 state spin-orbit coupling dominates, in theup-
to the excitation beam propagation direction. The re- per5d1 states themajor contribution tothesplitting isfrom
sults of measurements are shown in Fig.3d-f. With the the crystal field. It causes significant red shift of the posi-
tions of the 5d levels. b) Strengths of the transition dipoles
magneticfieldorientedalongthepropagationdirectionof
between the lowest 4f and the lowest 5d Kramer’s doublets.
theexcitationbeam,theamountsofthefluorescencecor-
The quantization axis is chosen along the z-axis of the local
respondingtoσ+ andσ− polarizationssignificantlydiffer frameoftheceriumsite[10]. c)Calculatedtimetracesofthe
in the beginning of the decay indicating non-equilibrium fluorescence corresponding to the ZPL of Ce3+ once the ion
populations of the excited spin-up and spin-downstates. ispumpedintooneofthelowest5dspinsublevels(leftinset).
The decay traces merge after some time. This means The magnetic field is along the z-axis of the local frame of
that the spin populations equilibriate due to some spin- cerium site. The σ− polarization (red curve) builds up due
flip processes, being most probably related to Orbachor to spin relaxation (central inset) while the σ+ polarization
(black curve) declines until it reaches the level of σ− polar-
phononRamanrelaxation. Theexponentialfittothedif-
ization (right inset). d) Calculated fluorescence oscillations
ferencebetweenthe spin-upandspin-downdecaysignals
with the external magnetic field applied along the x-axis of
gives the decay constant of T1 =28ns. This spin-lattice the local frame of cerium site. Randomly oriented hyperfine
relaxation lifetime is with excellent agreement with the field produced by the27Al nucleicauses fast dephasing.
previouslyreportedvalue[8]. Incaseofthemagneticfield
being perpendicular to the excitation beam propagation
4
a) )stinU .brA( ytisnetnI ecnecseroulF0000000.......001122305050500ss-+ 10 T20ime ( n3Bks0 ) |||| ((11411011)) 50 d))stnuoC( ytisnetnI ecnecseroulF11205050000000000 ss-1+0 T2im0e (ns3)0 40 50 ergioicnnomarpgooletiumhntmttneheaedtedgmeprmspcoootrparhsuyystoensiertbdtsaoaiditlnm4liuut.feiyrdleTaostotrwhoafatenttaeoewlffimlt-thtocoehhiinpcueecthtnsriiootycCannaolOeellego3dreapw+bndrriaidenesccvrpsgheuitiosnfelpsotumisrrrsneoplwsgylceaieenroxdsragfeseetlscmeu[oe1frsbroa2epintsus]ait.snmitwinCanoeosropdpttuotheaililnddet--
b))stinU .brA( ytisnetnI ecnecseroulF00000000........00112233050505050ss+- 5 Time1 0( nskB) |||| (1(1151110)) 20 e) Fluorescence Intensity (Counts)11205050000000000 ss-+5 Time1 0(ns) 15 20 eohitusnairresnttntirongihegelgonsleietscqimsieCnluieZcetalnaio3Pnmt+twtLeue[-1i.sm[wo5p1nF]o4induu]ianorlcwndttrrhsdoyaaeus[rlrs1tlelmtdoa3-uwel]o.ddahryrroeIotan,nshomtea-ftsdadutilotdtoriikpsnrceere,ame,sdlosalfaypioclnigtrrzginiyenceesactxttshrlaaopeemld-ialonieispnp-otepleetneihct,cmtheoayimteoaltonttipdnesrrersiouoeiicfaonpmolna---.
c) )stinU .brA( ytisnetnI ecnecseroulF0000000.......001122305050500ss-+10 T2i0me (n 3skB)0 =|0| (14101) 50 f) )stnuoC( ytisnetnI ecnecseroulF1105500000000ss-+10 T2im0e (ns3)0 40 50 [1] (S1H16o.95c9.8L3iA()n1;m,9R9.T5.B.)Y;W9aY,na.o9Sn,9.g2MB, (aa.1inM9ad9ni2tdT)su.RWn.a.KgaMa,cohasrnsudb.eONrgp..tU.OLepseutt.tg.iL.1eJ8t.,t.1O12p80t9.,
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