Single-shot readout of a single nuclear spin.

Abstract

Projective measurement of single electron and nuclear spins has evolved from a gedanken experiment to a problem relevant for applications in atomic-scale technologies like quantum computing. Although several approaches allow for detection of a spin of single atoms and molecules, multiple repetitions of the experiment that are usually required for achieving a detectable signal obscure the intrinsic quantum nature of the spin's behavior. We demonstrated single-shot, projective measurement of a single nuclear spin in diamond using a quantum nondemolition measurement scheme, which allows real-time observation of an individual nuclear spin's state in a room-temperature solid. Such an ideal measurement is crucial for realization of, for example, quantum error correction protocols in a quantum register.

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DOI: 10.1126/science.1189075
, 542 (2010);
329
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et al.Philipp Neumann,
Single-Shot Readout of a Single Nuclear Spin
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Single-Shot Readout of a Single
Nuclear Spin
Philipp Neumann,1Johannes Beck,1Matthias Steiner,1Florian Rempp,1Helmut Fedder,1
Philip R. Hemmer,2Jörg Wrachtrup,1* Fedor Jelezko1*
Projective measurement of single electron and nuclear spins has evolved from a gedanken
experiment to a problem relevant for applications in atomic-scale technologies like quantum
computing. Although several approaches allow for detection of a spin of single atoms and
molecules, multiple repetitions of the experiment that are usually required for achieving a
detectable signal obscure the intrinsic quantum nature of the spin’s behavior. We demonstrated
single-shot, projective measurement of a single nuclear spin in diamond using a quantum
nondemolition measurement scheme, which allows real-time observation of an individual nuclear
spin’s state in a room-temperature solid. Such an ideal measurement is crucial for realization of,
for example, quantum error correction protocols in a quantum register.
S
rated as quantum coprocessors. Much enthusiasm
arose when room-temperature nuclear magnetic
resonance (NMR) quantum computers were de-
veloped (1). However, these are essentially clas-
sical as they lack the ability to initialize and read
out individual spins at room temperature (2).
Recent efforts have focused on the development
of ultracold quantum processors like trapped ions
and superconducting qubits which operate at mil-
likelvin temperatures (3). Electronic and nuclear
spins associated with nitrogen-vacancy (NV) cen-
ters in diamond have been shown to be a room-
temperature solid-state system with exceptionally
long coherence times that fulfills most of the re-
quirements needed to build a quantum computer
(4–7).However,itlackedsingle-shotreadout(8),
and hence only the cryogenic version was con-
sidered to be applicable for most quantum infor-
mation applications. For example, projective
readout enables testing Bell-type inequalities
and active feedback in quantum error correction
protocols.Here,weexperimentallyshowedsingle-
shot readout of a single nuclear spin in diamond.
Our technique is based on the repetitive readout
of nuclear spins (9) and the essential decoupling
of the nuclear from the electronic spin dynamics
by means of a strong magnetic field (10).
The fluorescence time trace of a single NV
center shown in Fig. 1B represents the real-time
dynamics of a single nuclear spin and exhibits
well-defined jumps attributed to abrupt, dis-
continuous evolution of the nuclear spin state
ince the birth of quantum computing,
researchers have sought scalable room-
temperaturesystemsthatcouldbeincorpo-
(quantumjumps).Thespinusedinourexperiments
belongs to the nucleus of the nitrogen atom [14N;
nuclear spin I = 1 (11)] of a single NV defect in
diamond (Fig. 1B). In essence, the measurement
sequence consists of a correlation of the electron
spin state of the NV color center with the nuclear
spin state and a subsequent optical readout of
the electron spin, which exhibits the nuclear
spin state. Therefore, initially the electron spin is
optically pumped into the electron spin sublevel
j0e〉 (mS= 0) of its triplet ground state (S = 1) (8),
leaving the nuclear spin in an incoherent mixture
of its eigenstates ðjmI¼ 〉Þj−1n〉, j0n〉, and j1n〉
(here and below states are defined according to
electronandnuclearmagneticquantumnumbers,
mSand mI). The application of a narrowband,
nuclear spin state–selective microwave (MW) p
pulse flips the electron spin into the j−1e〉 state
conditional on the state of the nuclear spin. This
operationisequivalenttoacontrollednot(CNOT)
operation (Fig. 1A), in that it maps a specific
nuclear spin state onto the electron spin (e.g.,
j−1n〉j0e〉→j−1n〉j−1e〉, j0n〉j0e〉→j0n〉j0e〉).This
is possible because of the long coherence time of
the NV center, providing a spectral linewidth of
the electron spin transitions narrow enough to re-
solve the hyperfine structure. Because the fluores-
cence intensity differs by roughly a factor of 2 for
electron spin states j0e〉 and j−1e〉 (8, 12), these
target states can be distinguished by shining a short
laser pulse. This destroys the electron spin state but
leaves the nuclear spin state population almost un-
disturbed under the experimental conditions. Thus,
repeated application of this scheme allows non-
destructive accumulation of fluorescence signal in
order to determine the nuclear spin state optically.
The fidelity F to detect a given state in a
single shot [reaching F = 92 T 2% in our ex-
periments(13)]canbeextractedfromthephoton-
counting histograms (Fig. 2A), which show
distinguishable peaks corresponding to different
nuclear spin states. The fidelity is limited by the
measurement time (bounded by relaxation time
of the nuclear spin), fluorescence count rate, and
magnetic resonance signal contrast. Further im-
provement in readout speed can be achieved by
engineering of photon emission into photonic
nanostructures (14). A consecutive measurement
of the same spin state gives an identical result
with a probability of (F2) of ~82.5% (Fig. 2C).
Suchacorrelationbetweenconsecutivemeasure-
ments is the signature of so-called quantum non-
demolition(QND)protocols(15).Forthenitrogen
nuclear spin qubit initially in a superposition of
two states, the measurement affects its state by
projectionintooneoftheeigenstates,butdoesnot
demolish it (as happens with photons arriving at
a photomultiplier tube or fluorescent atoms that
are shelved in a dark state, which is not a qubit
state). Hence, the same nuclear spin eigenstate
can be redetected in consecutive measurements.
The difference between projective measure-
ment and a practical QND has been analyzed in
13rd Physics Institute and Research Center SCoPE, University
of Stuttgart, Pfaffenwaldring 57, Stuttgart 70550, Germany.
2Department of Electrical and Computer Engineering, Texas
A&M University, College Station, TX 77843, USA.
*To whom correspondence should be addressed. E-mail:
f.jelezko@physik.uni-stuttgart.de (F.J.); wrachtrup@physik.uni-
stuttgart.de (J.W.)
Fig. 1. Single-shot readout reveals quantum jumps of a single nuclear spin in real time. (A) Repre-
sentation of the single-shot readout scheme. (B) Normalized fluorescence time traces (gray) showing
quantum jumps of a single nuclear spin in real time. When MW pulses (controlled-NOT gates) are on, a
telegraph-like signal appears, revealing the projective nature of this measurement. Low fluorescence
intensity represents nuclear spin state j−1n〉, and high fluorescence intensity indicates j0n〉 or j+1n〉.
WhenMWpulsesareoff(uppertrace),thefluorescenceintensityremainshighbecauseitisnotcorrelated
with the nuclear spin state. Each data point was acquired by continuously repeating the readout
scheme for 5 ms (2000 repetitions).
0510
0.6
1.0
1.4
MW off
MW off
MW on
time (s)
relative fluorescence intensity

0.00.51.01.5
0.6
1.0
N
V
C
B
MW π pulse
|Ψn〉
|0e〉
repeat
AB
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detail (16, 17) and can be summarized as three
conditions that must be simultaneously fulfilled
in order to have a true QND measurement. Our
system observable is the nuclear spin%Iz, our
probeobservableistheelectronspin%Sz,andtheir
Hamiltonians are Hnand He, respectively (13).
The interaction Hamiltonian Hifor our case is
separable Hi= HA+ Hp, where HAdescribes the
hyperfine interaction and Hprepresents the MW
field applied in the experiment.
The first condition for QND is simply that
the probe observable%Szmust be measurably
influenced by the system observable%Iz that
we desire to measure. Therefore, the interac-
tion Hamiltonian Hihas to depend on Izand
must not commute with the probe observable
%Sz(½%Sz,Hi? ≠ 0) (16, 17). These demands are met
by the CNOT gate. The corresponding Hamil-
tonian Hp¼ W expðiwtÞ%Sx⊗j−1n〉 〈−1nj acts
for a time t and flips the electron spin by an angle
b = Wt only for the nuclear spin j−1n〉 subspace
(W, Rabi frequency; w, MW frequency). The
strength of the QND measurement can by tuned
by preparing the electron spin in a superposition
state rather than in an eigenstate before the action
of Hp(18).
The second QND condition requires that the
system observable state Izbe stable with respect
to back action of the measurement. This trans-
lates to the requirement that the system Hamil-
tonian must not be a function of the observable’s
conjugate (%Ixor%Iy) in order to avoid back action
of the measurement, which imposes a large un-
certainty on the conjugates. In our case, this con-
dition is fulfilled as long as the applied magnetic
field is exactly parallel to the NV center sym-
metry axis (13).
The third condition is that the probe and
system observables,%Szand%Izin our case, should
not be mixed by any interactions that are neither
intrinsic to the material nor created by the action
of the MW or laser probes (i.e., that the nuclear
spin is well isolated from the environment). In
other words (16, 17), the interaction Hamiltonian
must commute with the observable (½%Iz,Hi? ¼ 0).
Fulfillingthisconditionperfectlyisanimpossible
task for any experimental system, particularly in
the solidstate.However,defectcenter spinsindia-
mond are very close to an ideal system for QND
measurements. In the case of the NV center, the
nuclear spin–selective MW pulse on the electron
spin does not act on the nuclear spin subspace
(hence ½%Iz,Hp? ¼ 0). However, the hyperfine
coupling tensor A
¼contains contributions parallel
and perpendiculartothe symmetry axisoftheNV
center (A∥and A⊥), and the perpendicular com-
ponent is responsible for an undesirable mixing.
The first term of the hyperfine Hamiltonian HA¼
ð%Sþ%I−þ%S−%IþÞA⊥=2 þ%Sz%IzA∥ is noncommut-
ing with%Izand therefore induces nuclear-electron
spinflip-flopprocesses.Thismixingisresponsible
for the quantum jumps in Fig. 1B. The key to suc-
ceedingatQNDmeasurementsisthereforetomake
this jump time longer than the measurement time.
To quantify the hyperfine induced flip-flop
rate,assumeanisotropiccase(A∥≃ A⊥≃ A)and
usethe measuredA∥= 40MHzin theexcited state
(19, 20). Electron-nuclear spin dynamics occur
on a time scale of 2/A⊥~ 50 ns in the vicinity of
excited-state level anticrossing at magnetic field
B = 50 mT (19, 21) (Fig. 3A). Relaxation in the
ground state is expected to be slower owing to
a much weaker hyperfine coupling (13) and can
be neglected here. The relaxation process slows
down when the magnetic field along the NV
symmetry axis is increased owing to the grow-
ingenergymismatchbetweenelectronandnuclear
spin transitions due to increasing Zeeman shifts
(Fig. 3A). A detailed analysis (13) and exper-
imental data (Fig. 3B) show that the relaxation
rate g depends on the detuning d from the level
anticrossing(1.42GHz)asg ∼ ðA2
d2? (i.e., like a Lorentzian lineshape). Hence, we
expect a quadratic dependence of T1on the de-
tuning from the excited-state level anticrossing
⊥=2Þ=½ðA2
⊥=2Þþ
100140180
0
100
200
300
400
500
number of events
number of photons / 5 ms
threshold
100140 180
0
100
200
300
number of events
number of photons / 5 ms
100140180
0
20
40
60
80
0 200400600
0.2
0.4
0.6
probability for spin flip
rf pulse length (µs)
|Ψn〉
|0e〉
Rx(φ)
2000
|0n〉,|+1n〉
|0n〉,|+1n〉
|-1n〉
|-1n〉
|-1n〉
|0n〉,|+1n〉
ABC
Fig. 2. Readout fidelity and conditional gates using single-shot readout. (A) Photon-counting histogram
of a fluorescence time trace fitted by two Gaussian distributions (solid lines). Left and right peaks
correspond to the dark (j−1n〉) and bright (j0n〉, j+1n〉) states, respectively. By setting a threshold (red
line), the nuclear spin state j−1n〉 (fluorescence below threshold) can be distinguished from the other
nuclear spin states (fluorescence above threshold). For the given lifetimes at 0.65 T and fluorescence
levels, the fidelity to detect a given state correctly is 92 T 2%. (B) Conditional nuclear spin Rabi
oscillationsandhistograms.ThewirediagramontopillustratestheconditionalRabisequence.Onlyifthe
measurement outcome is j−1n〉, a resonant radio-frequency (rf) pulse of certain length is applied on the
nuclear spin transitionj−1n〉↔j0n〉 and a subsequent measurement is performed. Otherwise the sequence
is restarted immediately. (C) Conditional histograms. Two consecutive QND measurements have a high
probability (≈82%) of giving the same outcome (lower histogram). If a rf p pulse is applied after detecting
j−1n〉, this probability drops to ≈33% (upper histogram). Possible reasons for the Rabi contrast of <1 are,
for instance, the setup instability and imperfect initialization and readout of the electron spin.
50
|0e〉
|+1e〉
|-1e〉
EEZ
(GHz)
B (mT)
|-1n〉
0
450
1.42
|0n〉
|+1n〉
40MHz
50 250450650
0
20
40
60
80
spin lifetime T1 (ms)
magnetic field B (mT)
-11.0
spin flip
from ...
... to ...
0.2
0.4
0.6
0.8
spin flip probability
30
60
90
120
spin flip rate γ (Hz)
|+1n〉
|0n〉
|-1n〉
|+1n〉
|0n〉
|-1n〉
00.20.4
t (s)
0.6
|+1n〉
|0n〉
|-1n〉
ABC
Fig. 3. Tuningnuclearspindynamics.(A)Excited-statefinestructureasafunctionofthemagneticfieldB
(parallel to the NV axis). The inset shows the14N hyperfine structure (splitting of ~40 MHz). (B)
Experimental results (black dots) confirm the predicted quadratic dependence of nuclear spin lifetime on
the detuning from the level anticrossing [red line, T1= 230 ms·mT−2(B − 50 mT)2]. (C) At every point in
time, all three nuclear spin states were measured directly and atime trace was acquired. The upper graph
shows a part of the corresponding quantum state trajectory (computer fit to the data as in Fig. 1C). The
lower graph is the transition matrix calculated from analyzing ~10,000 quantum jumps. Off-diagonal
elements represent spin-flip probabilities and diagonal elements represent the probability of remaining
unchanged. The probabilities are proportional to spin flip rates under continuous application of the
readout sequence. Error bars indicate the uncertainty in nuclear state lifetime measurements.
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(T1¼ 1=g ∼ d2for d ≫ A2
confirm this behavior (Fig. 3B). This dependence
also explains why quantum jumps were not ob-
served in previous experiments with NV centers
performed at low magnetic fields [similar mag-
netic field–enabled decoupling of nuclear spin
was proposed recently for alkaline earth metal
ions (10, 22)]. The dominance of flip-flop pro-
cesses is also visible in the quantum state tra-
jectoryofthenuclearspinshowninFig.3C(top).
Here, jumps obey the selection rule DmI¼ T1
imposed by the flip-flop term HA. From analyz-
ing the whole quantum state trajectory, a matrix
showing the transition probabilities can be
obtained (Fig. 3C, bottom).
Single-shot measurement of a single nuclear
spin places diamond among leading quantum
computer technologies. The high readout fidelity
(92%) demonstrated in this work is already close
tothethresholdforenablingerrorcorrection(23),
although the experiments were carried out in a
moderate­strength magnetic field. Even though
the optical excitation induces complex dynamics
in the NV center (including passage into singlet
electronic state), the nuclear spin relaxation rates
are defined solely by electron-nuclear flip-flop
processesinducedbyhyperfineinteraction.There-
fore,weexpectimprovementofT1bytwoorders
of magnitude (reaching seconds under illumina-
tion) when a magnetic field of 5 T is used. This
will potentially allow readout fidelities compara-
ble with that achieved for single ions in traps
(24). The present technique can be applied to
multiqubit quantum registers (5, 6, 25), enabling
⊥). Experimental data
tests of nonclassical correlations. Finally, single-
shot measurements open new perspectives for
solid-statesensingtechnologies.Spinsindiamond
are considered to be among the promising candi-
datesfornanoscalemagneticfieldsensing(26,27).
Currently their performance is limited by photon
shot noise (26): “Digital” QND will provide im-
provement over conventional photon counting in
the case of short acquisition time. This requires
thattheelectronspinstateusedformagneticfield
sensingcanbemappedontothenuclearspinwith
high accuracy, but this was already shown to be
practical in NV diamond (5).
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28. We thank F. Dolde for fabrication of microwave
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J. Mayer and P. Bertet for helpful information on
QND measurements in superconducting qubits; and
M. D. Lukin, J. Twamley, F. Y. Khalili, and J. O’Brien for
comments and discussions. We thank G. Denninger for
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Supporting Online Material
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Methods
SOM Text
Figs. S1 to S6
References
3 March 2010; accepted 21 June 2010
Published online 1 July 2010;
10.1126/science.1189075
Include this information when citing this paper.
Strain-Induced Pseudo–Magnetic
Fields Greater Than 300 Tesla in
Graphene Nanobubbles
N. Levy,1,2*† S. A. Burke,1*‡ K. L. Meaker,1M. Panlasigui,1A. Zettl,1,2F. Guinea,3
A. H. Castro Neto,4M. F. Crommie1,2§
Recent theoretical proposals suggest that strain can be used to engineer graphene electronic states
through the creation of a pseudo–magnetic field. This effect is unique to graphene because of its
massless Dirac fermion-like band structure and particular lattice symmetry (C3v). Here, we present
experimental spectroscopic measurements by scanning tunneling microscopy of highly strained
nanobubbles that form when graphene is grown on a platinum (111) surface. The nanobubbles
exhibit Landau levels that form in the presence of strain-induced pseudo–magnetic fields greater
than 300 tesla. This demonstration of enormous pseudo–magnetic fields opens the door to both
the study of charge carriers in previously inaccessible high magnetic field regimes and deliberate
mechanical control over electronic structure in graphene or so-called “strain engineering.”
G
phene’s distinctive properties arise from a linear
band dispersion at low carrier energies (3) that
leads to Dirac-like behavior within the two-
dimensional (2D) honeycomb lattice—charge
carriers travel as if their effective mass is zero
raphene, a single atomic layer of carbon,
displays remarkable electronic and me-
chanical properties (1, 2). Many of gra-
(1). An intriguing recent prediction is that a dis-
tortionofthegraphenelatticeshouldcreatelarge,
nearly uniform pseudo–magnetic fields and give
rise to a pseudo–quantum Hall effect (4). Where-
as an elastic strain can be expected to induce a
shiftintheDiracpointenergyfromlocalchanges
in electron density, it is also predicted to induce
an effective vector potential that arises from
changes in the electron-hopping amplitude be-
tweencarbonatoms(5).Thisstrain-inducedgauge
field can give rise to large pseudo–magnetic
fields (Bs) for appropriately selected geometries
of the applied strain (1, 6). In such situations, the
charge carriers in graphene are expected to cir-
culate as if under the influence of an applied out-
of-plane magnetic field (7–10). It has recently
been proposed that a modest strain field with
triangularsymmetrywillgiveapproximatelyuni-
form, quantizing Bsupward of tens of tesla (4).
Here, we report the measurement of Landau
levels (LLs) arising from giant strain-induced
pseudo–magneticfieldsinhighlystrainedgraphene
nanobubbles grown on the Pt(111) surface. Lan-
1Department of Physics, University of California Berkeley,
Berkeley,CA94720,USA.2MaterialsScienceDivision,Lawrence
BerkeleyNationalLaboratory,Berkeley,CA94720,USA.3Instituto
de Ciencia de Materiales de Madrid (CSIC), Madrid 28049,
Spain.4Department of Physics, Boston University, Boston, MA
02215, USA.
*These authors contributed equally to this work.
†Present address: Center for Nanoscale Science and Technology,
National Institute of Standards and Technology, Gaithersburg,
MD 20899, USA.
‡Present address: Department of Physics and Astronomy and
Department of Chemistry, University of British Columbia, Van-
couver, BC V6T 121, Canada.
§To whom correspondence should be addressed. E-mail:
crommie@berkeley.edu
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