-
Protecting quantum spin coherence of nanodiamonds in living
cells
Q.-Y. Cao,1, 2 P.-C. Yang,1, 2, ∗ M.-S. Gong,1, 2 M. Yu,1, 2 A.
Retzker,3 M. B. Plenio,4, 2
C. Müller,5 N. Tomek,5 B. Naydenov,5 L. P. McGuinness,5 F.
Jelezko,5, 2 and J.-M. Cai1, 2, †
1School of Physics and Wuhan National Laboratory for
Optoelectronics,Huazhong University of Science and Technology,
Wuhan 430074, China
2International Joint Laboratory on Quantum Sensing and Quantum
Metrology,Huazhong University of Science and Technology, Wuhan
430074, China
3Racah Institute of Physics, The Hebrew University of Jerusalem,
Jerusalem, 91904 Givat Ram, Israel4Institut für Theoretische
Physik & IQST, Albert-Einstein Allee 11, Universität Ulm,
D-89081 Ulm, Germany
5Institut für Quantenoptik & IQST, Albert-Einstein Allee
11, Universität Ulm, D-89081 Ulm, Germany(Dated: February 13,
2020)
Due to its superior coherent and optical properties at room
temperature, the nitrogen-vacancy(N-V ) center in diamond has
become a promising quantum probe for nanoscale quantum
sensing.However, the application of N-V containing nanodiamonds to
quantum sensing suffers from theirrelatively poor spin coherence
times. Here we demonstrate energy efficient protection of N-V
spincoherence in nanodiamonds using concatenated continuous
dynamical decoupling, which exhibitsexcellent performance with less
stringent microwave power requirement. When applied to
nanodia-monds in living cells we are able to extend the spin
coherence time by an order of magnitude to theT1-limit of up to
30µs. Further analysis demonstrates concomitant improvements of
sensing per-formance which shows that our results provide an
important step towards in vivo quantum sensingusing N-V centers in
nanodiamond.
PACS numbers: 42.50.Dv, 07.55.Ge, 03.67.-a, 42.50.-p
I. INTRODUCTION
Nitrogen-Vacancy (N-V ) centers in diamond exhibitstable
fluorescence and have a spin triplet ground state,which can be
coherently manipulated by microwave fields[1]. Observation of
spin-dependent fluorescence providesan efficient way to readout the
spin state of N-V s. Theenergy splitting of the N-V spin depends on
physical pa-rameters, such as magnetic field [2–4], electric field
[5, 6],temperature [7–10] and pressure [11, 12]. A variety
ofquantum sensing protocols for precise measurement ofthese
physical parameters in different scenarios have beendeveloped
[13–26]. These protocols are all based on de-termining the N-V spin
energy splitting, which is whythe measurement sensitivity is
limited by the N-V spincoherence time.
Spin coherence in bulk diamond is mainly affected bysurrounding
electronic impurities (P1 centers) and nu-clear spins (natural
abundance of 13C isotope). The spinreservoir can be eliminated by
using isotopically engi-neered high-purity type IIa diamond [27].
In order tomitigate the influence of any residual impurities,
pulseddynamical decoupling has been widely exploited to pro-long
spin coherence time [28–30]. Its excellent perfor-mance when
applied to N-V s in bulk diamond is a re-sult of the quasi-static
characteristics of the spin reser-voir in bulk diamond and the high
available microwavepower. Unfortunately, these two factors may not
be sat-isfied for N-V centers in nanodiamonds, which are re-quired
for sensing applications in vivo. N-V s containedwithin
nanodiamonds typically exhibit poor spin coher-ence time, which has
been attributed to nanodiamond
surface spin noise and electric charge noise that
includeprominent high frequency components. Preserving thecoherence
of N-V s in nanodiamonds becomes even moreproblematic when they are
located in biological environ-ments which presents additional noise
sources. The mi-crowave power available to decouple N-V s within
livingcells can be limited by the large distance between mi-crowave
antenna and nanodiamond, and the damagingeffects that microwave
absorption may have on biologicaltissue. Therefore, the development
of an energy efficientstrategy to prolong coherence time of N-V s
in nanodia-mond under the constraint of limited microwave
powerrepresents a significant challenge for efficient
quantumsensing protocols for biology and nanomedicine [8,
31–35].
In this work, we address this key challenge with
theimplementation of concatenated continuous dynamicaldecoupling
(CCDD), which employs a microwave driv-ing field consisting of
suitably engineered multi-frequencycomponents [36–38], to prolong
coherence time of N-V scontained within nanodiamonds. The purpose
of themain frequency component of the microwave drive is tosuppress
fast environmental noise, while the other weakerfrequency
components compensate power fluctuations inthe main frequency
component. The key advantage ofCCDD compared to pulsed schemes is
that the decou-pling efficiency achievable at the same average
power (asquantified by the effective Rabi frequency Ω̄2 = 〈Ω2〉
av-eraged over time) is predicted theoretically to be superiorto
pulsed schemes [35]. We demonstrate experimentallythat CCDD
achieves a performance that significantly ex-ceeds that of pulse
dynamical decoupling strategies given
arX
iv:1
710.
1074
4v3
[qu
ant-
ph]
12
Feb
2020
-
2
the same microwave energy consumption. We show thatCCDD prolongs
coherence time of N-V s in nanodiamondup to tens of microseconds at
which point it reaches thelimit imposed by the N-V spin relaxation
time T1 in thesenanodiamonds inside living cells. Our result
representsan important step towards the development of
quantumsensing for in vivo applications with high achievable
sen-sitivity, and also demonstrates wide applications of quan-tum
control using amplitude and phase modulated driv-ing field [39,
40].
II. PROTECTING COHERENCE OF N-V SPININ NANODIAMOND
In our experiment, we use nanodiamonds obtained bymilling of
HPHT diamond from Microdiamant with di-ameters of approximately 43±
18 nm, as measured withatomic force microscope, see Fig.1(a-b). We
apply astatic external magnetic field of strength B along theN-V
axis, which leads to two allowed N-V spin transi-tions (ms = 0 ↔ ms
= +1 and ms = 0 ↔ ms = −1).The corresponding optically detected
magnetic resonance(ODMR) measurement is shown in Fig.1(c). We
firstcharacterize the coherence properties of single N-V cen-ters
in nanodiamonds by performing spin echo measure-
0 2 4 6 8T ( s)
0.4
0.6
0.8
1.0
2700 2800 2900 3000 3100
0.8
0.9
1.0(a) (c)
(b) (d)
10 20 30 40 50 60 70 80Size (nm)
0
10
20
30
40
Num
ber
0
+1
�12�Bk
!�1!+1
T
2
T
2
532 nm 532 nm
arb.
uni
ts
0 10
05
10
5x (μm)
y (μ
m)
Figure 1. Characteristics of N-V s in nanodiamond. (a)Atomic
force microscope image of nanodiamonds depositedon a mica plate.
(b) Histogram of nanodiamond sizes thatare predominantly within
25-61nm (43±18 nm). (c) TypicalODMR measurement of a nanodiamond
N-V center with anapplied magnetic field B‖ = 37.8G (�) and 66G
(◦). (d) Thetime evolution of the spin state population P|0〉 in
spin echoexperiment for three typical N-V s. By fitting the data
with afunction of (1/2)[1 + exp(−(T/TSE)α)], we estimate the
pa-rameters [TSE , α] as follows: [2.142 ± 0.018µs, 1.448 ±
0.026](N-V 1, ◦), [4.292 ± 0.133µs, 1.47 ± 0.10] (N-V 2, �), [2.990
±0.083µs, 1.576 ± 0.101] (N-V 3, O).
ments. Microwave control pulses are generated with anarbitrary
waveform generator (AWG) which are amplifiedby a microwave
amplifier. The power of microwave radi-ation determines the
frequency of Rabi oscillation. Spinecho measurement were performed
for several N-V s todetermine the spin coherence time, three
representativeexamples are shown in Fig.1(d). The data is fitted by
adecay function in the form of exp[−(t/TSE)α], where TSEdenotes the
spin echo coherence time. We extract thevalue of α, the statistic
of which shows α ∈ [1.08, 1.74],indicating decoherence is due to
both slow and fast en-vironmental fluctuations, see Appendix.
Universal dy-namical decoupling with a train of pulses, such as
Carr-Purcell-Meiboom-Gill and XY8 sequences, may prolongspin
coherence time by suppressing noise of low frequency[29, 30]. Our
Ramsey measurement under different mag-netic field strengths shows
that T ∗2 becomes longer asthe magnetic field increases (see
Appendix) which sug-gests that the noise in the present scenario is
dominatedby surface electric noise [41] rather than a slow spin
bath.
We apply XY8-N pulse sequences to several N-V cen-tres using a
train of 8N π-pulses, as shown in Fig.2(a).Fig.2(b) shows the
measurement results obtained by ap-plying up to 96 π-pulses. The
extended coherence timeT2 under dynamical decoupling increases as
the num-ber of XY8 cycles grows following the scaling (N−β
+TSE/T1)
−1 with N up to 12 [42], see Fig.2(c). We alsoobserve that the
coherence time saturates and any fur-ther increase of number of
pulses does not necessary leadsto a longer coherence time. Because
the XY8 pulse se-quence exhibits excellent pulse error tolerance
[43], theexperiment observation suggests that the limited
coher-ence time is likely due to fast noise dynamics and
limitedmicrowave power (pulse repetition rate).
To achieve high efficiency dynamical decoupling underthe
constraint of microwave power, we apply CCDD toprotect spin
coherence of nanodiamond N-V s. We beginby illustrating the basic
idea of CCDD as applied to thems = 0↔ ms = −1 transition of a
single N-V spin [36–38]. We would like to remark that the present
schemeis applicable to many other two-level quantum systems.We
introduce a microwave driving field with phase mod-ulation [37]
as
H̃ = (Ω1 + δx) cos
[ω0t+ 2
(Ω2Ω1
)sin(Ω1t)
]σx, (1)
where σx is Pauli operator, ω0 is the energy gap betweenms = 0
and ms = −1, Ω1 is the Rabi frequency asdetermined by microwave
power, Ω2 denotes the ratioof phase modulation, and the fluctuation
in microwavepower is denoted as δx. The effect of magnetic noiseis
suppressed by the driving field as long as the noisepower density
is small at frequency Ω1. In the interac-tion picture, the
effective Hamiltonian can be written as[37] HI2 = − (Ω2/2)σz +
δxσx. As the phase control inthe AWG is very stable, the
fluctuation in Ω2 is negli-
-
3
f
X Y532 nm 532 nmX X XY Y Y
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
⌧⌧ ⌧ ⌧⌧ ⌧ ⌧⌧
2
⌧
2
X Y X Y Y X Y X
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
0 10 20 300.4
0.6
0.8
1.0
0 3 6 9 125
10
15
20
0 10 20 300.4
0.6
0.8
1.0
xy8-1___omega1-8.5MHz_new
xy8-4___omega1-8.5MHz_newxy8-10___omega1-8.5MHzxy8-12___omega1-8.5MHz
0 10 20 300.4
0.6
0.8
1.0
xy8-1___omega1-8.5MHz_new
xy8-4___omega1-8.5MHz_newxy8-10___omega1-8.5MHzxy8-12___omega1-8.5MHz
0 10 20 300.4
0.6
0.8
1.0
xy8-1___omega1-8.5MHz_new
xy8-4___omega1-8.5MHz_newxy8-10___omega1-8.5MHzxy8-12___omega1-8.5MHz
(a)
(b)
c
532 nm 532 nm
(d)
0 10 20 300.0
0.5
1.0
15.2 15.4 15.6 15.80.0
0.5
1.0
25 25.2 25.4 25.60.0
0.5
1.0
(c)
(e)
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
⌧⌧ ⌧ ⌧⌧ ⌧ ⌧⌧
2
⌧
2
X Y X Y Y X Y X
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
⌧⌧ ⌧ ⌧⌧ ⌧ ⌧⌧
2
⌧
2
X Y X Y Y X Y X
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
⌧⌧ ⌧ ⌧⌧ ⌧ ⌧⌧
2
⌧
2
X Y X Y Y X Y X
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
⌧⌧ ⌧ ⌧⌧ ⌧ ⌧⌧
2
⌧
2
X Y X Y Y X Y X
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
⌧⌧ ⌧ ⌧⌧ ⌧ ⌧⌧
2
⌧
2
X Y X Y Y X Y X
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
⌧⌧ ⌧ ⌧⌧ ⌧ ⌧⌧
2
⌧
2
X Y X Y Y X Y X
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
⌧⌧ ⌧ ⌧⌧ ⌧ ⌧⌧
2
⌧
2
X Y X Y Y X Y X
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
⌧⌧ ⌧ ⌧⌧ ⌧ ⌧⌧
2
⌧
2
X Y X Y Y X Y X
APD
532 nm
APD
532 nm
APD
(⇡
2)x (
⇡
2)x
532 nm
APD
Figure 2. The performance of concatenated continuous dy-namical
decoupling as compared with XY8 pulse dynamicaldecoupling. (a) XY8
pulse sequence. (b) Coherence timeof nanodiamond N-V is extended by
XY8-N pulse sequencewith the number of pulses up to 96 (8 × N). The
Rabi fre-quency of π-pulse is 8.5 MHz. The data is fitted with
thedecay function (1/2)[1 + exp(−(T/T2)α)] which indicates
theachievable coherence time of T2 = 15.22 ± 0.63µs. (c) showsthe
scaling of T2 with the number of XY8 cycles N , which fits(N−β
+TSE/T1)
−1 [42] with β = 0.319±0.064. (d) Concate-nated continuous
dynamical decoupling scheme with phasemodulated driving. (e) The
extended spin coherence time byCCDD reaches TC = 31.22 ± 3.14µs.
The signal envelope isfitted by (1/2)[1 + exp(−(T/TC))]. The
driving parametersare Ω1 = 8.06 MHz, and (Ω2/Ω1) = 0.1. The
subpanels (1)-(2) show zoomed views over different measurement
intervals.The applied magnetic field is B‖ = 508 Gauss.
gible. As long as the power spectrum of δx is negligibleat
frequencies larger than Ω2, the noise will only lead toa second
order effect, i.e.,
(δ2x/Ω2
)σz [44]. As compared
with pulsed dynamical decoupling strategy, CCDD canachieve
better performance with the same average mi-crowave power [35] as
we will confirm in our experimenton nanodiamonds in living cells.
In our experiment, aschematic of the microwave and readout sequence
to im-plement CCDD is shown in Fig.2(d). A π2 -pulse preparesN-V
spin in a superposition state of |0〉 and |−1〉. Thephase varying
driving field as in Eq.(1) is generated withan AWG and acts on the
N-V spin for time T . A finalπ2 -pulse maps spin coherence
information into the state|0〉 population as measured by APD
(avalanche photo-diode gate). Fig.2(e) shows coherent oscillation
by ap-plying the CCDD scheme which leads to an extended
coherence time Tc = 31.22±3.14µs, which is of the sameorder of
the relaxation time T1 (which we measured tobe 87.35± 7.50µs) as T2
is limited by T1/2 [45].
The requirement of low microwave power is of practi-cal
importance for quantum sensing applications in vivo,because
microwave radiation is absorbed by biologicaltissues which may lead
to heating and subsequent dam-age or denaturing of protein
molecules. To demonstratethe performance of CCDD aimed at
biosensing, we ex-ploit the scheme to protect the spin coherence of
N-V sin nanodiamonds up-taken by living cells. The cells weuse in
experiment are the NIH/3T3 cells that are adher-ent to the upper
surface of the cover glass. To avoid thestrong fluorescence of the
nutrient solution, we replace itwith phosphate buffered saline
(PBS) which has almostno fluorescence and wash the cells 3 times to
remove nan-odiamonds not internalised by the cells. Fig.3(a) shows
aconfocal scan image of the cell sample where fluorescenceis gated
around the N-V emission spectrum. With mem-brane labelling and
depth scan tomography, we clearlyidentify nanodiamonds that are
taken up by the cells andlocated in the cell cytosol. We perform
ODMR (Fig.3b)and spin echo measurements (Fig.3c) to characterize
theproperties of those nanodiamond N-V s in cells. We com-pare the
performance of CCDD with XY8 pulsed dynam-ical decoupling for the
protection of N-V spin coherence
0 4 8 12 16 200.0
0.5
1.0
0 10 20 30 40
0.4
0.6
0.8
1.0
0 10 20 30 40
0.4
0.6
0.8
1.0
0 10 20 30 40
0.4
0.6
0.8
1.0
0 10 20 30 40
0.4
0.6
0.8
1.0
0 10 20 30 40
0.4
0.6
0.8
1.0
0 10 20 30 40 50
40
20
0
10
30
2
1 2 3 4 5 6 7 8T2(µs) 4.84±0.009 4.3±0.069 2.142±0.018 1.3±0.24
4.292±0.133 8.71±0.203 2.99±0.083 2.711±0.078↵ 1.082±0.045
1.542±0.056 1.448±0.026 1.447±0.295 1.47±0.1 1.392±0.068
1.576±0.101 1.74±0.1125
TABLE I: Spin echo measurement for nanodiamond NVs. The
normalized experiment data is fitted with the function P|0i(t) =
(1/2)[1 +e�(t/TS E )
↵]. The table lists the estimated value of TS E and ↵ for 8
nanodimonad NVs.
AFM, we measure the height of nanodiamonds to estimate their
sizes. The statistics of nanodiamond size is shown in Fig.S1.The
average nanodiamond size is about 43 nm, with the diameters
predominantly within 25 � 60 nm (43 ± 18 nm), and thenanodiamond
concentration is about 2.
FIG. S2: (a) Dependence of T ⇤2 on the strength of magnetic
field. (b) and (c) show the data of Ramsey measurement with
magnetic field B = 5G (b) and B = 25 G (c).
To characterize the properties of spin noise, we perform Ramsey
measurement applying magnetic field of di↵erent strengthalong NV
axis. The dependence of T ⇤2 on the applied magnetic field is shown
in Fig.S2. It can be seem that T
⇤2 increases
with a larger magnetic field, which suggests that electric noise
may be a dominant source of spin dephasing in the presentsample
[2]. We also perform spin echo measurement of NVs in several
nanodiamonds. Owing to the di↵erent environment fordi↵erent
nanodiamond NVs. The experiment data is normalized through Rabi
oscillation, and then is fitted with the functionP|0i(t) = (1/2)[1
+ e�(t/TS E )
↵
]. The result shows that ↵ 2 [1.08, 1.74] and TS E for the
average spin echo coherence time is around3µs, see Table I. In
Fig.S3, we plot the experiment data for the relaxation time
measurement of the NV center shown in Fig.2 ofthe main text. The
normalized experiment data is fitted with the function P|0i(t) =
(1/2)[1 + e�(t/T1)], which gives an estimationof T1 = 87.35 ±
7.5µs.
0 100 200 300
T ( s)
0.4
0.6
0.8
1
FIG. S3: The relaxation time of nanodiamond NV. The normalized
experiment data is fitted with the function P|0i(t) = (1/2)[1 +
e�(t/T1)].The applied magnetic field is Bk = 508 Gauss.
2
12
34
56
78
T2(µ
s)4.
84±0
.009
4.3±
0.06
92.
142±
0.01
81.
3±0.
244.
292±
0.13
38.
71±0
.203
2.99±0
.083
2.71
1±0.
078
↵1.
082±
0.04
51.
542±
0.05
61.
448±
0.02
61.
447±
0.29
51.
47±0
.11.
392±
0.06
81.
576±
0.10
11.
74±0
.112
5
TAB
LE
I:Sp
inec
hom
easu
rem
entf
orna
nodi
amon
dN
Vs.
The
norm
aliz
edex
peri
men
tdat
ais
fitte
dw
ithth
efu
nctio
nP|0 i
(t)=
(1/2
)[1+
e�(t/T
SE
)↵].
The
tabl
elis
tsth
ees
timat
edva
lue
ofT
SE
and↵
for8
nano
dim
onad
NV
s.
AFM
,we
mea
sure
the
heig
htof
nano
diam
onds
toes
timat
eth
eir
size
s.T
hest
atis
tics
ofna
nodi
amon
dsi
zeis
show
nin
Fig.
S1.
The
aver
age
nano
diam
ond
size
isab
out
43nm
,w
ithth
edi
amet
ers
pred
omin
antly
with
in25�
60nm
(43±
18nm
),an
dth
ena
nodi
amon
dco
ncen
trat
ion
isab
out
FIG
.S2:
(a)D
epen
denc
eof
T⇤ 2
onth
est
reng
thof
mag
netic
field
.(b)
and
(c)s
how
the
data
ofR
amse
ym
easu
rem
entw
ithm
agne
ticfie
ldB=
5G
(b)a
ndB=
25G
(c).
Toch
arac
teri
zeth
epr
oper
ties
ofsp
inno
ise,
we
perf
orm
Ram
sey
mea
sure
men
tapp
lyin
gm
agne
ticfie
ldof
di↵
eren
tstr
engt
hal
ong
NV
axis
.T
hede
pend
ence
ofT⇤ 2
onth
eap
plie
dm
agne
ticfie
ldis
show
nin
Fig.
S2.
Itca
nbe
seem
that
T⇤ 2
incr
ease
sw
itha
larg
erm
agne
ticfie
ld,
whi
chsu
gges
tsth
atel
ectr
icno
ise
may
bea
dom
inan
tso
urce
ofsp
inde
phas
ing
inth
epr
esen
tsa
mpl
e[2
].W
eal
sope
rfor
msp
inec
hom
easu
rem
ento
fN
Vs
inse
vera
lnan
odia
mon
ds.
Ow
ing
toth
edi↵
eren
tenv
iron
men
tfor
di↵
eren
tnan
odia
mon
dN
Vs.
The
expe
rim
entd
ata
isno
rmal
ized
thro
ugh
Rab
iosc
illat
ion,
and
then
isfit
ted
with
the
func
tion
P|0 i
(t)=
(1/2
)[1+
e�(t/T
SE
)↵].
The
resu
ltsh
ows
that↵2[
1.08,1.7
4]an
dT
SE
fort
heav
erag
esp
inec
hoco
here
nce
time
isar
ound
3µs,
see
Tabl
eI.
InFi
g.S3
,we
plot
the
expe
rim
entd
ata
fort
here
laxa
tion
time
mea
sure
men
toft
heN
Vce
nter
show
nin
Fig.
2of
the
mai
nte
xt.T
heno
rmal
ized
expe
rim
entd
ata
isfit
ted
with
the
func
tion
P|0 i
(t)=
(1/2
)[1+
e�(t/T
1) ]
,whi
chgi
ves
anes
timat
ion
ofT
1=
87.3
5±
7.5µ
s.
0100
200
300
T (
s)
0.4
0.6
0.81
FIG
.S3:
The
rela
xatio
ntim
eof
nano
diam
ond
NV.
The
norm
aliz
edex
peri
men
tdat
ais
fitte
dw
ithth
efu
nctio
nP|0 i
(t)=
(1/2
)[1+
e�(t/T
1) ]
.T
heap
plie
dm
agne
ticfie
ldis
Bk=
508
Gau
ss.
150
100
50
0
2770 2820 2870 2920 2970
0.9
1.0
(d)
NV
arb.
uni
ts
x (μm)
y (μ
m)
(c)
(b)(a)
Figure 3. Protecting quantum spin coherence in living cells.(a)
Confocal image of cell with an uptake of fluorescent nan-odiamonds.
The red curve indicates the cell boundary. Thenanodiamonds in the
dashed rectangular are located in thecytoplasm. The photon counts
are in the unit of kcs/s. (b)ODMR measurement of a nanodiamond N-V
center in cellwith an applied magnetic field B‖ = 25 Gauss. (c) N-V
co-herence time in living cell is extended by spin echo and
XY8pulse sequences (XY8-N) with the number of pulses up to 96.The
Rabi frequency of π-pulse is 9.6 MHz. (d). The CCDDsignal indicates
a spin coherence time of 29.4 ± 3.6µs with aRabi frequency Ω1 = 4.6
MHz, and Ω2 = Ω1/10.
-
4
0 4 810
20
30
40
10 15 20 25100
101
102
103(a) (b)
Figure 4. (a) The extended coherence times as achievedby CCDD
scheme (�) and XY8 pulse dynamical decoupling(◦) as a function of
the effective Rabi frequency. The val-ues in panel are the number
of XY8 cycles (up to 12) thatachieve the longest possible coherence
time. (b) The esti-mated sensitivity for the measurement of an
oscillating fieldusing CCDD (�) and XY8 (◦) scheme. The achievable
Rabifrequency is Ω = 8.5MHz, the coherence time is assumed asT2 =
15.22µs (XY8) and Tc = 31.22µs (CCDD). The oscillat-ing field
strength is γb = (2π)100kHz. The other experimentparameters are the
same as Fig.2.
in cells. Fig.3(c-d) show the measurement data obtainedby
applying a microwave of the power that correspondsto a Rabi
frequency of 9.6 MHz and 4.6 MHz in XY8pulse dynamical decoupling
and CCDD scheme respec-tively, the N-V spin coherence time is
extended up to29.4± 3.6µs by CCDD scheme while XY8 pulsed
schemereaches only 17.49 ± 1.43µs. We note that the advan-tage of
CCDD scheme to become more prominent as theavailable microwave
power is reduced and T1 time is in-creased by nanodiamond material
design. To characterisethe damage effect of microwave radiation, we
apply theexperiment sequences and monitor the temperature in-crease
of sample. The results suggest that the tempera-ture increase due
to the pulse sequences would be about10 ◦C more than that due to
CCDD when achieving sim-ilar coherence times, see Appendix. Such a
differencein temperature increase is expected to have a
significanteffect on biological tissue [46, 47].
Apart from avoiding the damaging effect on biologicaltissues
(which is mainly dependent on the average mi-crowave power), the
constraint of microwave power onpulsed dynamical decoupling
efficiency when combiningwith (in vivo) quantum sensing, may arise
from anotherorigin. The maximal microwave power, which
determinesthe achievable Rabi frequency, may be limited due toe.g.
the relatively large distance between microwave an-tenna and
nanodiamond especially when compared tobulk diamond experiments. We
perform measurementsusing different peak microwave power and
compare withXY8 pulsed dynamical decoupling, the number of
whichachieves the longest possible coherence time. Our resultas
shown in Fig.4(a) demonstrates that given the sameeffective Rabi
frequency, i.e. the same average microwavepower, the CCDD scheme
clearly outperforms the XY8dynamical decoupling sequences in
extending spin coher-ence time. We remark that, unlike XY8 pulsed
schemewhere the decoupling efficiency in our experiments is
lim-
ited by the constraint of microwave power, the achievedcoherence
time by CCDD is predominantly limited bythe T1 time of
nanodiamonds, which can be improved bymaterial design.
III. APPLICATION IN QUANTUM SENSING
For sensing applications inside living cells, one has totake the
constraint of microwave power arising from bothorigins discussed
above into account. We consider a typ-ical scenario of detecting an
oscillating magnetic fieldwith a frequency ωs. We remark that the
underlyingprinciple is essentially similar to the detection of
elec-tron (nuclear) spin, where the characteristic frequencyis
Larmor frequency of the target spins. One potentialinteresting
example is the detection of the emergence ordisappearence of
radicals and functional molecule groupsof nuclear spins. Pulsed
scheme detects the field by engi-neering the time interval τp
between pulses to match thefield frequency, namely τc = k(π/ωs).
For ideal instanta-neous π-pulses (requiring infinite microwave
power), theestimated measurement sensitivity is ηc = kπ/(4γ
√T2),
where γ is the electronic gyromagnetic ratio and for sim-plicity
we assume a unit detection efficiency. However,the limited
achievable pulse peak Rabi frequency Ω (incomparison with the field
frequency ωs) leads a constrainton the resonant condition k ≥
(ωs/Ω) and would decreasethe signal contrast. This fact restricts
pulsed schemes towork only for frequencies below ∼ 10 MHz when the
pulserepetition rate and microwave power are limited which isquite
likely in biological systems. The present CCDDscheme can detect the
field on resonance when Ω1 = ωsand ω0−ωs = ±Ω1 with the estimated
measurement sen-sitivity ηc = 1/(γ
√Tc) and 2/(γ
√Tc) respectively [37].
We remark that the resonance condition can be satisfiedby tuning
ω0 (via the external magnetic field), thus itis flexible to choose
Ω1 and Ω2 following the principleto optimise the improvement of
coherent time. There-fore, the advantage of CCDD scheme as compared
withthe pulsed scheme in quantum sensing is not only theimprovement
of coherence time, but also its capabilityto increase sensitivity
in the presence of limited aver-age microwave power constraint. In
Fig.4(b), we com-pare the estimated measurement sensitivity for
CCDDand the pulsed scheme under the same average powerconstraint.
It can be seen that CCDD shows superiorperformance for signal
frequencies above 10 MHz. Po-tentially interesting examples include
but not limited tothe detection of molecules (containing nuclear
spins) inhigh field magnetic resonance spectroscopy and
electron(radicals). Besides the sensitivity enhancement, we
alsoremark that CCDD scheme may avoid the misidentifica-tion of
frequency components in classical fields or singlemolecule
spectroscopy [48–50] due to the relatively longpulse duration (as
microwave power is not sufficiently
-
5
high). The present scheme (with both the sensitivityand the
linewidth limited by the extended T2) would thusadvance the
application of N-V based quantum sensingin vivo using nanodiamonds,
offering new methodologycomplementary to continuous wave ESR
resonance mea-surement (the sensitivity is limited by the short T
∗2 ) andrelaxation spectroscopy (the linewidth is limited by T ∗2
)[18].
IV. CONCLUSION AND DISCUSSION
To conclude, we implement a concatenated continu-ous dynamical
decoupling strategy to prolong the quan-tum spin coherence time of
N-V centers in nanodiamondseven inside living cells. We demonstrate
significantly in-creased performance with less stringent
requirement onmicrowave power in comparison with pulsed schemes,
andthus causing less severe damage effect to living cells.
Theconcatenated continuous dynamical decoupling strategythus
provides a valuable tool to achieving long spin co-herence time
quantum sensors when the available andfeasible microwave power is
low or has to be limited,e.g. to avoid damage to biological tissue.
It also enablesrelatively high-frequency magnetic field sensing
with asubstantial enhancement in the measurement sensitivity.The
ability to extend spin coherence times in living cellsalong with
enhanced measurement sensitivity raises newpossibilities for the
applications of nano diamond basedquantum sensing in the
intra-cellular environment andrelated biological events.
V. ACKNOWLEDGEMENTS
We thank Jianwei Wang, Quan Gan, Yuzhou Wu andYuan Zhuang for
help in sample preparation, MichaelFerner, Manfred Bürzele, Z.-J.
Shu, J.-Y. He, R.-F.Hu and H.-B. Liu for technical assistance and
ItsikCohen for fruitful discussion. We acknowledge sup-port by
National Natural Science Foundation of China(11874024, 11690032),
and the Open Project Programof Wuhan National Laboratory for
Optoelectronics NO.2019WNLOKF002. A.R acknowledges the support of
theERC grant QRES. M. B. P. is supported by the DFG(FOR1493), the
EU via DIADEMS and HYPERDIA-MOND, the ERC Synergy grant BioQ and
the IQST.C. M., N. T., B. N., L. P. M., F. J. are supported byDFG
(FOR 1493, SFB TR21, SPP 1923), VW Stiftung,BMBF, ERC, EU
(DIADEMS), BW Stiftung, Ministryof Science and Arts, Center for
Integrated quantum sci-ence and technology (IQST).
APPENDIX
A. Principle of concatenated continuous dynamicaldecoupling
To suppress the effect from both environment noiseand microwave
fluctuation, we implement concatenatedcontinuous dynamical
decoupling by introducing a mi-crowave driving field with
time-dependent phase modu-lation [37]. We repeat here the
derivation for self consis-tency. We start with the
Hamiltonian:
H =ω02σz+(Ω1+δx) cos
[ω0t+ 2
Ω2Ω1
sin (Ω1t)
]σx (A1)
By moving to the interaction picture with respect to:
H =[ω0
2+ Ω2 cos(Ω1t)
]σz (A2)
we get:
H1 =
(Ω1 + δx
2
)σx − Ω2 cos(Ω1t)σz (A3)
Moving again to the interaction picture with respect toΩ1σx we
get:
H2 = δxσx − (Ω2/2)σz (A4)
as Ω2 is generated by the time dependent phase we as-sume that
the noise is negligible. As Ω2 � δx and weassume that the amount of
Ω2 in the power spectrum ofδx is negligible the deleterious effect
of the noise will onlymanifest itself in second order, i.e.,
Hnoise =(δ2x/Ω2
)σz (A5)
as (Ω2/Ω1) is kept at 10−1 and δx is of the order of 1% of
Ω1 the effect of the noise is of the order of 10−3Ω1. It is
noteworthy that this effect could be further suppressedby adding
a higher drive by an extra time dependentphase term. In our
experiment, we first apply a (π/2)ypulse to prepare the N-V centre
spin in a superpositionstate |ψ(0)〉 = (1/
√2)(|0〉 + |1〉). After an evolution for
time t, the N-V centre spin state evolves to
|ψ(t)〉 = exp [(−itΩ1/2)σx] exp [(−itΩ2/2)σz] |ψ(0)〉 .(A6)
The fluorescence measurement after another (π/2)y pulsegives the
state population
P|0〉 = |〈ψ(0)|ψ(t)〉|2 =1
2[1 + cos(Ω1t) cos(Ω2t)] . (A7)
Two frequency components Ω1 and Ω2, in additional tothe effect
of unpoloarized nitrogen nuclear spin, leadsto the beating pattern
in the oscillating signal, whichexplain our experiment observation
and is also verifiedby numeric simulation. The extended coherence
timecan be inferred from the decay of the envelope.
-
6
1 2 3 4 5 6 7 8T2(µs) 4.840±0.009 4.300±0.069 2.142±0.018
1.30±0.24 4.292±0.133 8.710±0.203 2.990±0.083 2.711±0.078α
1.082±0.045 1.542±0.056 1.448±0.026 1.447±0.295 1.47±0.10
1.392±0.068 1.576±0.101 1.740±0.113
Table I. Spin echo measurement for nanodiamond N-V s. The
normalized experiment data is fitted with the functionP|0〉(t) =
(1/2)[1 + e
−(t/TSE)α ]. The table lists the estimated value of TSE and α
for 8 nanodimonad N-V s.
B. Characteristics of nanodiamonds
The nanodiamonds are spin-coated on the mica plateand scanned
after drying, we choose different areas toperform AFM scan and
count the statistics of nanodi-amond size. Considering the
broadening effect of AFM,we measure the height of nanodiamonds to
estimate theirsizes. The statistics of nanodiamond size is shown
inFig.1(b) in the main text. The average nanodiamondsize is about
43 nm, with the diameters predominantlywithin 25 − 60 nm (43 ± 18
nm), and the nanodiamondconcentration is about 50 per (10µm)2.
5 25 45
60
95
130(a)
200 400 600 8000.2
0.4
0.6
0.8
1
200 400 600 8000.2
0.4
0.6
0.8
1(b)
(c)
Figure 5. (a) Dependence of T ∗2 on the strength of
magneticfield. (b) and (c) show the data of Ramsey measurementwith
magnetic field B = 5 G (b) and B = 25 G (c).
0 100 200 300
T ( s)
0.4
0.6
0.8
1
Figure 6. The relaxation time of nanodiamond N-V . The
nor-malized experiment data is fitted with the function P|0〉(t)
=
(1/2)[1 + e−(t/T1)]. The applied magnetic field is B‖ =
508Gauss.The relaxation time is estimated to be T1 = 87.35
±7.50µs.
To characterize the properties of spin noise, we per-form Ramsey
measurement applying magnetic field ofdifferent strength along N-V
axis. The dependence of T ∗2on the applied magnetic field is shown
in Fig.5. It canbe seem that T ∗2 increases with a larger magnetic
field,which suggests that electric noise may be a dominantsource of
spin dephasing in the present sample [41]. Wealso perform spin echo
measurement of N-V s in severalnanodiamonds. Owing to the different
environmentfor different nanodiamond N-V s, they exhibit
differentcoherence times. The experiment data is normalizedthrough
Rabi oscillation, and then is fitted with thefunction P|0〉(t) =
(1/2)[1+exp (−(t/TSE)α)]. The resultshows that α ∈ [1.08, 1.74] and
TSE for the averagespin echo coherence time is around 3µs, see
Table I. InFig.6, we plot the experiment data for the
relaxationtime measurement of the N-V center shown in Fig.2 ofthe
main text. The normalized experiment data is fittedwith the
function P|0〉(t) = (1/2)[1 + exp (−(t/T1))],which gives an
estimation of T1 = 87.35± 7.50µs.
In the main text, we present experiments in which weapply XY8-N
pulse sequences to extend coherence timeof N-V centres using a
train of (8×N) π-pulses. The ex-tended coherence time T2 under
pulsed dynamical decou-pling increases as the number of XY8 cycles
grows, andreaches a saturates value. In Fig.4(a) of the main
text,we apply π-pulses with different peak Rabi frequency
andmeasure the achievable saturate coherence time. The av-erage
microwave power can be quantified by the average
-
7
effective Rabi frequency which is defined as follows
Ω̄ =
[1
T
∫ T0
Ω2(t)dt
]1/2(B1)
In Table II, we list the peak Rabi frequency, the
averageeffective Rabi frequency and the number of XY8 cyclesof the
pulse sequences that achieve the best coherencetime as shown in
Fig.4(a) of the main text.
C. Cell culture and sample preparation
NIH/3T3 cells were cultured in Dulbecco’s modifiedEagle’s medium
(DMEM) supplemented with fetalbovine serum and
penicillin/streptomycin. Nanodia-monds were diluted in DMEM. Then
cells were seeded oncover slips and incubated with the
DMEM-nanodiamondsuspension (37◦C, 5% CO2) for 20 hours, which
allowedcells to adherent to the surface of the cover glass.
Aftertreatment, the media was removed and the cover glasswas washed
3 times with phosphate buffered saline(PBS). The cultured NIH/3T3
cells were immersed inPBS throughout the measurement, and the
temperaturewas kept around 22◦C. The confocal imaging was
per-formed through the cover glass, using an oil immersionlens. The
N-V center measured in this work was locatedabout 2.5 micrometers
above the cover glass. Quantummeasurements were performed on the
N-V centers byapplying a microwave signal along a copper wire (with
adiameter ∼20µm) which is about ∼30µm far away fromthe N-V
center.
D. Cell membrane staining and identifyingnanodiamonds in
cells
In order to identify those nanodiamonds that weretaken in cells,
we first use the 1,
1′-Dioctadecyl-3,3,3′,3′-tetramethylindocarbocyanine
perchlorate(DiIC18(3))which is a kind of lipophilic fluorescent
dyes to label thecytomembrane. After the procedure of cellular
uptake,the cell culture medium was removed, and the cells werethen
incubated with 200 µL DiIC18(3) (0.0486 µM/L)solution for about 1
hour (37◦C, 5% CO2). The samplewas washed 5 times with PBS before
it was imaged witha home-built confocal setup. The stained cell
imageswith clear profile are shown in Fig.7(a,c), which
demon-strate clearly the cytomembrane labelled by DiIC18(3)and the
cell nucleus. Fig.7(b) shows a zoom in areawhere we identify three
nanodiamonds in cell, which isfurther confirmed by our XZ confocal
scan, see Fig.7(d-f).
E. Influence of microwave radiation on living cells
The main influence of microwave radiation on livingcells arise
from the heating effect. We perform measure-ments to clarify the
following two issues: (1) The depen-dence of the heating effect on
the microwave power; (2)Whether the difference in the required
microwave powerto achieve the same coherence times under pulsed
andCCDD schemes matters, i.e. whether it may lead to non-negligible
difference in the heating of the sample. Therole of microwave power
in the manipulation of N-V s ismanifested by the observed Rabi
frequency. In Fig.8, wecalibrate the dependence of Rabi frequency
on the ampli-tude of AWG output by measuring Rabi frequencies
forseveral N-V s in nanodiamond when applying magneticfields of
different strengths. The measurement shows thatRabi frequencies are
proportional to the amplitude of theAWG output that is quantified
by the peak-to-peak volt-age. The results also provide us
information on the re-quirement of microwave power to achieve a
certain Rabifrequency. For example, Rabi frequency is promoted
by3-6 MHz with an increase of AWG output amplitude by100mV for
typical nanodiamonds that locate within adistance of 5−15µm to the
microwave wire. For the mea-surement in Fig.4 of the main text,
Rabi frequency of 9.6MHz (4.6 MHz) is achieved by an AWG output of
400mV (200 mV) and 30% (25%) amplification percentage.As Ω2 � Ω1,
one can easily verify that the microwaveradiation power is
determined by the amplitude Ω1.
It has been shown that the main damage of microwave(MW)
radiation applied to cells is caused by the heat-ing effect. The
viability of cells may be influenced sub-stantially as the
temperature increases by 10◦C, see e.g.Ref.[46, 47]. In our
experiment, we apply microwave ofpulse and CCDD schemes and monitor
the temperatureof sample under similar conditions in the
experiments aspresented in the main text. We glue a coverslip
(2.4cm× 2.4cm), adhere to which cells grow, on a PCB board
incontact with a copper wire that delivers microwave. Thethermistor
(Thorlabs TH10K) attached to the coverslipallows us measure the
temperature of the sample whenapplying microwave sequences. We add
1mL phosphatebuffered saline (PBS) which was used to maintain
gentleconditions for living cells.
We denote the peak-to-peak voltage of AWG output asA (mV), which
quantifies the peak power of microwaveradiation. We first apply
CCDD scheme with the follow-ing parameters: the duration of
continuous microwavedriving is Ton = 30µs (which is similar to the
extendedcoherence time as observed in our experiment), the
com-bination of laser pulse and idle time is set as Toff =
3.8µs(which is similar to the corresponding time in our
ex-periments). As there is time during which microwaveis switched
off, we define the average amplitude of mi-
-
8
1 2 3 4 5Peak Rabi frequency (MHz) 1.98 5.10 7.14 8.50
16.20Average effective Rabi frequency (MHz) 1.94 4.13 4.89 5.19
8.25XY8 cycles 6 12 12 12 14
Table II. The detailed information on the XY8 pulse sequences
that achieve the coherence time of N-V s in nanodiamond asshown in
Fig.4(a) of the main text.
NV1 NV2NV3
NV1 NV2 NV3
a b
c d e f
Figure 7. (a) Confocal scan of a living cell with cytomembrane
lipophilic fluorescent dyes. The zoom in area in the
dashedrectangular is shown in (b). Three nanodiamonds are
identified in the cell, which is confirmed by XZ scan as shown in
(c-f).The photon count is in the unit of kcs/s.
50 100 150 200 250 300 350 400 4500
5
10
15
20
25
30
Rab
i fre
quen
cy (
MH
z)
Figure 8. Dependence of Rabi frequency on the
peak-to-peakvoltage of AWG output for several N-V s in
nanodiamond.Rabi measurements are performed at frequencies as shown
inthe figure when applying different magnetic fields along theN-V
axis. The amplification percentage of the amplifier isfixed as
45%.
crowave radiation as follows
〈A〉 = A√
TonTon + Toff
. (E1)
We monitor the temperature of the sample every 60 sec-onds and
record the stable temperature which usually isreached in ∼ 15
minutes. The result is shown in Fig.9(◦). For comparison, we also
apply XY8-12 scheme (i.e.the total number of pulses is N = 96) with
the followingparameters: the π-pulse duration is τπ = 50 ns, and
thetime between pulses (i.e. no microwave) is τf = 100(4)ns, the
combination of laser pulse and idle time is setas Toff = 3.8µs. In
this case, the average amplitude ofmicrowave radiation is given
by
〈A〉 = A√
NτπNτπ +Nτf + Toff
. (E2)
The results are shown in Fig.9 (� for τf = 100 ns and � forτf =
4 ns). Although we choose certain specific parame-ters of pulses
(which are close to those parameters used inour experiments), we
find that the heating effect is mainly
-
9
50 100 150 200 250 300 350 40010
20
30
40
50
60
Figure 9. The increase of sample temperature as a functionof the
average amplitude of AWG output. The amplificationpercentage of the
amplifier is fixed as 45%. The results forCCDD scheme are shown in
◦ as compared with the pulsescheme (� and �).
determined by the average microwave power (as quanti-fied by the
average amplitude of AWG output definedin Eq.E1 -E2) for both pulse
and CCDD schemes whileis weakly dependent on the details of
microwave pulses.The sample temperature would heat up by ∼ 12◦C
whenthe average amplitude of AWG increases by 100 mV(which
corresponds to ∼3-5 MHz improvement in Rabifrequency). We remark
that the exact difference in heat-ing effect may also depend on the
other factors such asthe distance between the microwave wire and
the orien-tation of the N-V axis, nevertheless, our
measurementstrongly suggests that the more stringent requirement
onmicrowave power by pulse schemes will cause more se-vere heating
effect to biological tissues. For example, wecompare the data in
Fig.4 of the main text. The averagemicrowave power for CCDD to
achieve ∼ 15µs coher-ence time is less than 1 MHz, while it
requires 4 − 5MHz for pulse scheme. Therefore, according to the
ob-served characteristics of heating effect due to
microwaveradiation, the temperature increase due to the pulsed
se-quences would be about 10 ◦C more than that due toCCDD, which
can be expected to have a significant ef-fect on biological tissues
[46, 47].
F. Sensitivity comparison under the constraint ofmicrowave
power
We consider a typical scenario of quantum sensing,namely the
detection of a weak oscillating magneticfield b(t) = b cos(ωst)
with a frequency ωs and anamplitude b. The underlying principle is
similar to thedetection of electron (nuclear) spin in essence,
wherethe characteristic frequency is Larmor frequency of thetarget
spins. One possible interesting example is thedetection of radicals
inside cells. In N-V spin sensor
based magnetic spectroscopy, the Larmor frequency ofthe target
spins would usually exceed ∼ 10 MHz, e.g.for electron spin or
nuclear spin in high-field magneticresonance spectroscopy.
Depending on the relativeorientation of the magnetic field with
respect to the N-Vaxis (denoted as the ẑ axis that connects the
nitrogenatom and the vacancy site) and the field frequency ωs,the
N-V centre spin sensor may be sensitive to either thefield
components along the ẑ direction or the x̂ direction.In order to
investigate the achievable measurementsensitivity under the
constraint of microwave power, wedenote the available (maximum)
Rabi frequency as Ωmax.
We first consider quantum sensing in combination withthe present
CCDD scheme. In the first case of ωs ≤Ωmax, we can choose to
measure the field along the ẑdirection by tuning the orientation
of the N-V axis inparallel with the polarisation of the magnetic
field. In theinteraction picture, when setting Ω1 = ωs, the
effectiveHamiltonian becomes
H2 = (Ω2/2)σz + (γb/2)σz, (F1)
where γ is the electronic gyromagnetic ratio [37]. Thefield
parameter b can be determined via a Ramsey exper-iment, and the
measurement sensitivity with an interro-gation time t = Tc is
estimated to be
ηc =
√∆2p
C(∂p/∂b)√
1/Tc' 1/
(γC√Tc
), (F2)
where Tc is the extended coherence time, p =(1/2) [1 +
cos(γbTc)] is the result of Ramsey experiment,C represents the
detection efficiency [4]. As ωs ≤ Ωmax,it is always feasible to
choose Rabi frequency Ω1 = ωs.In the second case of ωs > Ωmax,
we choose to measurethe field along the x̂ direction by tuning the
orientationof the N-V axis perpendicular to the polarisation of
themagnetic field. In the interaction picture, when settingΩ1 = ω0
− ωs, the effective Hamiltonian becomes [37]
H3 = −(γb/4)σz. (F3)
⌧c
⌧f⌧⇡
Figure 10. Pulse scheme with non-instantaneous π-pulses.The
π-pulse duration is denoted as τπ = (π/Ω) where Ω isRabi frequency
of pulses. The inter-pulse free evolution timeis τf . The time
interval τc = τπ + τf between pulses shallmatch the oscillating
field frequency, namely τc = k(π/ωs),where k = 1, 3, 5, · · · . The
role of π-pulses is to change thesign of the magnetic field that
acting on the N-V centre spin,so that its effect can be accumulated
constructively.
-
10
148 150 152
0
0.2
0.4
0.6
0.8
1
99 100 101 74.5 75 75.50 0.05 0.1 0.15 0.2 0.25 0.30
0.2
0.4
0.6
0.8
(a) 1(b)
Figure 11. Quantum sensing using pulse scheme with
non-instantaneous π-pulses. (a) The signal as a function of the
timeinterval close to the resonant condition τc = 3(π/ωs) for an
oscillating magnetic field with different frequencies ωs = 10
MHz,15 MHz, 20 MHz. The field strength is (γb) = (2π)100 kHz. (b)
The signal p as a function of the oscillating field strength b.In
(a-b), the interrogation time is set as T2 = 15.22µs. The pulse
Rabi frequency is Ω = 8.5 MHz.
The measurement sensitivity via a Ramsey experimentwith an
interrogation time t = Tc is estimated to be
ηc =
√∆2p
C(∂p/∂b)√
1/Tc' 2/
(γC√Tc
), (F4)
where the signal of Ramsey experiment is p =(1/2) [1 +
cos(γbTc/2)].
Pulse scheme detects an oscillating field by engineeringthe time
interval τc between pulses (see Fig.10) to matchthe field
frequency, namely τc = k(π/ωs) [14]. For idealinstantaneous
π-pulses (i.e. requiring infinite microwavepower), τc = τf where τf
is the free evolution betweenpulses. In our experiment, we first
apply a (π/2)y pulseto prepare the N-V centre spin in a
superposition state|ψ(0)〉 = (1/
√2)(|0〉 + |1〉). After an interrogation time
for time t, the N-V centre spin state evolves to the fol-lowing
state as
|ψ(t)〉 = exp [−iγb(2/π)tσz] |ψ(0)〉 . (F5)
The factor (2/π) comes from the average of the modu-lated
oscillating field. The state population measurementafter another
(π/2)y pulse leads to the signal of Ramseyexperiment as follows
p = |〈ψ(0)|ψ(t)〉|2 = 12
+1
2cos [γb(4/π)t] . (F6)
The estimated measurement sensitivity with an interro-gation
time T2 is
ηp =
√∆2p
C(∂p/∂b)√
1/T2' kπ/(4γC
√T2). (F7)
Given a field with a frequency ωs, the required power isΩ2 for
the CCDD scheme with Ω = ωs. For the pulsedscheme, the pulse
repetition rate shall be π/ωs, namelythe time interval between two
pulses is τc = k(π/ωs).The pulse duration τπ should be much smaller
than τc
(see Fig.10 in supplementary information), namely theratio a =
τπ/τc � 1. Thus, one can estimate that therequired power for the
pulsed scheme is Ω2/a. It can beseen that the power required by the
CCDD scheme isless than the pulsed scheme by a factor of a = τπ/τc
� 1.
For non-instantaneous π-pulses realised by finite mi-crowave
power, τp = τπ+τf , where τπ = π/Ω is the pulseduration and τf is
the free evolution between pulses, seeFig.10. As we are considering
pulse scheme, we requireτf > 0, otherwise the pulse scheme would
become con-tinuous. However, the limited pulse Rabi frequency Ω(in
comparison with the field frequency ωs) leads to aconstraint on the
resonant condition k ≥ (ωs/Ω) andwould decrease the signal
contrast. In Fig.11, we shownthe signal contrast for the
measurement of an oscillatingmagnetic field with different
frequencies using pulses ofthe same duration (namely the same
available Rabi fre-quency). It can be seen that the signal contrast
decreaseswith an increasing field frequency, see Fig.11(a). Thisis
also confirmed by the less steep signal slope (∂p/∂b)for an
oscillating field with a higher frequency ωs, seeFig.11(b). In
Fig.4 of the main text, we compare theestimated measurement
sensitivity by CCDD and pulsescheme according to the achieved
coherence time. Theenhanced sensitivity by the present CCDD scheme
arisesfrom both the prolonged coherence time and also thelimit of
microwave power constraint in pulse scheme.
∗ [email protected]† [email protected]
[1] M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko,J.
Wrachtrup, L. C. L. Hollenberg, The nitrogen-vacancycolour centre
in diamond, Phys. Reports 528, 1 (2013).
[2] J. R. Maze, P. L. Stanwix, J. S. Hodges, S. Hong, J.
M.Taylor, P. Cappellaro, L. Jiang, M. V. G. Dutt, E. Togan,A. S.
Zibrov, A. Yacoby, R. L. Walsworth, M. D. Lukin,
mailto:[email protected]:[email protected]://www.sciencedirect.com/science/article/pii/S0370157313000562
-
11
Nanoscale magnetic sensing with an individual electronicspin in
diamond, Nature (London) 455, 644 (2008).
[3] G. Balasubramanian, I. Y. Chan, R. Kolesov, M. Al-Hmoud, J.
Tisler, C. Shin, C. Kim, A. Wojcik, P. R. Hem-mer, A. Krueger, T.
Hanke, A. Leitenstorfer, R. Brats-chitsch, F. Jelezko, J.
Wrachtrup, Nanoscale imagingmagnetometry with diamond spins under
ambient con-ditions, Nature (London) 455, 648 (2008).
[4] J. M. Taylor, P. Cappellaro, L. Childress, L. Jiang,
D.Budker, P. R. Hemmer, A. Yacoby, R. Walsworth, M.D. Lukin,
High-sensitivity diamond magnetometer withnanoscale resolution,
Nature Phys. 4, 810 (2008).
[5] F. Dolde, H. Fedder, M. W. Doherty, T. Nobauer, F.Rempp, G.
Balasubramanian, T. Wolf, F. Reinhard, L.C. L. Hollenberg, F.
Jelezko, J. Wrachtrup, Electric-fieldsensing using single diamond
spins, Nature Phys. 7, 459(2011).
[6] F. Dolde, M. W. Doherty, J. Michl, I. Jakobi, B. Nay-denov,
S. Pezzagna, J. Meijer, P. Neumann, F. Jelezko,N. B. Manson, J.
Wrachtrup, Nanoscale Detection of aSingle Fundamental Charge in
Ambient Conditions Us-ing the NV− Center in Diamond, Phys. Rev.
Lett. 112,097603 (2014).
[7] V. M. Acosta, E. Bauch, M. P. Ledbetter, A. Waxman,L.-S.
Bouchard, D. Budker, Temperature Dependence ofthe Nitrogen-Vacancy
Magnetic Resonance in Diamond,Phys. Rev. Lett. 104, 070801
(2010).
[8] G. Kucsko, P. C. Maurer, N. Y. Yao, M. Kubo, H. J.Noh, P. K.
Lo, H. Park, M. D. Lukin, Nanometre-scalethermometry in a living
cell, Nature. 500, 54 (2013).
[9] D. M. Toyli, C. F. de las Casas, D. J. Christle, V.
V.Dobrovitski, D. D. Awschalom, Fluorescence thermome-try enhanced
by the quantum coherence of single spins indiamond, Proc. Natl.
Acad. Sci. U.S.A. 110, 8417 (2013).
[10] P. Neumann, I. Jakobi, F. Dolde, C. Burk, R. Reuter,
G.Waldherr, J. Honert, T. Wolf, A. Brunner, J. H. Shim, D.Suter, H.
Sumiya, J. Isoya, J. Wrachtrup, High-PrecisionNanoscale Temperature
Sensing Using Single Defects inDiamond, Nano Lett. 13, 2738
(2013).
[11] M. W. Doherty, V. V. Struzhkin, D. A. Simpson, L.
P.McGuinness, Y.-F. Meng, A. Stacey, T. J. Karle, R. J.Hemley, N.
B. Manson, L. C. L. Hollenberg, S. Prawer,Electronic Properties and
Metrology Applications of theDiamond NV− Center under Pressure,
Phys. Rev. Lett.112, 047601 (2014).
[12] J.-M. Cai, F. Jelezko, M. B. Plenio, Hybrid sensors basedon
colour centres in diamond and piezoactive layers, Nat.Commun. 5,
4065 (2014).
[13] R. Schirhagl, K. Chang, M. Loretz, C. L.
Degen,Nitrogen-Vacancy Centers in Diamond: Nanoscale Sen-sors for
Physics and Biology, Annu. Rev. Phys. Chem.65, 83 (2014).
[14] C. L. Degen, F. Reinhard, P. Cappellaro, Quantum sens-ing,
Rev. Mod. Phys. 89, 035002 (2017).
[15] M. Hirose, C. D. Aiello, P. Cappellaro, Continuousdynamical
decoupling magnetometry, Phys. Rev. A 86,062320 (2012).
[16] K. Fang, V. M. Acosta, C. Santori, Z. Huang, K. M.Itoh, H.
Watanabe, S. Shikata, R. G. Beausoleil, High-Sensitivity
Magnetometry Based on Quantum Beats inDiamond Nitrogen-Vacancy
Centers, Phys. Rev. Lett.110, 130802 (2013).
[17] A. Cooper, E. Magesan, H. Yum, P. Cappellaro, Time-resolved
magnetic sensing with electronic spins in dia-
mond, Nat. Commun. 5, 3141 (2014).[18] L. T. Hall, P. Kehayias,
D. A. Simpson, A. Jarmola,
A. Stacey, D. Budker, L. C. L. Hollenberg, Detection ofnanoscale
electron spin resonance spectra demonstratedusing nitrogen-vacancy
centre probes in diamond, Nat.Commun. 7, 10211 (2016).
[19] T. Joas, A. M. Waeber, G. Braunbeck, F. Reinhard,Quantum
sensing of weak radio-frequency signals bypulsed Mollow absorption
spectroscopy, Nat. Commun. 8,964 (2017).
[20] A. Stark, N. Aharon, T. Unden, D. Louzon, A. Huck,
A.Retzker, U. L. Andersen, F. Jelezko, Narrow-bandwidthsensing of
high-frequency fields with continuous dynami-cal decoupling, Nat.
Commun. 8, 1105 (2017).
[21] S. Schmitt, T. Gefen, F. M. Stürner, T. Unden, G. Wolff,C.
Müller, J. Scheuer, B. Naydenov, M. Markham, S.Pezzagna, J.
Meijer, I. Schwarz, M. Plenio, A. Retzker,L. P. McGuinness, F.
Jelezko, Submillihertz magneticspectroscopy performed with a
nanoscale quantum sensor,Science 356, 832 (2017).
[22] J. M. Boss, K. S. Cujia, J. Zopes, C. L. Degen,
Quantumsensing with arbitrary frequency resolution, Science 356,837
(2017).
[23] Haibin Liu, Martin B. Plenio, and Jianming Cai, Schemefor
Detection of Single-Molecule Radical Pair ReactionUsing Spin in
Diamond, Phys. Rev. Lett. 118, 200402(2017).
[24] S. Hsieh, P. Bhattacharyya, C. Zu, T. Mittiga, T. J.Smart,
F. Machado, B. Kobrin, T. O. Höhn, N. Z. Rui,M. Kamrani, S.
Chatterjee, S. Choi, M. Zaletel, V. V.Struzhkin, J. E. Moore, V. I.
Levitas, R. Jeanloz, N.Y. Yao, Imaging stress and magnetism at high
pressuresusing a nanoscale quantum sensor, Science 366,
1349(2019).
[25] King Yau Yip, Kin On Ho, King Yiu Yu, Yang Chen,Wei Zhang,
S. Kasahara, Y. Mizukami, T. Shibauchi, Y.Matsuda, Swee K. Goh, Sen
Yang, Measuring magneticfield texture in correlated electron
systems under extremeconditions, Science 366, 1355 (2019).
[26] Margarita Lesik, Thomas Plisson, L. Toraille, J. Renaud,F.
Occelli, M. Schmidt, O. Salord, A. Delobbe, T. De-buisschert, L.
Rondin, P. Loubeyre, J.-F. Roch, Mag-netic measurements on
micrometer-sized samples underhigh pressure using designed NV
centers, Science 366,1359 (2019).
[27] G. Balasubramanian, P. Neumann, D. Twitchen, M.Markham, R.
Kolesov, N. Mizuochi, J. Isoya, J. Achard,J. Beck, J. Tissler, V.
Jacques, P. R. Hemmer, F. Jelezko,J. Wrachtrup, Ultralong spin
coherence time in isotopi-cally engineered diamond, Nature
Materials. 8, 382-387(2009).
[28] G. de Lange, Z. H. Wang, D. Ristè, V. V. Dobrovitski,R.
Hanson, Universal Dynamical Decoupling of a SingleSolid-State Spin
from a Spin Bath, Science 330, 60-63(2010).
[29] B. Naydenov, F. Dolde, L. T. Hall, C. Shin, H. Fedder,L. C.
L. Hollenberg, F. Jelezko, J. Wrachtrup, Dynamicaldecoupling of a
single-electron spin at room temperature,Phys. Rev. B 83, 081201
(2011).
[30] H. S. Knowles, D. M. Kara, M. Ataüre. Observing bulk
di-amond spin coherence in high-purity nanodiamonds, Na-ture
Materials. 13, 21 (2014).
[31] L. P. McGuinness, Y. Yan, A. Stacey, D. A. Simpson,L. T.
Hall, D. Maclaurin, S. Prawer, P. Mulvaney, J.
http://dx.doi.org/10.1038/nature07279http://dx.doi.org/10.1038/nature07278http://dx.doi.org/10.1038/nphys1075http://dx.doi.org/10.1038/nphys1969http://dx.doi.org/10.1038/nphys1969http://link.aps.org/doi/10.1103/PhysRevLett.112.097603http://link.aps.org/doi/10.1103/PhysRevLett.112.097603https://doi.org/10.1103/PhysRevLett.104.070801https://www.nature.com/nature/journal/v500/n7460/full/nature12373.htmlhttp://www.pnas.org/content/110/21/8417.abstracthttp://dx.doi.org/10.1021/nl401216yhttps://doi.org/10.1103/PhysRevLett.112.047601https://doi.org/10.1103/PhysRevLett.112.047601https://www.nature.com/articles/ncomms5065https://www.nature.com/articles/ncomms5065http://www.annualreviews.org/doi/abs/10.1146/annurev-physchem-040513-103659http://www.annualreviews.org/doi/abs/10.1146/annurev-physchem-040513-103659https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.89.035002https://doi.org/10.1103/PhysRevA.86.062320https://doi.org/10.1103/PhysRevA.86.062320https://doi.org/10.1103/PhysRevLett.110.130802https://doi.org/10.1103/PhysRevLett.110.130802https://www.nature.com/articles/ncomms4141https://www.nature.com/articles/ncomms10211https://www.nature.com/articles/ncomms10211https://doi.org/10.1038/s41467-017-01158-3https://doi.org/10.1038/s41467-017-01158-3https://www.nature.com/articles/s41467-017-01159-2http://science.sciencemag.org/content/356/6340/832http://science.sciencemag.org/content/356/6340/837http://science.sciencemag.org/content/356/6340/837https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.200402https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.200402https://science.sciencemag.org/content/366/6471/1349https://science.sciencemag.org/content/366/6471/1349https://science.sciencemag.org/content/366/6471/1355/tab-article-infohttps://science.sciencemag.org/content/366/6471/1359https://science.sciencemag.org/content/366/6471/1359https://www.nature.com/articles/nmat2420https://www.nature.com/articles/nmat2420http://science.sciencemag.org/content/330/6000/60http://science.sciencemag.org/content/330/6000/60https://journals.aps.org/prb/abstract/10.1103/PhysRevB.83.081201http://www.nature.com/nmat/journal/v13/n1/full/nmat3805.htmlhttp://www.nature.com/nmat/journal/v13/n1/full/nmat3805.html
-
12
Wrachtrup, F. Caruso, R. E. Scholten, L. C. Hollenberg,Quantum
measurement and orientation tracking of flu-orescent nanodiamonds
inside living cells, Nature Nan-otechnology. 6, 358 (2011).
[32] D. Le Sage , K. Arai, D. R. Glenn, S. J. DeVience, L.
M.Pham, L. Rahn-Lee, M. D. Lukin, A. Yacoby, A. Komeili,R. L.
Walsworth, Optical magnetic imaging of living cells,Nature. 496,
486-489 (2013).
[33] G. Balasubramanian, A. Lazariev, S. R. Arumugam, etal.
Nitrogen-Vacancy color center in diamond-emergingnanoscale
applications in bioimaging and biosensing,Current Opinion in
Chemical Biology. 20, 69-77 (2014).
[34] Y. Wu, F. Jelezko, M.B. Plenio, T. Weil, Diamond Quan-tum
Devices in Biology, Angewandte Chemie - Interna-tional Edition 55,
6586 - 6598 (2016).
[35] G. Gordon, G. Kurizki, D. A. Lidar. Optimal
DynamicalDecoherence Control of a Qubit, Phys. Rev. Lett.
101,010403 (2008)
[36] J.-M. Cai, B. Naydenov, R. Pfeiffer, L. McGuinness,
K.Jahnke, F. Jelezko, M.B. Plenio, A. Retzker, Robust dy-namical
decoupling with concatenated continuous driving,New J. Phys. 14,
113023 (2012).
[37] I. Cohen, N. Aharon, A. Retzker, Continuous
dynamicaldecoupling utilizing time-dependent detuning,
Fortschr.Phys. 64, 1521 (2016).
[38] D. Farfurnik, N. Aharon, I. Cohen, Y. Hovav, A. Retzker,N.
Bar-Gill, Experimental realization of time-dependentphase-modulated
continuous dynamical decoupling, Phys.Rev. A 96, 013850 (2017).
[39] Zijun Shu, Yu Liu, Qingyun Cao, Pengcheng Yang, Shao-liang
Zhang, Martin B. Plenio, Fedor Jelezko, and Jian-ming Cai,
Observation of Floquet Raman Transition ina Driven Solid-State Spin
System, Phys. Rev. Lett.121,210501 (2018).
[40] M. Yu, P.-C. Yang, M.-S. Gong, Q.-Y. Cao, Q.-Y. Lu, H.-B.
Liu, M. B. Plenio, F. Jelezko, T. Ozawa, N. Gold- man,S.-L. Zhang,
and J.-M. Cai, Experimental measurementof the quantum geometric
tensor using coupled qubits indiamond, Natl. Sci. Rev. nwz193,
10.1093/nsr/nwz193(2019).
[41] P. Jamonneau, M. Lesik, J. P. Tetienne, I. Alvizu, L.Mayer,
A. Dréau, S. Kosen, J.-F. Roch, S. Pezzagna, J.Meijer, T. Teraji,
Y. Kubo, P. Bertet, J. R. Maze, V.Jacques, Competition between
electric field and magneticfield noise in the decoherence of a
single spin in diamond,Phys. Rev. B 93, 024305 (2016).
[42] J. Medford, L. Cywiński, C. Barthel, C. M. Marcus, M.
P.Hanson, A. C. Gossard, Scaling of dynamical decouplingfor spin
qubits Phys. Rev. Lett. 108, 086802 (2012).
[43] M. A. Ali Ahmed, G. A. Álvarez, D. Suter, Robustness
ofdynamical decoupling sequences, Phys. Rev. A 87,
042309(2013).
[44] N. Aharon, I. Cohen, F. Jelezko, A. Retzker. Fully
robustqubit in atomic and molecular three-level systems, NewJ.
Phys. 18, 123012 (2016).
[45] N. Bar-Gill, L.M. Pham, A. Jarmola, D. Budker,
R.L.Walsworth, Solid-state electronic spin coherence time
ap-proaching one second, Nat. Commun. 4, 1743 (2013).
[46] Im-Sun Woo, In-Koo Rhee, and Heui-Dong Park, Differ-ential
Damage in Bacterial Cells by Microwave Radiationon the Basis of
Cell Wall Structure, Appl. Environ. Mi-crobiol. 66, 2243
(2000).
[47] Y. Shamis, R. Croft, A. Taube, R. J. Crawford, E. P.
Ivanova, Review of the specific effects of microwave ra-diation
on bacterial cells, Appl Microbiol Biotechnol 96,319 (2012).
[48] M. Loretz, J. M. Boss, T. Rosskopf, H. J. Mamin, D.Rugar,
C. L. Degen, Spurious Harmonic Response ofMultipulse Quantum
Sensing Sequences, Phys. Rev. X 5,021009 (2015).
[49] J. F. Haase, Z.-Y. Wang, J. Casanova, M. B.
Plenio,Pulse-phase control for spectral disambiguation in quan-tum
sensing protocols, Phys. Rev. A 94, 032322 (2016).
[50] Z.-J. Shu, Z.-D. Zhang, Q.-Y. Cao, P.-C. Yang, M. B.Plenio,
C. Müller, J. Lang, N. Tomek, B. Naydenov, L.P. McGuinness, F.
Jelezko, J.-M. Cai, Unambiguous nu-clear spin detection using an
engineered quantum sensingsequence, Phys. Rev. A 96, 051402
(2017).
http:// DOI: 10.1038/NNANO.2011.64http:// DOI:
10.1038/NNANO.2011.64http://www.nature.com/nature/journal/v496/n7446/full/nature12072.htmlhttps://www.ncbi.nlm.nih.gov/pubmed/24875635http://onlinelibrary.wiley.com/doi/10.1002/anie.201506556/fullhttp://onlinelibrary.wiley.com/doi/10.1002/anie.201506556/fullhttp://iopscience.iop.org/article/10.1088/1367-2630/14/11/113023/meta;jsessionid=66B1A2EA818E2A18AEBC591BF41189EF.c1.iopscience.cld.iop.orghttp://onlinelibrary.wiley.com/doi/10.1002/prop.201600071/fullhttp://onlinelibrary.wiley.com/doi/10.1002/prop.201600071/fullhttps://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.013850https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.013850https://doi.org/10.1103/PhysRevLett.121.210501https://doi.org/10.1103/PhysRevLett.121.210501https://doi.org/10.1093/nsr/nwz193https://doi.org/10.1093/nsr/nwz193https://journals.aps.org/prb/abstract/10.1103/PhysRevB.93.024305https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.086802https://doi.org/10.1103/PhysRevA.87.042309https://doi.org/10.1103/PhysRevA.87.042309http://iopscience.iop.org/article/10.1088/1367-2630/aa4fd3/metahttp://iopscience.iop.org/article/10.1088/1367-2630/aa4fd3/metahttps://www.nature.com/articles/ncomms2771https://doi.org/10.1128/AEM.66.5.2243-2247.2000https://doi.org/10.1128/AEM.66.5.2243-2247.2000https://doi.org/10.1007/s00253-012-4339-yhttps://doi.org/10.1007/s00253-012-4339-yhttps://journals.aps.org/prx/abstract/10.1103/PhysRevX.5.021009https://journals.aps.org/prx/abstract/10.1103/PhysRevX.5.021009https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.032322https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.051402
Protecting quantum spin coherence of nanodiamonds in living
cellsAbstractI IntroductionII Protecting coherence of N-V spin in
nanodiamondIII Application in quantum sensingIV Conclusion and
discussionV Acknowledgements AppendixA Principle of concatenated
continuous dynamical decouplingB Characteristics of nanodiamondsC
Cell culture and sample preparationD Cell membrane staining and
identifying nanodiamonds in cellsE Influence of microwave radiation
on living cellsF Sensitivity comparison under the constraint of
microwave power
References