pacs numbers: 42.50.dv, 07.55.ge, 03.67.-a, 42.50.-p · pacs numbers: 42.50.dv, 07.55.ge, 03.67.-a,...

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

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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-

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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-

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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

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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

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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,

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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

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