Injection of a single electron from static to moving quantum dots

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by  Benoit Bertrand

Injection of a single electron from static to moving quantum dots
Benoit Bertrand,1,2 Sylvain Hermelin,1,2 Pierre-Andr´e Mortemousque,1,2 Shintaro Takada,1,2,3 Michihisa
Yamamoto,3,4 Seigo Tarucha,3,5 Arne Ludwig,6 Andreas D. Wieck,6 Christopher B¨auerle,1,2 and Tristan Meunier1,2
1Univ. Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France
2CNRS, Inst NEEL, F-38042 Grenoble, France
3Department of Applied Physics, University of Tokyo, Tokyo, 113-8656, Japan
4PRESTO-JST, Kawaguchi-shi, Saitama 331-0012, Japan.
5RIKEN Center for Emergent Matter Science (CEMS),
2-1 Hirosawa, Wako-Shi, Saitama 31-0198, Japan
6Lehrstuhl fu¨r Angewandte Festko¨rperphysik, Ruhr-Universita¨t Bochum,
6
Universita¨tsstrasse 150, 44780 Bochum, Germany
1
(Dated: January 12, 2016)
0
2 We study the injection mechanism of a single electron from a static quantum dot into a moving

n quantum dot created in a long depleted channel with surface acoustic waves (SAWs). We demon-
a stratethatsuchaprocessischaracterizedbyanactivationlawwithathresholdthatdependsonthe
J SAW amplitude and the dot-channel potential gradient. By increasing sufficiently the SAW mod-
1 ulation amplitude, we can reach a regime where the transfer is unitary and potentially adiabatic.
1 This study points at the relevant regime to use moving dots in quantum information protocols.

] PACSnumbers: 73.63.-b
l
l
a
h The ability to displace controllably and on-demand a ulation potential overcomes the one of the static poten-
- single electron on a chip is an important prerequisite for tial. The calibration of the SAW modulation amplitude
s
e the realization of electronic circuits at the single elec- [9], and the analysis of the electron injection probabil-
m
tron level. It opens the route to interconnect nodes of ity allow us to precisely estimate the value of the static
. a spin-based quantum nanoprocessor [1–4] or to perform potential gradient for a given gate configuration. This
t
a quantum optics experiments with itinerant electrons [5– knowledgeisusedtoidentifythe injectionprocessmech-
m
8]. The recent demonstration of fast and on-demand anism. Moreover, it is possible to trigger the electron
- transferofasingleelectronisafirststeptowardsthisgoal injection for a nanosecond with a unitary efficiency. We
d
[9, 10]. In these experiments, the electron is transported showthatthisfastinjectiontechniqueiscompatiblewith
n
o in moving quantum dots isolated in an AlGaAs/GaAs an adiabatic injection in which the electron remains in
c heterostructure. They are created in a 4µm-long one- the ground state of the trapping potentials.
[ dimensionaldepletedchannelbyexcitingasurfaceacous-

1 tic wave (SAW) [11]. Due to the piezoelectric properties AWG +–
v of (Al)GaAs, the SAW induces a propagating sinusoidal V
5 potential that adds up to the potential of the channel. VR 100 MΩ bias
8 The resulting moving potential is able to confine and VL
4
transfer electrons. Such moving quantum dots have per-
2 RF
0 mittedtotransferanensembleofelectronsoverdistances
. approaching 100µm while preserving its spin coherence
1 V
1 µm L'
[12, 13]. To reach the on-demand single electron transfer
0 IDT
6 regime, anelectronisinitiallyisolatedinanelectrostatic 100 MΩ V
R'
1 quantum dot located next to the channel entrance, and Vbias –
v: isthentransferredtoamovingquantumdot[9]. Inorder +
i to use such a tool in quantum information protocols, it
X
is of importance to understand the mechanism responsi- FIG. 1: SEM picture of a sample similar to the one used for
r ble for the injection of the electron from the static into a thiswork,andmainelectronicset-up. AnIDTisplaced2mm
a
moving quantum dot. totheleftofthestructure(schematicallysketchedontheleft
of the figure).
In this Letter, we experimentally investigate the injec-
tion process from the static to a moving quantum dot.
More specifically, we analyzed the influence of two rele- The sample used in this work is shown in Fig. 1.
vant parameters: the SAW modulation amplitude and It is fabricated on a GaAs/AlGaAs heterostructure,
the static potential induced by the gates defining the host of a 2DEG 100nm below the surface, of density
source static dot and the channel [14, 15]. The injec- 1.35×1011cm−2 and mobility 1.5×106cm2V−1s−1. It
tionoftheelectrontoamovingquantumdotoccursonly is constituted of two laterally defined quantum dots, the
when the potential gradient induced by the SAW mod- sourceandthereceptiondots, connectedtogetherwitha
2
4µmlongdepletedchannel. Aninterdigitatedtransducer (a) (b) 0.2
(IDT) is placed 2mm to the left of the gate structure in
-0.2
order to generate a SAW. It counts 70 pairs of 60µm
qloTonurnaegtnnhcsfiepynoIgD(reRtTrFsm,)weitaietsrxhuecsriaoetamn1taeiµnontnmtlsyowtefhxaravcomieutleepgsnlhigattuthhSd.eAeWWlAefShtaAet(Wnr2i.ga6ihs3rt2a)a3dpqGipoulfHairenezd--. δV (V)L --00..43 (δVL,δVR)T 0 ∆I (nA)QPC
tumdotallowedustocharacterizetheenergyneededfor -0.05
-0.2 -0.1 0 0.1-0.2 -0.1 0 0.1
an electron to enter the dot, called the charging energy δV (V) δV (V)
R R
(2.5meV),andthesingle-particleorbitalenergysplitting
0.6
(400µeV). Thechargestateofthequantumdotsismon- -0.2 (c) (d)
itored thanks to the adjacent Quantum Point Contacts
-0.3
io(sQpeaPrnCactshi)no,rgteydaptitacoabltlahyseeDmtCei-mxbipinaegsreacdthuawrmeitbhoef3r500o0fmµaeKVd..iluTthioensafrmidpglee δV (V)L --00..45 P 0 ∆I (nA)QPC
The experimental sequence that we perform to trans- -0.6 T
fertheelectronbetweenthetwostaticquantumdotswas -0.7
initially presented in Ref. 9. The source dot is isolated -0.2 -0.1 0 -0.2 -0.1 0 -0.6
from the lead allowing to trap the electron 5meV above δVR (V) δVR (V)
the Fermi energy. We then add a 10µs voltage pulse
250 1
on V and V , characterized by a voltage displacement (e) (f)
R L 0.1 y
(δVL, δVR) called the sending pulse. As a result, the 200 0.8bilit
potential gradient between the channel and the source V) 0.05 )s150 0.6ba
ddoretdisnafunrotsheecronrdedRucFe-dexdciutraitniognthiseappupllsiee.d oAnftehwe hIDunT- δV (LT 0 τn( WAS100 0.4ction pro
to generate a SAW modulation within the duration of -0.05 50 0.2nje
the sending pulse, ensuring the electron transfer. The I
-0.1 0
presence/absence of the electron can be inferred in both 1 1.5 2 2.5 3 0.6 0.8 1 1.2 1.4 1.6
A (V) A (V)
thesourcedotandthereceptiondotviachargemeasure- SAW SAW
ments [9, 16].
Tostudytheinfluenceofthedotpotentialontheinjec-
FIG.2: (coloronline)DifferenceoftheQPCcurrentrecorded
tionprocessfromthesourcetothemovingdots, wevary withthechargedetector(eitheronthesourceorthereception
(δV , δV ) and probe the charge present in the source dot)beforeandafterapplyingasendingpulse(δV ,δV )on
L R L R
dot after the sending pulse [see Fig. 2(a-c)]. Without thesourcedot. Eachpointistheresultofasinglerealization
SAW modulation [Fig. 2(a)], the electron remains in the of the experiment. Red and blue points correspond to the
respective cases where one electron leaves or is added to the
isolated dot (white region) except for the sending pulses
dot after the sending pulse. White points corresponds to no
with the most positive V and the most negative V
L R change in the dot charge configuration. In (a) and (b), we
(red region): the dot isolation is no longer sufficient and
concentrate on the source dot charge configuration, respec-
the electron is lost to the neighbor reservoir. With SAW tivelywithoutandwithSAWmodulationduringthesending
modulation[Fig.2(b,c)],anewregionwheretheelectron pulse. (c) and (d) present respectively the QPC response of
leavesthesourcedot,calledthetransferregion,ispresent the source and the reception dots with the SAW modulation
forthemostnegativeV andV (bottomleftcorner). It applied during the sending pulse. The observed correlations
L R
between the two plots confirm that an electron arrives in the
corresponds to the process where the electron has been
receptiondotonlyforthesendingpulsecorrespondingtothe
injected in a SAW moving quantum dot and leaves the
transfer region. It is worth noting that the two sets of data
source dot. A confirmation of these two regions label-
(a,b) and (c,d) correspond to slightly different gate voltage
ing is obtained by analyzing the correlation between the configurations. (e) Evolution of the position of the voltage
electron leaving the source dot [Fig. 2(c)] and arriving threshold δV as a function of A [set of data (a,b)]. (f)
LT SAW
in the reception dot (initially empty) after the transfer Emission probability as a function of ASAW and τSAW with a
sequence [Fig. 2(d)]. An electron is indeed detected in sendingpulse(δVL =−0.55V,δVR =0V)[setofdata(c,d)]
recordedover500experimentalrealizations. (Inset)Fitofthe
the reception dot after the transfer only for the sending
datawithanactivationlawwithathresholdA =0.98Vand
pulses corresponding to the transfer region. T
a typical timescale τ =63ns.
IDT
The sending pulse amplitude has to be more negative
thanacertainthresholdon(δV ,δV )[seeFig.2(c)],de-
L R
fined bythe limit (δV ,δV ) , that separatesthe trans-
L R T
fer region and the region where the electron remains in of the transfer for δV =0. We find that the transfer is
R
thesourcedot. Inthefollowing,weanalyzethebehavior activated only below a certain threshold δV , that lin-
LT
3
earlydependsonASAW[seeFig.2(e)]. Indeedforalarger (a) (b) e
m
AulSaAtWion, tohveerpcootmenetsiamlogrreadeiaesniltyimthpeoosnede breysuthlteinSgAfWrommothde- ng ti
si
gatevoltages. Itresultsinawiderrangeofgatevoltages ea
where the injection of the electron to a moving quantum d ncr
o i
dotispossible. Thisdemonstratesthedependenceofthe eri
p
two important parameters for the electron transfer: the W
potential gradient induced by the SAW, and the static a.u.) SA
dot potential. We conclude that the electron transfer is al (
activated above a threshold defined by two interdepen- nti
e
dent parameters AT and VT. pot
This model has to be refined by taking into account
the risetime of the SAW modulation that is due to the
finitebandwidthoftheIDT.Toinvestigatepreciselythis
aspect, we set the sending pulse parameters (δV , δV )
L R
to (0V, −0.55V) and varied both A and the RF-
SAW
excitation duration τ . The resulting probability to
SAW
emit the electron is represented in Fig. 2(f). The in-
0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
jection of the electron to a moving quantum dot occurs position (a.u.) position (a.u.)
only when A reaches the amplitude threshold A .
SAW T
As expected from the risetime of the SAW modulation,
FIG. 3: (color online) Time evolution of the dot potential
a shorter τ is needed to reach A when A is in-
SAW T SAW
for two different amplitudes of SAW excitation. The time
creased. A fit of the data is performed assuming an acti-
increases going from top to bottom traces and the time dif-
vationlaw[seeinsetofFig.2(f)]. Itenablesustodeduce
ferencebetweentwoconsecutivetracesisT/13,whereT isthe
the risetime of the SAW modulation (about 63ns) and periodoftheSAWexcitation. Thepotentialgradient∆V in-
g
the value of AT (about 1V). From the relation between ducedbythegatevoltagesisthesamein(a)and(b). (a)The
δVLT and ASAW, obtained from Fig. 2(e), and the gate potential gradient induced by the SAW excitation ∆VSAW is
lever arm (≈ 20mV/meV), we estimate that AT corre- comparable to ∆Vg and shallow moving quantum dots are
defined. Tunnelling back of the electron to the source dot
sponds to a SAW-induced potential gradient seen by the
is possible (see orange arrows), leading to a stochastic injec-
electron ∆V ≈ 30meV/µm. As explained earlier, it
SAW tionprocedure. In(b)∆V islargerthan∆V anddeeper
SAW g
correspondsalsotothedot-channelpotentialgradientin
moving quantum dots are defined.
the specific gate configuration of Fig. 2(f).
To have a better insight into the injection process, we
sketched the time dependent potential seen by the elec- Fig. 2(f), we infer that the injection process is certainly
tron in the presence of the SAW excitation (see Fig. 3). stochasticand,accordingtothepreviousdiscussion,non-
At a fixed potential gradient induced by the gate volt- adiabatic. OnecannoticeonFig.2(f)thattheelectronis
ages ∆V , the transfer process depends on ∆V . For expelledfromthedotafteratleastafewtensofnanosec-
g SAW
∆V lowerthan∆V [Fig.3(a)],shallowSAWmoving ondscorrespondingtothetimeneededforA toreach
SAW g SAW
dots are created and a thin tunneling barrier separates A . Theelectronexperiencestheexcitationofafewhun-
T
them from the source dot. As a consequence, a process dreds of moving quantum dots before being transferred
where the electron can tunnel back to the source dot with most part of it at A below A , in a config-
SAW T
after being caught is likely to happen [14, 15]. Consider- uration similar to Fig. 3(a). The emission probability
ingthe30meV/µmdot-channelpotentialgradientprevi- reaches unity only because the electron has the possi-
ouslyestimated, theenergydetuningbetweenthesource bility to be injected in a considerable number of SAW
andthemovingquantumdotsinthetunneling-backcon- periods. It also results in the exploration of the excited
figurationisexpectedtobelargerthantheorbitalenergy states of the source dot and in a non-adiabatic injection
splittingofthesourcedot. Therefore,thetunneling-back process. To be able to probe the adiabatic limit, it is
events will certainly result in the excitation of higher or- therefore necessary to characterize the electron transfer
bitalstatesofthesourcedot,andconsequentlytheinjec- ataconstantSAWmodulationamplitudeandforatime
tion process will be non-adiabatic in this situation. For as short as possible.
∆V bigger than ∆V [Fig. 3(b)], the tunnel barrier To this aim, a modified transfer sequence was utilized
SAW g
becomes too thick and no tunneling-back process is pos- fortheinjectionofasingleelectron. τ wasreducedto
SAW
sible. In this situation, the injection process is expected its minimum duration allowed by the SAW risetime, and
to be adiabatic and happens when the source and the we added a 1ns pulse on gate V synchronized with the
L
moving quantum dot are overlapping. SAW modulation [9]. This gate pulse is used to rapidly
Therefore, under the experimental conditions of change the potential gradient between the dot and the
4
channel. Practically,thedotpotentialistunedtoapoint to the end of the SAW excitation burst, when the am-
P [see Fig. 2(c)] where the potential gradient is too large plitude is maximal. For A = 1.5V, the injection
SAW
for the SAW to transfer the electron into the moving probability follows the same shape with a lower success
quantumdot. Onlyforthe1nspulse,thesystemistuned rate. When the SAW excitation is lengthened from 58ns
to point T [see Fig. 2(c)] where the dot-channel poten- to 70ns at 1.5V, the maximum SAW amplitude reached
tial gradient is reduced. As a consequence the electron atthedotincreasesduetotheSAWmodulationrisetime,
is expected to be transported by the SAW only during and therefore the highest probability reached rises.
the nanosecond pulse. This technique allows us to probe
Figure4(b)showstheevolutionofthemaximumemis-
the injection process only for two periods of the SAW
sion probability at ∆t = 865ns as a function of the
max
excitation and more importantly at constant A .
SAW SAW amplitude. As previously demonstrated, the SAW
amplitude needs to reach a threshold to be able to catch
200
((aa)) A , τ : the electron and the injection process shows an activa-
SAW SAW
1.78V, 62ns tion law with respect to the SAW amplitude. At high
s
nt150 1.50V, 58ns SAW amplitude, the injection process has a probability
u
co 1.50V, 62ns closetounity,andisexpectedtobeadiabatic[Fig.3(b)].
n
o 1.50V, 66ns Figure 4(c) shows the evolution of the maximum emis-
missi100 1.50V, 70ns sionprobabilityat∆tmax asafunctionofthenanosecond
e
n pulseamplitudefortwodifferentpointsPfromwhichthe
o
ctr 50 nanosecondpulseisapplied. Similarlytotheresultspre-
e
el sented in Fig. 2(f) for the SAW amplitude, we obtain a
threshold behavior in gate voltage. It is worth noting
0 that no broadening of the distribution is observed when
840 845 850 855 860 865 870 875 880 885 890
Δts (ns) the electron is buried deeper into the source dot. This is
consistent with the electron staying in the ground state
500
(b) (c) of the source dot potential during the injection process.
s
nt400 In conclusion, we have studied the injection process of
u δV =-0.41V
o L
sion c300 δVL=-0.39V ainsdiuncgeledemleocvtirnognqfruoamntuamstadtoitc.qFuoarnatusmpedciofitcindtoot-achSaAnWne-l
s
mi potential gradient at the injection position, the injection
e200
n probability can be tuned from zero to one by varying
o
ectr100 the SAW amplitude, pointing at a probabilistic process.
el At sufficiently large SAW amplitude, only one period of
0 theSAWmodulationisrequiredtotransfertheelectron.
1.3 1.4 1.5 1.6 1.7 -4 -3 -2 -1 0
A (V) gate pulse amplitude (V) In this regime, the injection process is expected to be
SAW
adiabatic, with the electron remaining, at any time, in
the ground orbital state of the trapping potential. Such
FIG.4: (coloronline)(a)Electronemissioncountsoutof200 a regime will be relevant to reduce errors in quantum
repetitionsasafunctionofthedelaybetweentheSAWburst
protocolswheresingleelectronsaretransferredinmoving
generation and the nanosecond pulse for different A and
SAW quantum dots.
τ . (b) and (c) Electron emission counts out of 500 repe-
SAW
titions at ∆tmax as a function of the ASAW (b) and the gate We acknowledge technical support from the “Poles”
pulse amplitude (c). τSAW is fixed at 62ns in both cases. of the Institut N´eel as well as from Pierre Perrier.
M.Y. acknowledges financial support by JSPS, Grant-
Figure 4(a) shows the injection counts as a function of in-Aid for Scientific Research A (No. 26247050) and
the delay ∆t between the SAW burst and the nanosec- Grant-in-Aid for Challenging Exploratory Research (No.
s
ondpulseappliedtothegate. ForA =1.78V,thein- 25610070). S. Tarucha acknowledges financial support
SAW
jection probability reaches almost unity for a delay close by JSPS, Grant-in-Aid for Scientific Research S (No.
to ∆t = 865ns. The delay is explained by the finite 26220710), MEXT KAKENHHI “Quantum Cybernet-
max
SAW velocity of 2867m/s [17] and the distance between ics,” MEXT project for Developing Innovation Systems,
the IDT and the sending dot. Before and after ∆t , and JST Strategic International Cooperative. A.L. and
max
A is not high enough to ensure a unity transfer pro- A.D.W. acknowledges DFG via TRR160, the support of
SAW
cessandtheelectroncanbeback-scatteredtothesource the BMBF Q.com-H 16KIS0109, Mercur Pr-2013-0001
dot. AnexponentialRCrising/fallingtimelawforA and the DFH/UFA CDFA-05-06. B.B. acknowledges fi-
SAW
due to the finite risetime of the SAW excitation explains nancial support from “Fondation Nanosciences.” T.M.
qualitativelytheasymmetricshapeoftheemissionprob- acknowledges financial support from ERC “QSPINMO-
abilityasafunctionof∆t . ∆t correspondstherefore TION.”
s max
5
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