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RESEARCH ARTICLE

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Quantum Dot Molecule Devices with Optical Control of

Charge Status and Electronic Control of Coupling

Frederik Bopp,* Jonathan Rojas, Natalia Revenga, Hubert Riedl, Friedrich Sbresny,

Katarina Boos, Tobias Simmet, Arash Ahmadi, David Gershoni, Jacek Kasprzak,

Arne Ludwig, Stephan Reitzenstein, Andreas Wieck, Dirk Reuter, Kai Müller,

and Jonathan J. Finley*

Tunnel-coupled pairs of optically active quantum dots—quantum dot

molecules (QDMs)—oﬀer the possibility to combine excellent optical

properties such as strong light-matter coupling with two-spin singlet–triplet

(S−T0) qubits having extended coherence times. The S−T0basis formed

using two spins is inherently protected against electric and magnetic ﬁeld

noise. However, since a single gate voltage is typically used to stabilize the

charge occupancy of the dots and control the inter-dot orbital couplings,

operation of the S−T0qubits under optimal conditions remains challenging.

Here, an electric ﬁeld tunable QDM that can be optically charged with one

(1h) or two holes (2h) on demand is presented. A four-phase optical and

electric ﬁeld control sequence facilitates the sequential preparation of the 2h

charge state and subsequently allows ﬂexible control of the inter-dot coupling.

Charges are loaded via optical pumping and electron tunnel ionization. One-

and two-hole charging eﬃciencies of (93.5 ±0.8)% and (80.5 ±1.3)% are

achieved, respectively. Combining eﬃcient charge state preparation and

precise setting of inter-dot coupling allows for the control of few-spin qubits,

as would be required for the on-demand generation of 2D photonic cluster

states or quantum transduction between microwaves and photons.

F. Bopp, J. Rojas, N. Revenga, H. Riedl, T. Simmet, A. Ahmadi,

J. Kasprzak, J. J. Finley

Walter Schottky Institut

Department of Physics and MCQST

Technische Universität München

Am Coulombwall 4, 85748 Garching, Germany

E-mail: [email protected]; ﬁ[email protected]

F. Sbresny, K. Boos, K. Müller

Walter Schottky Institut

Department of Electrical and Computer Engineering and MCQST

Technische Universität München

Am Coulombwall 4, 85748 Garching, Germany

The ORCID identiﬁcation number(s) for the author(s) of this article

can be found under https://doi.org/10.1002/qute.202200049

Wiley-VCH GmbH. This is an open access article under the terms of the

Creative Commons Attribution License, which permits use, distribution

and reproduction in any medium, provided the original work is properly

cited.

DOI: 10.1002/qute.202200049

1. Introduction

Long coherence times, strong light-matter

coupling, and tunability lie at the heart

of spin-photon interfaces required for dis-

tributed quantum technologies.[1] Semicon-

ductor quantum dots (QDs) provide these

characteristics due to their robust polariza-

tion selection rules that allow for mapping

between spin and optical polarization,[2–4]

dominant emission into the zero-phonon

line at low temperatures,[5] nearly Fourier-

limited optical linewidths[6] and integrata-

bility into devices to facilitate tunability

and to enhance single spin-photon cou-

pling eﬃciencies.[7] Together, these proper-

ties make QDs promising as spin-photon

interfaces[8] for the on-demand generation

of 1D photonic cluster states[9,10] or quan-

tum transduction between microwave and

infrared photons.[11]

The growth of vertically stacked pairs

of tunnel-coupled dots—quantum dot

molecules(QDMs)—opensthewaytoform

D. Gershoni

Physics Department and Solid State Institute

Technion-Israel Institute of Technology

Haifa 32000, Israel

J. Kasprzak

Institut Néel

Grenoble INP, CNRS

Université Grenoble Alpes

Grenoble 38000, France

A. Ludwig, A. Wieck

Applied Solid State Physics

Faculty of Physics and Astronomy

Ruhr-Universität Bochum

Universitätsstraße 150, 44801 Bochum, Germany

S. Reitzenstein

Technische Universität Berlin

Hardenbergstraße 36, 10623 Berlin, Germany

D. Reuter

Universität Paderborn

Department Physik

Warburger Str. 100, 33098 Bochum, Germany

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multi-spin qubits that are less susceptible to decoherence than

single QDs (or spins in single QDs).[12] In particular, the singlet–

triplet (S−T0) logical qubit formed by two spins[13–15] occupy-

ing the hybridized orbitals of tunnel-coupled dots is expected

to provide more than an order of magnitude longer coher-

ence times (T(∗)

2) than observed for single QDs due to the ex-

istence of a sweet spot at which the S−T0qubit energy is

insensitive to magnetic and electrical noise. This expectation

has been conﬁrmed for both optically active[16] and electrostat-

ically deﬁned coupled QDs.[17] QDMs have also been theoreti-

cally suggested to facilitate the deterministic (on-demand) gen-

eration of 2D photonic cluster states,[18] a key resource needed

for measurement-based quantum computation[19] and memory-

free quantum communication.[20,21] To facilitate these applica-

tions, QDMs must be operated in a regime where they are sta-

bly occupied by two spins, while the inter-dot tunnel coupling

of s-orbital states can be freely tuned, for example, using the

voltage (VG) applied to a gate electrode. Thus, the charge occu-

pancy of bottom (SB)andtop(ST) dots in the molecule should re-

main in the (SB,S

T)∈{(2,0),(1,1),(0,2)} subspace and the tun-

nel coupling of the orbital states should be freely tunable without

changing n=SB+ST=2. In previous experiments, all require-

ments have been demonstrated individually.[22–26] However, in-

dependent control of nand tunneling induced hybridization of

orbital states has been diﬃcult to achieve until now since nis typ-

ically regulated via Coulomb blockade of carrier tunneling from

a proximal doped contact[16,27] using a single gate electrode. The

same gate electrode is also used to tune the orbital states into res-

onance, the proximity of the QDM to the doped contact, dot–dot

spacing (s) and height (h) of the two dots forming the molecule

must be precisely controlled during growth to allow for tunnel

coupling between the s-orbital states in the QDM while remain-

ing in the n=2 charge stability region.

Here, we demonstrate all-optical, sequential, and independent

preparation of the n=1andn=2 charge states of the QDM

in a device geometry that leaves the gate potential free to con-

trol the orbital tunnel coupling between the two dots. Our device

geometry is an n-i-Schottky diode with the QDMs embedded at

the midpoint of the i-region (see Experimental Section). An Al-

GaAs tunneling barrier is grown 5 nm above the QDM layer to

inhibit hole tunneling escape from the QDM, while electrons can

freely escape at a rate determined by VG. We have previously used

similar approaches to achieve selective optical charging of single

QDs with electrons or holes.[28,29] Consequently, using our ap-

proach spin state preparation and control is possible at precisely

and arbitrarily adjustable coupling conditions by controlling the

polarization and frequency of the optical charging laser relative

to the discrete absorption resonances of the QDM. Moreover, we

demonstrate that the optical charging process can be repeated

to sequentially switch from the n=0 to 1 to 2 hole state, open-

ing the way to access S−T0logical qubits that are insensitive to

magnetic and electric ﬁeld noise to ﬁrst order while being fully

tunable within the two-spin logical state space.[16]

2. Results

2.1. Measurement Scheme

The sample investigated was grown by solid-source molecular

beam epitaxy (MBE) and is an n-i-Schottky photometer with a 315

nm thick i-region. Two layers of vertically stacked self-assembled

InAs QDs were grown at the mid-point of the i-region and

have a wetting layer-to-wetting layer spacing of s=7.6nm.The

dot height was precisely ﬁxed at h=2.2 nm using the In-ﬂush

method.[30] After growth of the top QD layer, a 10 nm thick GaAs

capping layer was deposited before a 20 nm thick AlxGa(1−x)As

tunnel barrier was grown (x=0.33). As depicted schematically

in Figure 1b, this barrier serves to prolong the tunneling time of

the hole compared to the electron, thereby allowing selective op-

tical charging.[28] Since both n-contact and the surface metallic

electrode are ≥100 nm away from the QDM, tunneling induced

charging from the contacts into the QDM is inhibited. Thereby,

the QD molecule in our sample is largely decoupled and the op-

tically prepared ST+SBcharge state remains unaﬀected by tun-

neling from the contacts for the bias conditions used during op-

eration.

Our measurement scheme for charging and probing a two

hole state is illustrated schematically in Figure 1a. It consists of

four phases: Reset (I), charging of ﬁrst hole (II), charging of sec-

ond hole (III), and readout (IV). The four phases are schemati-

cally depicted in Figure 1b. During phase I, a strong reverse bias

of VG=VI=−4 V is applied for 550 ns. VGinduces an axial elec-

tric ﬁeld F=(VBI −VG)∕dIalong the growth direction, where VBI

is the built-in voltage and dIis the thickness of the intrinsic re-

gion. A strong electric ﬁeld, as applied in phase I, facilitates fast

tunneling escape of both electrons and holes from the molecule

to initialize the QDM into the neutral state, with n=0holes.In

phase II of the measurement protocol, the gate voltage is tuned to

VII in the range ≤−0.8 V to produce electric ﬁeld conditions for

which the photogenerated electron tunnels out of the molecule

on timescales faster than the neutral exciton lifetime, while the

hole remains stored.[28] Phase II lasts 400 ns during which a 200

ns laser pulse tuned resonant to the neutral exciton transition

(X0) in the bottom QD is gated on using an acousto–optical mod-

ulator (AOM—red colored pulse in Figure 1a). The resonant na-

ture of the excitation combined with the discrete electronic struc-

ture of the QDM ensures that the n=1 charge state is reached.

Hereby, a maximum of one single electron–hole pair is gener-

ated in the QDM and, thereby, the system remains optically ac-

tive until charged by a single hole, whereupon the absorption of

the trion shifts out of resonance with the driving laser ﬁeld. In

this way, the resonant excitation ensures that only a single hole

is generated. Once the n=1 hole charge state has been reached,

the discrete absorption of the QDM shifts to one of the positively

charged trion transitions. As such, the molecule becomes photo-

sensitive again by tuning the driving laser frequency or switching

VGto induce a DC Stark shift and re-establishing resonance with

the positive trion (X+). Thus, as depicted schematically in Fig-

ure 1b(III), moving from the n=1ton=2 charge conﬁguration

involves switching the laser frequency or electric ﬁeld to a new

value (VG=VIII)wherebyX+is resonantly excited. As before, a

photon is absorbed whereupon the photogenerated electron tun-

nels out of the QDM leaving two holes in the system. Once the

QDM has been optically charged with two holes, the voltage is

switched to a higher level (VIV ≥−0.6 V), for which electrons no

longer tunnel out of the molecule and quantum optical exper-

iments such as photoluminescence or resonance ﬂuorescence

can be performed to conﬁrm the presence of the optically gener-

ated hole(s) in the QDM. Figure 1b(IV) depicts the readout of the

charge state, denoted phase IV. Readout of the charge status nin

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Figure 1. Optical charging of a QDM. a) Measurement scheme for charging and probing two hole states, consisting of four phases: Reset (I), charging

one hole (1h) (II), charging two holes (2h) (III), readout (IV). The black line symbolizes the gate voltage VGwith voltage plateaus VIto VIV. The colored

boxes indicate laser pulses for charging and readout. b) Band structure of QDM with double potential well (red, blue) and tunneling barrier (gray). Four

sequence phases are illustrated: Reset (I), low gate voltage leads to tunneling of electrons and holes to empty the QDM; charging one/two holes (II,

III), resonant laser pulse creates electron–hole pair. Via tunneling ionization, charges are separated and QDM loaded with one/two holes; Readout,

resonant s- or p-shell excitation is applied to probe charge state (IV). c) Voltage dependent photoluminescence measurement showing X0,X+,andX++

transitions.

the QDM is performed by tuning a third laser ﬁeld into resonance

with an excited state transition of either X0,X+, or the doubly

charged positive trion (X++) to pump a luminescence recycling

transition. Due to the quantum conﬁned stark eﬀect (QCSE),[31]

the laser energies used to charge the QDM are signiﬁcantly fre-

quency detuned by Δ=−1470 GHz (≫𝛿≈10 kHz linewidth),

from the readout laser allowing clean spectral ﬁltering between

charging and readout signals. As soon as two holes are prepared

inside the QDM, the gate voltage is widely adjustable during the

readout phase IV, for example, to control spin–spin orbital cou-

pling in the 2h-molecule and explore the S−T0qubit state space.

The boundaries are imposed by the voltage where electron tun-

neling is fast compared to the measurement time in reverse bias

(−0.6 V) and the diode is ﬂooded with carriers in forward bias (0.7

V). Within this range, any coupling condition can be addressed

since the charge state is pre-set. For the measurements presented

here the scheme presented in Figure 1a is continuously repeated

at 420 kHz.

Depending on the charge state required we switch between

n=0, 1, and 2 hole charging. This is done by either gating oﬀ the

charging laser or tuning the gate voltage such that the laser does

not match the resonance condition with either the X0transition

(1h) or the X0and X+transitions (2h). To identify readout tran-

sitions for probing zero, one, and two hole states, we recorded

voltage dependent photoluminescence data. Figure 1c shows typ-

ical voltage dependent photoluminescence recorded under non-

resonant excitation into the wetting-layers (1458 meV) as a func-

tion of the DC voltage (VIV) applied to the Schottky contact. For

this measurement the reset phase I is applied, while the charging

pulses in phases II and III of the measurement scheme are gated

oﬀ. By exciting electron–hole pairs in the wetting layers, charg-

ing of the QDM occurs probabilistically. Thus, the charge occu-

pancy statistically ﬂuctuates leading to photoluminescence sig-

nals from diﬀerent charge states in the time integrated spectrum

that allows simultaneous monitoring of diﬀerent charge states.

Crossings and avoided crossings characteristic for QDMs are ob-

served. They arise due to the orbital hybridization of hole states.

Hybridization takes place in both, ground and excited state, lead-

ing to charge state speciﬁc patterns.[32,33] In this way X0,X+,and

X++ transitions are identiﬁed and marked in Figure 1c. These

transitions link the n=0, 1, and 2 hole ground to excited states

and are therefore used to probe the resulting charge state of the

QDM after switching on the 1h and/or 2h charging laser pulses.

2.2. One Hole Charging

To evaluate the performance of the all-optical 1h charging scheme

outlined above, we implemented the experimental protocol de-

picted in Figure 1a including only the 1h charging pulse (II),

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Figure 2. Emission of X0and X+when charging one hole. a) Excitation

scheme used to identify 1h charging resonance. Due to overlapping p-

shells, X0(blue)/X+(red) is detected when vacuum (vac)/1h ground state

is predominant. b) Emission spectrum at −0.2 V under p-shell excitation

with and without charging pulse of phase II applied (red/blue). X0tran-

sition fades when charging takes places, while X+rises. c) 2D colormap

showing the X0intensity as a function of VII and ℏ𝜔1h. Yellow (blue) indi-

cates high (low) count rates during the readout phase IV of the measure-

ment. The red cross indicates the settings used in the rest of the article

for 1h charging. White dashed line marks −1.1 V, from where the line cut

is extracted (right). Example of the anti-correlated integrated intensities of

X0and X+transitions when modifying the energy of the 1h charging laser

to identify charging resonances at phase-II of the measurement (right).

while omitting the 2h charging pulse (III). During the readout

phase IV of the measurement, the QDM was excited via an ener-

getically higher lying discrete interband transition (p–p). In this,

as well as in the following experiment, we drive transitions where

the excited orbital state exciton is in the lower QD. As depicted

schematically in Figure 2a, the neutral exciton p–p transition

(X0

[p−p]) and the positive trion p–p transition (X+

[p−p]) energetically

overlap at 1341.5 meV. This provides a common cycling transi-

tion for both, the empty QD and the 1h ground state. Phonon-

mediated relaxation from the p- to the s- orbital leads to domi-

nant photon emission from the lowest orbital transition. Even if

the excitation is not charge state selective, the resulting emission

is. The X0/X+emission obtained when exciting the vacuum/

1h ground state are separated spectrally. Therefore, we can de-

duce from the emission intensities on the predominant charge

ground state.

The data presented in Figure 2b speciﬁcally compare mea-

surements performed with (blue) and without (red) resonant 1h

charging pulse applied. VIV was set to −0.2 V. If the 1h charging

laser is blocked then the X0emission is observed, since the QDM

remains uncharged. In contrast, upon gating the charging laser

on during phase II of our measurement cycle, the X0emission

signal vanishes during the readout phase of the measurement.

This reﬂects the fact that if charging has occurred the QDM is no

longer in the X0charge conﬁguration, and thus is not emitting

on the same transition. On the other hand, when the 1h charging

pulse is blocked, X+emission is not observed whereas gating on

the 1h charging laser results in an anti-correlated increase in the

intensity of X+emission at the expense of X0emission. These

observations clearly indicate that selective, all optical single hole

charging of the molecule has taken place.

To identify X0resonances for charging one hole, the inte-

grated intensity of X0and X+were monitored as a function of

the 1h charging laser frequency (𝜔1h), with the device biased at

the charging voltage VII. Figure 2c shows a 2D false-color map

of the integrated emission intensity from X0for varying VII and

ℏ𝜔1h (left). The white dashed line marks VII =−1.1V,wherea

line cut of X0and X+emission along energies between 1315 and

1321.5 meV is recorded and presented in the rightmost panel.

When the 1h-charging laser matches the energy of a transition

related to X0, an electron–hole pair is generated and single hole

charging occurs. A transition related to X0include s-orbital and

excited state X0transitions of both dots forming the molecule,

as well as indirect exciton transitions. Tunnel ionization leaves

one hole in the ground state resulting in a weakening of the

X0emission observed during the readout phase of the measure-

ment. This occurs at 1318 and 1320 meV as shown in the line

cut presented in Figure 2c. Concurrently, an anti-correlated in-

crease of the X+emission is expected and observed as a ﬁn-

gerprint of the deterministic single hole charging. Thus, mon-

itoring X0and X+emission intensities allows for identiﬁcation

of 1h charging transitions in a voltage regime where charging

takes place.

Besides adjusting the frequency of the charging laser the opti-

mal charging voltage has to be identiﬁed. For increasingly nega-

tive VGthe axial electric ﬁeld becomes larger and hole tunneling

times become shorter than the temporal width of the charging

plateau (phase II). A similar statement applies to the electron tun-

neling times becoming too long as VGbecomes more positive and

the axial electric ﬁeld reduces. For both cases, the probability of

selective charging during phase II of our measurement protocol

reduces. A compromise between eﬃcient electron tunneling and

suﬃciently long hole retention times is found by sweeping ℏ𝜔1h

for diﬀerent VII (Figure 2c, left). The detected resonance energies

reduce with decreasing VII due to the DC Stark eﬀect. In addition,

as the electron tunneling becomes the lifetime of the excited state

decreases, broadening the linewidth of the charging resonance.

By analyzing the voltage-dependent full-width half-maximum of

the resonance at VII, we estimate the electron tunneling time to

be ≤2ps.

[34]

Based on the data presented in Figure 2 and the above dis-

cussion, we select VII =−1.08 V while the charging laser energy

is ﬁxed at ℏ𝜔1h =1317.8 meV to generate a single hole in the

molecule. This optimal working point is marked by a red cross in

Figure 2c and is used in the next section for sequential 2h charg-

ing of the QD-molecule.

2.3. Two Hole Charging

As discussed above in relation to Figure 1, sequential optical

charging of the QDM from n=0 to 1 and 2 is achieved by switch-

ing on the charging laser during phase III of the measurement

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Figure 3. Two hole charging resonances. a) VIII and ℏ𝜔2h dependent X0emission (left), showing shifted resonances for 2h charging, compared to

Figure 2c. Red triangles (green circles) indicates X0(X+) charging transitions, marked as X0

1,2(X+

1,2). The two hole charging voltage is marked by the

green square. The red dashed line illustrates the required charging energy. The vertical white dashed line marks VIII =−1.08 V at which a line cut is

presented (right). Comparison of X0emission with (green curve) and without (red curve) 1h charging laser applied, when sweeping phase III laser

energy. The charging resonances shift as the system switches between resonantly addressing the X0and X+transition for charging one and two holes,

respectively. The blue curve shows the contrast between 1h and 2h charging. The resonances marked are the same as in the left panel. b) Resonance

ﬂuorescence emission of the X++ transition for charging zero/one/two holes (blue/red/green).

protocol. Analogously to the 1h charging experiment discussed

in the previous section, we repeated the optimization procedure

to ﬁnd VIII and ℏ𝜔2h, while using the optimal parameters VII and

ℏ𝜔1h found for 1h charging. The readout voltage VIV was set to

−0.2 V. The green and red curves presented in the line cut of

Figure 3a show the integrated emission intensity of X0as a func-

tion of the laser energy in phase III of our protocol (ℏ𝜔2h), with

and without the 1h charging laser having previously been applied

in phase II. VIII is set to match VII, making the charging res-

onances of both phases comparable. Since the X+and X++ op-

tical transitions partly spectrally overlap, the two hole charging

resonances are in a ﬁrst step identiﬁed indirectly via the reduc-

tion of the X0transition intensity. Reducing the laser power of

both charging pulses to only 60% of the usual saturation power

(240 nW) and the simultaneous presence of Auger discharging

processes[35] allows for observing of the X0emission, even if

charging took place during the charging phase of the measure-

ment. The red curve presented in Figure 3a (right) shows reso-

nances (e.g., at 1317.8 and 1319.9 meV) observed when applying

the second charging pulse while omitting the ﬁrst. As discussed

in Section 2.2, the QDM can be charged with 1h via the excita-

tion of X0. This leads to the observation of the same resonances

as in Figure 2. In contrast, when applying ﬁrst the charging pulse

(green curve), the second pulse can only excite the positive trion

and result in the occupation of the QDM by a second hole. The

charging of a second hole reduces the probability of ﬁnding the

QDM in an empty state. This leads to a reduction of the intensity

of the X0emission in the readout phase of the measurement,

allowing the identiﬁcation of the X+charging transition. Since

the X+energy is shifted compared to the X0energy, we observe

a shift of charging resonances (e.g., at 1318 meV). This can be

most clearly observed in the contrast of the data with and with-

out the ﬁrst (phase II) charging laser switched on presented in

the rightmost panel of Figure 3a (blue). Pre-charging the QDM

results in the activation of a second resonance at slightly higher

energy than the neutral exciton transitions marked by a green

circle. These resonances can also be discerned in the raw data

(leftmost panel) and are labeled X+

1and X+

2.TheX+

1resonance is

used to charge a second hole into the QDM.

Similar to the situation discussed in the context of Figure 2c,

the DC Stark shift of the X+transition is observed when record-

ing the intensity of the X0emission while varying VIII and ℏ𝜔2h.

Typical results are presented in Figure 3a. The energy and voltage

of phase II are chosen as described above. A comparison with Fig-

ure 2c helps to identify voltages for which sequential 1h and 2h

hole charging is achievable for the same resonant laser energy.

This allows us to sequentially charge two holes into the QDM

with only one laser energy by modifying the gate voltage while

the resonant charging laser is gated on. Utilizing one laser only,

as done in the following experiments is desirable to reduce the

complexity of the charging scheme. When maintaining the 1h

charging energy ℏ𝜔1h =1317.8 meV, the voltage of phase III has

to be set to VIII =−1.34 V to enable the sequential charging of a

second hole during phase III. The conditions to have sequential

resonances between the charging laser and the 1h and 2h charg-

ing voltages are indicated in Figure 3a by a red triangle and a

green square, respectively.

Up to now, the charging of a second hole has been demon-

strated only indirectly via the reduction of the X0emission. In

the following, the presence of two holes in the QDM is directly

veriﬁed by performing resonance ﬂuorescence on the doubly

charged exciton transition X++. In contrast to the measurements

discussed above, where readout was performed via luminescence

by pumping an excited state of the neutral (X0

[p−p]) or positively

charged exciton (X+

[p−p]), here we resonantly excite and probe the

s-shell doubly charged exciton X++ transition during phase IV

of our measurement. To ﬁlter out the readout laser, a cross-

polarized resonance ﬂuorescence setup was used.[36] Figure 3b

shows the X++ emission upon charging zero, one, and two holes

into the QDM in phases II and III of the measurement. For all

three datasets the charging laser remained on throughout phases

II and III of the measurement. VGwas adjusted to facilitate either

0h, 1h, or 2h charging. When charging zero and one hole(s) the

signal consists mainly of unsuppressed laser light. However, as

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soon as the QDM is loaded with two holes, the X++ emission rises

by a factor of >18. Besides the main emission peak at 1322.95

meV, a side peak at 1323.05 meV is observable. This side peak is

identiﬁed as an indirect X++ transition by comparison with Fig-

ure 1c. The observed increase of the emission intensity proves

that 2h selective optical charging of the QDM has occurred.

Even if 1h and 2h charging is demonstrated, the experiments

presented do not conclusively show that holes are sequentially

added to the QDM, that is, the charge status is sequentially

shifted from n=0 to 1, to 2 using optical pumping. To prove

the sequentiality of the charging in our experiments and deter-

mine the typical photon ﬂuxes required for charging, we continue

to show that charging takes place primarily during the intended

phases of the voltage sequence (II and III) and, thereby, conﬁrm

the sequential, all optical preparation of the 2h charge state of

the QDM.

2.4. Sequential Charging

To conﬁrm sequentiality of the charging process, we performed

a measurement using a single charging pulse having a tempo-

ral width of 400 ns. This charging pulse was swept through the

two charging plateaus of phase II and III, each of which is 200

ns long. This procedure is illustrated schematically in Figure 4,

showing the measurement sequence and the temporal advance

of the charging laser pulse 𝜏.At𝜏<0, the charging laser over-

laps solely with phase I of the measurement sequence and is,

therefore, ineﬀective in charging the QDM. The charging pulse

is then shifted through phases II (1h charging), III (2h-charging)

of the measurement protocol until it overlaps solely with phase IV

(readout). By advancing the time when the charging pulse is ap-

plied, its temporal overlap with the two charge plateaus changes.

Figure 4 shows the emission of X0,X+,andX++ transitions as

a function of the temporal advance 𝜏and the applied charging

power. The charging energy and the voltage plateaus of phase II

and III are set as previously deﬁned for two hole charging. In

addition, the second charging laser was turned oﬀ for this experi-

ment. Readout was performed via luminescence driven by pump-

ing p-shell transitions at −0.2 V to detect X0(Figure 4—upper

panel), X+(middle panel), and X++ (lower panel) emission, si-

multaneously.

Complete embedding of the charging pulse in phase I (𝜏<

0 ns) does not result in charging. X0therefore dominates the X+

and X++ emission. At 𝜏=0 ns, the laser pulse enters the 1h charg-

ing plateau of phase II. As a result, the emission intensity of X+

rises as charging of the QDM with a single hole takes place. At the

same time, the emission intensity of X0reduces while the X++ re-

mains close to the background level indicative of the charge state

of the QDM being enhanced to n=1. For low power, this eﬀect

occurs at longer values of 𝜏, which corresponds to a larger overlap

between laser pulse and charging plateau. This reﬂects the fact

that the charging eﬃciency is reduced—charging is probabilistic

due to the tunneling process and weaker photon ﬂuxes require

longer times to establish the n=1 charge state. The two hole

charging plateau is reached at 𝜏=200 ns. While the X0emis-

sion remains at a low level, the intensity of X++ progressively

rises with 𝜏and the intensity of X+simultaneously reduces in

an anti-correlated manner. This key observation shows that the

Figure 4. Sequential two hole charging. Measurement sequence, visual-

izing the temporal sweep (𝜏) of the 400 ns charging pulse over the two

200 ns charging voltage plateaus. At 𝜏=0 ns, the charging laser (dashed

red box) enters the ﬁrst charging plateau. The readout is performed via

p-shell excitation while detecting the spectrally detuned s-shell emissions

of X0,X+,andX++. Below: integrated emission of X0,X+,andX++ (top

to bottom) is logarithmically plotted for varying charging pulse delay and

charging power. Magenta dashed lines indicate the edges of the 1h and 2h

charging plateaus.

number of charged holes sequentially increased from n=1to2.

The second hole is accordingly mainly charged during phase III

due to the ﬁnite orbital degeneracy of the states excited. Up to 𝜏=

600 ns 2h charging is performed, as the laser pulse overlaps with

both charging plateaus. After 𝜏=600 ns the pulse leaves the ﬁrst

charging plateau, whereupon n=1 charging has not occurred

anymore. As a result, the X+transition cannot be excited dur-

ing phase III, and the charge status of the QDM remains close

to n=0. Consequently, the emission from X0reappears while

X++ progressively decreases. We attribute the small increase of

X+emission with 𝜏to the nonzero probability of charging one

hole during phase III. As the resonances broaden with decreas-

ing voltage and X0and X+charging transitions spectrally overlap,

the selectivity of the charging process is reduced. This makes the

generation of unwanted charge states more likely.

3. Discussion and Summary

To quantify the eﬃciency of the proposed charging scheme we

calculated P(n|m), the conditional probability for charging n

holes, given mcharging pulses are applied. The reset probabil-

ity is extremely close to unity (P(0|0) =1), and considering only

states with n≤2 to reﬂect the degeneracy of a single QD orbital,

www.advancedsciencenews.com www.advquantumtech.com

we obtain 1h/2h charging probabilities of ≥(93.5 ±0.8)%/ ≥

(80.5 ±1.3)%, respectively (see Experimental Section). These re-

sults show that the sequential, all-optical preparation of desired

number of charges is a robust and reliable process. Certainly,

the optical preparation of charges is more complex compared

to QDM charging via tunneling from a diode contact. For in-

stance, additional voltage plateaus and laser pulses are required.

Furthermore, the repetition rate of the sequence is currently

limited to 740 kHz due to the duration of reset and charging

pulses. However, this limitation is mainly caused by the RC time

constant of the diode. By using micron scale photodiodes hav-

ing low RC time constants,[37] this can be increased to up to

500 MHz. Moreover, it is superior to optimize protocols for in-

creasing the readout phase IV duty cycle. This can be done by

performing several readout cycles after having previously pre-

pared the charge state. The limit of such approaches will be de-

termined by the extent to which measurement back action in-

ﬂuences the charge status of the QDM, for example via Auger

auto-ionization.[35] Furthermore, the demonstrated scheme does

not pose any restrictions on the readout voltage to obtain cer-

tain charge states. The X0,X+,andX++ intensities shown in

Figure 4 are acquired at the same gate voltage, showing its

independence.

In summary, we have proposed and demonstrated a four-

phase measurement sequence that allows independent control of

charge status and inter-dot coupling of a single, electrically tun-

able QDM. We demonstrated one and two hole charging via op-

tical excitation and tunnel ionization. The addressability of the

generated charge state was thereafter not aﬀected by the gate

voltage, facilitating electrically-tunable spin–spin interactions in-

duced using the exchange coupling between the two spins.[38] By

combining eﬃcient charging and separate gate voltage control

the proposed method of optical charging is therefore suitable to

replace and outperform previous charging approaches with re-

spect to controllability and ﬂexibility. Independent charge state

preparation paired with the ability to manipulate the inter-dot

coupling paves the way for protocols requiring simultaneous spin

and coupling control, as for example needed for 2D cluster state

generation.[18]

4. Experimental Section

Sample Structure:The QDM investigated was grown by solid-source

molecular beam epitaxy. It consisted of two laterally stacked InAs quantum

dots embedded in a GaAs matrix. The inter-dot coupling strength was de-

termined by the wetting layer to wetting layer separation of 7.6 nm. The in-

dividual height of both QDs forming the molecule was ﬁxed to 2.2 nm via

the In-ﬂush technique during growth. By growing a series of samples with

nominally identical growth conditions for the two dot layers, but diﬀerent

relative truncation heights hole couplings could be achieved by choosing

the same height (2.2 nm) in both layers. The QDM device was designed

to facilitate electric ﬁeld induced tunnel coupling of orbital states in the

valence band.[39] A 20 nm thick AlxGa(1−x)As tunnel barrier (x=0.33) was

grown 10 nm above the QDM to prolong hole tunneling times and en-

able tunnel ionization charge state preparation. Furthermore, the molecule

was embedded into an n-i-Schottky diode to apply electric ﬁelds along the

growth direction of the sample. The n-doped region and the Schottky sur-

face metallic electrode were used as contacts. Both diode contacts were

more than 100 nm away from the molecule to prevent uncontrolled charge

tunneling into the QDM and, non-optical or selective modiﬁcation of the

charge status. All measurements were performed at 10 K. For preparation

and readout of the charge state tunable diode lasers were used.

Fidelity Calculation:To estimate a lower boundary of the one and two

hole charging ﬁdelities, the reset phase I is assumed to be perfect: P(0|0)

=1. This expectation was likely to be achieved in this experiment since

the discharging electric ﬁeld was high and the duration of the initialization

phase of the measurement was suﬃciently long. Here, P(n|m) is the prob-

ability of charging nholes, given mcharging pulses were applied. This

assumption could be justiﬁed, as duration and voltage of phase I could

be chosen to make the presence of charges negligible. Furthermore, only

charge states with n≤2 were taken into account due to the orbital struc-

ture of the charged QDM.

By monitoring the X0emission with and without applying one charging

pulse, the probability of charging a non-zero number of holes P(¬0|1) =

0−N0

could be calculated. Where Na

bis the number of counts observed

for transition Xa,witha∈{0,+,++}andb∈{0,1,2} on the other hand

indicates the number of charge pulses applied. The probability for selec-

tively charging one hole, given that a single hole should get charged, could

be written as P(1|1) =P(¬0|1) −P(2|1).

The probability for charging two holes when only one was intended can

be written as: P(2|1) ≤N++

N++

. The counts obtained was normalized moni-

toring the X++ transition when planned to charge one hole by the counts

of the X++ transition when planned to charge two holes. This indicates in

which proportion of the overall cases the dot with two holes was charged

if only one was wanted. In the case of a perfect two holes charging proce-

dure, this inequality changed to an equation.

The ﬁdelity of charging one hole can now be written as

P(1|1) ≥

0−N0

−N++

N++

(1)

The two hole charging ﬁdelity could be calculated by estimating its counter

events: P(2|2) =1−P(1|2) −P(0|2). The probability of charging zero holes

for this case was estimated via the counter event of charging zero holes,

given a charging pulse was applied: P(0|2) ≤1−P(¬0|1). The probability

for loading one hole given two holes were intended, the same argumen-

tation as for calculating P(2|1) were followed. However, the X+transition

was monitored and the counts of the two hole were divided by the one

hole charging case: P(1|2) ≤N+

N+

This allowed to write the two hole charging ﬁdelity as

P(2|2) ≥

0−N0

−N+

N+

(2)

Supporting Information

Supporting Information is available from the Wiley Online Library or from

the author.

Acknowledgements

The authors gratefully acknowledge ﬁnancial support from the Ger-

man Federal Ministry of Education and Research (BMBF) via Q.Link.X

(16KIS0874, 16KIS086), QR.X (16KISQ027, 16KISQ014, 16KISQ012 and

16KISQ009), the European Union’s Horizon 2020 research and innovation

program under grant agreement 862035 (QLUSTER) and the Deutsche

Forschungsgemeinschaft (DFG, German Research Foundation) via SQAM

(FI947-5-1), DIP (FI947-6-1), and the Excellence Cluster MCQST (EXC-

2111, 390814868). F.B. gratefully acknowledges the Exploring Quantum

Matter (ExQM) programme funded by the State of Bavaria. F.S., K.B., and

K.M. gratefully acknowledges the BMBF for ﬁnancial support via project

MOQUA (13N14846).

Open access funding enabled and organized by Projekt DEAL.

www.advancedsciencenews.com www.advquantumtech.com

Conﬂict of Interest

The authors declare no conﬂict of interest.

Data Availability Statement

The data that support the ﬁndings of this study are available from the cor-

responding author upon reasonable request.

Keywords

charge state control, electron tunneling, hole storage, inter-dot coupling,

optical charging, quantum dot molecules

Received: May 20, 2022

Revised: July 15, 2022

Published online: August 25, 2022

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