Phonon-mediated versus coulombic backaction in quantum dot circuits.
ABSTRACT Quantum point contacts (QPCs) are commonly employed to detect capacitively the charge state of coupled quantum dots (QDs). An indirect backaction of a biased QPC onto a double QD laterally defined in a GaAs/AlGaAs heterostructure is observed. Energy is emitted by nonequilibrium charge carriers in the leads of the biased QPC. Part of this energy is absorbed by the double QD where it causes charge fluctuations that can be observed under certain conditions in its stability diagram. By investigating the spectrum of the absorbed energy, we find that both acoustic phonons and Coulomb interaction can be involved in the backaction, depending on the geometry and coupling constants.
- SourceAvailable from: Sergei Studenikin[Show abstract] [Hide abstract]
ABSTRACT: Spin qubits have been successfully realized in electrostatically defined, lateral few-electron quantum dot circuits. Qubit readout typically involves spin to charge information conversion, followed by a charge measurement made using a nearby biased quantum point contact. It is critical to understand the back-action disturbances resulting from such a measurement approach. Previous studies have indicated that quantum point contact detectors emit phonons which are then absorbed by nearby qubits. We report here the observation of a pronounced back-action effect in multiple dot circuits where the absorption of detector-generated phonons is strongly modified by a quantum interference effect, and show that the phenomenon is well described by a theory incorporating both the quantum point contact and coherent phonon absorption. Our combined experimental and theoretical results suggest strategies to suppress back-action during the qubit readout procedure.Nature Physics 01/2013; · 19.35 Impact Factor
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ABSTRACT: The capacitive couplings between gate-defined quantum dots and their gates vary considerably as a function of applied gate voltages. The conversion between gate voltages and the relevant energy scales is usually performed in a regime of rather symmetric dot-lead tunnel couplings strong enough to allow direct transport measurements. Unfortunately, this standard procedure fails for weak and possibly asymmetric tunnel couplings, often the case in realistic devices. We have developed methods to determine the gate voltage to energy conversion accurately in the different regimes of dot-lead tunnel couplings and demonstrate strong variations of the conversion factors. Our concepts can easily be extended to triple quantum dots or even larger arrays.The Review of scientific instruments 12/2011; 82(12):123905. · 1.52 Impact Factor
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ABSTRACT: Managing energy dissipation is critical to the scaling of current microelectronics and to the development of novel devices that use quantum coherence to achieve enhanced functionality. To this end, strategies are needed to tailor the electron-phonon interaction, which is the dominant mechanism for cooling non-equilibrium ('hot') carriers. In experiments aimed at controlling the quantum state, this interaction causes decoherence that fundamentally disrupts device operation. Here, we show a contrasting behaviour, in which strong electron-phonon scattering can instead be used to generate a robust mode for electrical conduction in GaAs quantum point contacts, driven into extreme non-equilibrium by nanosecond voltage pulses. When the amplitude of these pulses is much larger than all other relevant energy scales, strong electron-phonon scattering induces an attraction between electrons in the quantum-point-contact channel, which leads to the spontaneous formation of a narrow current filament and to a renormalization of the electronic states responsible for transport. The lowest of these states coalesce to form a sub-band separated from all others by an energy gap larger than the source voltage. Evidence for this renormalization is provided by a suppression of heating-related signatures in the transient conductance, which becomes pinned near 2e(2)/h (e, electron charge; h, Planck constant) for a broad range of source and gate voltages. This collective non-equilibrium mode is observed over a wide range of temperature (4.2-300 K) and may provide an effective means to manage electron-phonon scattering in nanoscale devices.Nature Nanotechnology 01/2014; · 31.17 Impact Factor
arXiv:0910.4093v2 [cond-mat.mes-hall] 20 Apr 2010
Phonon-mediated vs. Coulombic Back-Action in Quantum Dot circuits
D. Harbusch,1D. Taubert,1H.P. Tranitz,2W. Wegscheider,3and S. Ludwig1
1Center for NanoScience and Fakult¨ at f¨ ur Physik, Ludwig-Maximilians-Universit¨ at M¨ unchen,
Geschwister-Scholl-Platz 1, D-80539 M¨ unchen, Germany
2Institut f¨ ur Experimentelle Physik, Universit¨ at Regensburg, D-93040 Regensburg, Germany
3Laboratory for Solid State Physics, ETH Z¨ urich, CH-8093 Z¨ urich, Switzerland
Quantum point contacts (QPCs) are commonly employed to detect capacitively the charge state
of coupled quantum dots (QD). An indirect back-action of a biased QPC onto a double QD laterally
defined in a GaAs/AlGaAs heterostructure is observed. Energy is emitted by non-equilibrium charge
carriers in the leads of the biased QPC. Part of this energy is absorbed by the double QD where it
causes charge fluctuations that can be observed under certain conditions in its stability diagram. By
investigating the spectrum of the absorbed energy, we identify both acoustic phonons and Coulomb
interaction being involved in the back-action, depending on the geometry and coupling constants.
PACS numbers: 03.67.-a, 63.22.-m, 72.70.+m, 73.21.La, 73.23.Hk
Coupled quantum dots (QDs) are promising candi-
dates for applications as qubits in solid state quantum
information processing schemes . One important cri-
terion is the scalability of the qubit number. In a complex
layout it will pose a great challenge to implement readout
techniques that address singe qubits without adding de-
coherence to the coupled QDs. Direct transport through
an array of QDs is limited due to Coulomb blockade.
However, a single biased quantum point contact (QPC)
in a separate circuit can act as charge detector for sev-
eral QDs [2, 3]. QPCs are straightforward to implement,
yield sufficient sensitivity, and can be operated as wide
bandwidth detectors [4, 5].
quantum information processing where a rapid detection
scheme is needed. The suitability of QPCs as fast detec-
tors has been demonstrated in single-shot readout [6, 7]
and counting statistics experiments [8, 9]. Increasing the
bandwidth, however, requires a high signal-to-noise ra-
tio which makes it necessary to operate the QPC at a
relatively high bias voltage.
The latter is desirable in
A biased QPC employed as a charge detector causes
back-action. Its quantum limit can be traced back to
statistical charge fluctuations at the QPC capacitively
coupled to QDs . Shot noise only contributes to back-
action if the QPC has resistive leads . In addition to
these direct Coulomb back-action mechanisms, the solid
state environment provides possibilities for indirect back-
action [11–14]. A biased QPC emits non-equilibrium
charge carriers into its leads that then relax via electron-
electron interaction, the emission of plasmons, or acoustic
phonons . Partial reabsorption of the emitted energy
can result in charge fluctuations in (coupled) QDs, hence
causing indirect back-action. Usually these fluctuations
are too fast to be detected in measurements with limited
bandwidth, but under certain conditions they can be ob-
served in the stability diagram of coupled QDs . In
this Letter we present a systematic investigation of such
back-action-induced charge fluctuations in a double QD.
We find that both acoustic phonons and Coulomb inter-
action can play an important role for the back-action in
Our device is based on a GaAs/AlGaAs heterostruc-
ture containing a two-dimensional electron system 90nm
beneath the surface. Charge carrier density and mo-
bility are ne = 2.78 × 1015m−2and µ = 140m2/Vs.
QDs and QPCs are electrostatically defined by apply-
ing negative voltages to metallic gates fabricated by e-
beam lithography. The gate layout is shown in Fig. 1a.
The measurements are performed at an electron temper-
ature of Tel? 130mK. Although the gate layout is de-
signed for three QDs , here we define only a double
QD (gates d1, b1 and α are grounded). Unless other-
wise stated, only one of the implemented QPCs (black
arrows in Fig. 1a), namely QPC-I, is biased by applying
a voltage VQPCto contact IV. Since all other contacts are
grounded and QPC-I is operated near pinch-off, the dou-
ble QD is virtually unbiased. The dc current IQPCflow-
ing through QPC-I is measured with a bandwidth of only
10Hz; IQPCtherefore probes the average charge configu-
ration of the double QD. We obtain transconductance
data dIQPC/dVβ by numerical differentiation of IQPC.
We have observed back-action in a wide range of charge
configurations, but here we focus on two electrons or less
occupying the double QD. Solid lines in Fig. 1b sketch
the expected charge stability diagram. Ground state con-
figurations are denoted (NB,NC), indicating that QD B
(C) is occupied by NB(NC) electrons.
For the experiments presented here, it is essential to
adjust the tunnel couplings of the double QD to be very
asymmetric . In a symmetric configuration, funda-
mental laws of thermodynamics prevent the observation
of the back-action effects discussed here (see supplemen-
tary material ). In our case the right tunnel barrier
b2 between QD C and lead III is almost closed, resulting
in a tunneling rate of only Γb2 ≃ 25kHz. The inter-
dot tunneling rate Γt2 ≃ 0.7 GHz between QD B and
C, as well as Γt1 between QD B and lead II are much
higher. The measured charge stability diagram in Fig.
FIG. 1: (a) Scanning electron micrograph of a nominally iden-
tical device. Metal gates (light gray) are negatively biased,
darker gates are grounded. QDs B and C, current paths (ar-
rows), and ohmic contacts (roman numbers) are indicated.
(b) Sketch of a double QD charge stability diagram. Numbers
in brackets indicate stable charge configurations (NB, NC) of
the double QD. The gray triangle features back-action (com-
pare d). (c) Level diagram of the double QD. Dotted lines
depict the electron excitation spectrum of QD C. (d) Mea-
sured transconductance dIQPC/dVβ (gray scale) as a function
of voltages applied to gates β and γ for VQPC = −1.6mV and
PQPC = 0.64pW.
1d shows the transconductance dIQPC/dVβin gray scale
as a function of the gate voltages Vβand Vγ. Two devia-
tions from the usual honeycomb pattern (without signs of
back-action) are observed. First, charge reconfiguration
lines are split into double lines (circled in Fig. 1d). In be-
tween these two white lines the dc current IQPCversus Vβ
exhibits a plateau at a value reflecting an equal occupa-
tion of the configurations (1,0) and (0,1) . This can be
explained with rapid transitions between the symmetric
and antisymmetric combinations of the two almost de-
generate configurations . The energy source driving
these transitions is discussed below.
The second irregularity is a triangular-shaped region
in the center of Fig. 1d described in more detail in Ref.
. Within the triangle, the charge in one of the QDs
(here QD C) fluctuates. An electron from QD C tun-
nels to QD B and from there into lead II and vice versa:
(1,1) ↔ (2,0) ↔ (1,0). As can be seen in Fig. 1c, which
shows the chemical potentials of the QDs and leads, these
charge fluctuations require the absorption of energy. One
of the border lines of the triangle in Fig. 1d is parallel
to the charge reconfiguration lines (white double lines).
Along this border line the energy difference ∆ (asymme-
try energy) between the ground state configurations (1,1)
and (2,0) is thus constant (Figs. 1b and 1c). With the
charging energy of QD B (2.5meV) the size of the trian-
FIG. 2: (a,b): Transconductance dIQPC/dVβ (gray scale) as
a function of Vβ and Vγ. (c) Observed maximum of absorbed
energy Emax (compare Fig. 1d) as a function of PQPC and
VQPC. Arrows show where (a) and (b) are located in this
graph. See main text for details.
gle can be converted into an energy Emax(Figs. 1b and
1d). We interpret Emaxas the maximum energy that QD
C absorbs in a single process.
Figs. 2a and 2b plot stability diagrams similar to that
in Fig. 1d for two very different bias voltages VQPC. The
triangle size clearly grows with increasing bias indicating
that QPC-I acts as energy source. Fig. 2c underlines this
result. Emaxis plotted as a function of VQPCand the dis-
sipated power PQPC= IQPCVQPC with each data point
corresponding to the size of one triangle. The curved
surface fitted to the data is a guide to the eye. The gray
plane in Fig. 2c is defined by Emax = eVQPC. This is
the largest energy quantum the QPC can emit and the
expected Emaxfor back-action mediated by direct (first-
order) Coulomb interaction, as compellingly suggested
by previous data for the case of shot-noise . In our
measurements, the open circles lie above this plane while
the closed circles are below it. The apparently missing
clear cut-off at Emax = eVQPC  in Fig. 2c suggests
that in our data direct back-action is unimportant. This
has to be seen in the context of the very small conduc-
tance of our QPC, GQPC≪ 0.5G0, where G0= 2e2/h.
In this regime the direct back-action related to shot noise
of IQPCor charge fluctuations at the QPC is expected to
be strongly suppressed [10, 17, 20]. Especially, the devia-
tions at large VQPC, where we find Emax< eVQPC, imply
indirect back-action with energy dissipated in the leads
of the QPC. During the relaxation processes the energy
spectrum is likely shifted towards lower energies before
some of the resulting energy quanta are reabsorbed by
the double QD.
Emaxstrongly increases with PQPCbefore it saturates
at PQPC ≃ 0.5pW (Fig. 2c). The observation Emax <
eVQPCfor very small PQPCis another indication that the
high energy end of the spectrum emitted by the QPC is
suppressed in the absorption spectrum of the double QD.
This again suggests indirect back-action where multiple
scattering processes in the leads of the QPC alter the
original emission spectrum.
Our scenario of indirect back-action fails to explain
Emax > eVQPC in the regime of small VQPC, and is in
contrast to the observed lower bound of Emax≃ 0.6meV
(open circles in Fig. 2c). In the present experiment, this
marks the limit of external non-thermal noise. It mainly
consists of 50Hz signals which stem from electronic in-
struments. Apparently, an asymmetrically coupled dou-
ble QD can be employed as a sensitive noise detector.
The stability diagrams in Figs. 3a and 3b plot the cur-
rent change δIQPCat QPC-I (also compare Fig. 1b). In
Fig. 3a back-action is visible in the shape of a triangle
of enhanced δIQPC. Converting the gate voltage along
the white line in Fig. 3a into the asymmetry energy ∆
(defined in Fig. 1c) we plot cross sections through such
triangles in Figs. 3c – 3e. In thermal equilibrium we ex-
pect the double QD to occupy its ground state configura-
tion because of the low Tel≃ 130mK. The y-axis shows
∆IQPCwhich is calculated from IQPCby subtracting the
equilibrium value in configuration (1,1). To achieve com-
parability, the curves are scaled so that ∆IQPC = 1 in
(1,0). The white line in Fig. 3a starts in configuration
(2,0), crosses the area of (1,1) and ends in (0,1). The cor-
responding average values of ∆IQPC measured at these
configurations are indicated in Figs. 3c – 3e as a shaded
background. Fig. 3c displays curves for different VQPCin
the high power limit of Fig. 2c, while the power depen-
dence is investigated in Fig. 3d. All these curves follow
approximately the behavior expected for thermal equilib-
rium (shaded background). Deviations are observed only
at the back-action induced triangles located in the (1,1)
area. Within these triangles the data display a general
trend of an increasing ∆IQPC with growing VQPC and
PQPC. However, ∆IQPC ≃ 1 represents an upper limit
for all our measurements. Since the intermediate config-
uration (2,0) decays very fast into (1,0), ∆IQPCindicates
the average occupation number difference of the config-
urations (1,1) and (1,0). Wherever ∆IQPC≃ 1 in Figs.
3c – 3e, the higher energy configuration (1,0) is strongly
occupied. This can only be explained in terms of a non-
equilibrium energy source driving the transitions.
All triangles induced by back-action of QPC-I can be
divided into two regimes. For 0 < ∆ ? 1.04meV (verti-
cal dashed line in Figs. 3c – 3e) we observe a featureless
region where the current tends to saturate at ∆IQPC≃ 1.
At ∆ ≃ 1.04meV the current sharply drops, and for
∆ > 1.04meV, we find ∆IQPC< 1 even for large VQPC
and PQPC. This region, however, features an additional
substructure, best seen in Fig. 2a, namely lines of con-
stant transconductance parallel to the charge reconfigu-
ration lines. These lines correspond to constant detuning
∆ between (1,1) and (2,0). They reveal the quantum me-
chanical excitation spectrum of QD C (compare Fig. 1c)
FIG. 3: (a,b) δIQPC(gray scale) as a function of Vβand Vγ. A
plane fit is subtracted from IQPC (resulting in δIQPC) to cor-
rect for capacitances between gates and the QPC. In (a) only
QPC-I is biased with VQPC = −0.8mV and PQPC = 2.5pW;
for (b) the values are VQPC = −0.1mV and PQPC = 0.01pW.
QPC-II is additionally biased in with VQPC = −2.0mV and
PQPC = 72pW in (b).(c–e) Normalized current change
∆IQPC versus asymmetry energy ∆ (compare Fig. 1c) along
the white line in (a). ∆IQPC corresponding to configurations
(2,0), (1,1) and (0,1) are highlighted in gray.
. Whenever an electron in QD C is lifted to an excited
state (1,1)*, that is in resonance with the ground state
of (2,0), tunneling between the two QDs is enhanced.
This leads to the observed alternating occupation prob-
ability as a function of ∆. Although we expect addi-
tional excited states of QD C, we do not observe them at
∆ < 1.04meV.
We explain the sharp current drop at ∆ ≃ 1.04meV
as follows. In Ref.  phonon-mediated interaction be-
tween mesoscopic circuits has been demonstrated. Back-
scattering of an electron defines an upper limit Eph
2?kFvsfor the energy that can be transferred to an acous-
tic phonon . With our Fermi energy of EF≃ 10meV
and the maximum sound velocity vs ≃ 6000m/s from
Ref. , we find Eph
max≃ 1.04meV. Just at this asym-
metry ∆ = Eph
maxthe current drops sharply (Figs. 3c–e).
We conclude that for ∆ ? 1.04meV the back-action is
mainly caused by phonons emitted in the leads of the bi-
ased QPC and reabsorbed by a QD. In principle, absorp-
tion of multiple phonons could account for back-action
observed for ∆ > 1.04meV. However, the existence of
two different interaction mechanisms seems more likely,
because of the observation of the excitation spectrum of
QD C only for ∆ > 1.04meV.
For the data shown in Figs. 3b and 3e, QPC-II is
strongly biased and used as energy emitter (while the
weakly biased QPC-I is still the detector). Fig. 3e dis-
plays two measurements for QPC-II as emitter and one
measurement for QPC-I (gray solid line) as emitter.
When QPC-II is strongly driven, ∆IQPC drops all the
way to zero near ∆ ≃ 1.04meV. Then, for ∆ > 1.04meV,
a second triangle of charge fluctuations appears, as can
be best observed in Fig. 3b. Both triangles have no sub-
structure. This is in direct contrast to the results ob-
tained with QPC-I as emitter, where we observe a char-
acteristic substructure for ∆ > 1.04meV (parallel lines
in Fig. 2a), namely the excitation spectrum of QD C.
An important difference between the two QPCs is,
that the capacitive coupling between the double QD and
QPC-I is roughly twice as large compared to QPC-II.
Experimentally we find that the excitation spectrum of
QD C can only be resolved if QPC-I is emitter, where
the capacitive coupling between QD C and the energy
emitting QPC (and its leads) is strong. These results
imply that Coulomb interaction is the dominant back-
action mechanism for ∆ > 1.04meV. At the same time,
the observed back-action must be indirect (as discussed
above, see Fig. 2c). We suggest a mechanism in which
non-equilibrium charge carriers are emitted by QPC-I to
lead III. Next, excited carriers in lead III exchange en-
ergy with QD C via Coulomb interaction. This scenario
explains the remaining back-action for ∆ > 1.04meV in
the case of QPC-I being emitter.
The position of the second (lower) triangle in Fig.
3b indicates transitions involving the configurations
(1,1)↔(0,1)↔(1,0) compared to (1,1)↔(2,0)↔(1,0)
for the upper triangle. Here the electron in QD B tun-
nels to lead II after absorbing energy, then the elec-
tron in QD C relaxes to QD B (and emits energy). To
first order, the transition (1,1)→(0,1) cannot be driven
by phonons ((1,1)→(2,0) for the upper triangle) when-
ever the energy difference between these two configu-
rations exceeds Eph
max≃ 1.04meV. In fact, the size of
both triangles in Fig. 3b (and the width of both local
maxima in Fig. 3e) are identical and equal to Eph
This result strongly points to phonon-mediated back-
action for both triangles. Note that for PQPC> 15pW,
the second phonon-mediated triangle is also weakly vis-
ible with QPC-I as emitter . The apparent differ-
ence in interaction strength can be partly explained by
the anisotropic coupling tensors between electrons and
phonons and the sample geometry.
In conclusion, we demonstrate a method to directly
measure back-action of a biased QPC on a double QD
causing charge fluctuations. Back-action spectroscopy al-
lows us to identify phonon-induced back-action as well as
features most likely caused by Coulomb interaction. The
observed back-action is indirect in nature, distinguishing
it from the direct Coulomb interaction between charge
fluctuations at the QPC and the electrons confined in
QDs. Comparing two different QPCs reveals a strong
dependence of the back-action on geometry which needs
further investigation. Our results will help to develop
detectors with reduced back-action.
We thank J.P. Kotthaus, G.J. Schinner, T. Ihn, and
D.M. Eigler for fruitful discussions. Financial support by
the German Science Foundation via SFB 631 and SFB
689, the German Israel program DIP, the German Ex-
cellence Initiative via the ”Nanosystems Initiative Mu-
nich (NIM)”, and LMUinnovativ (FuNS) is gratefully ac-
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