Abstract
Triggered sources of entangled photon pairs are key components in most quantum communication protocols. For practical quantum applications, electrical triggering would allow the realization of compact and deterministic sources of entangled photons. Entangledlightemittingdiodes based on semiconductor quantum dots are among the most promising sources that can potentially address this task. However, entangledlightemittingdiodes are plagued by a source of randomness, which results in a very low probability of finding quantum dots with sufficiently small fine structure splitting for entangledphoton generation (∼10^{−2}). Here we introduce straintunable entangledlightemittingdiodes that exploit piezoelectricinduced strains to tune quantum dots for entangledphoton generation. We demonstrate that up to 30% of the quantum dots in straintunable entangledlightemittingdiodes emit polarizationentangled photons. An entanglement fidelity as high as 0.83 is achieved with fast temporal post selection. Driven at high speed, that is 400 MHz, straintunable entangledlightemittingdiodes emerge as promising devices for high datarate quantum applications.
Introduction
A source of triggered entangled photon pairs is a fundamental element in quantum information science and plays a key role in a number of photonic quantum technologies such as linear quantum computation^{1}, quantum teleportation^{2} and quantum relays^{3}. So far, generation of polarizationentangled photon pairs is mostly obtained through spontaneous parametric downconversion^{4} and fourwave mixing^{5} in nonlinear optical media. At present, these sources are optically driven with lasers, which increases the complexity of the systems. In addition, the nonlinear optical process occurs randomly so that the emission of entangled photon pairs is probabilistic. This results in the generation of zero or multiple entangledphoton pairs in most excitation cycles and unavoidably limits the success of realizing deterministic photonic quantum technologies.
These complications could be alleviated by employing solidstate quantum systems such as colour centres in diamond^{6}, intrinsic defects in silicon carbide^{7} and semiconductor quantum dots (QDs)^{8}. They exhibit atomiclike optical transitions and therefore allow the generation of deterministic single photons. Most importantly, they can be easily embedded in a lightemitting diode so that electrically driven singlephoton emission from these systems can be realized^{9,10,11}. However, to date, colour centres in diamond and intrinsic defects in silicon carbide are limited to emit single photons and the generation of entangledphoton pairs from these two systems has not been demonstrated yet. In contrast, semiconductor QDs are proven candidates for generation of deterministic entangledphoton pairs. In the last decade we have witnessed tremendous advancements in the field, for instance, ultrabright^{12,13} and highly indistinguishable polarizationentangled photons^{14} and timebin entangled photons^{15} have been demonstrated successfully with semiconductor QDs. Remarkably, a robust and compact entangledlightemittingdiode (ELED)^{16} based on semiconductor QDs has been realized, which represents a significant progress in the field of entangledphoton sources. Furthermore, the recent seminal realization of quantum teleportation with ELEDs^{17,18} has indicated the desirability and the ultimate feasibility of using such ELEDs for various future quantum applications.
In analogy to the cascade emission in atomic systems^{19}, electrical injection of electrons and holes into an ELED containing QDs switches on the radiative decay of biexciton (XX) to the exciton (X) and finally to the ground state (0)^{20}. The two ideally degenerate intermediate X states (spin±1) ensure emission of polarizationentangled photon pairs and the twophoton quantummechanical state can be expressed with the Bell state (H and V denote the orthogonally horizontal and vertical polarizations). In real QDs, however, a reduced structural symmetry due to the anisotropy in strain, composition and shape results in the appearance of an energetic splitting between the two bright X states, the socalled fine structure splitting (FSS)^{21}. In the presence of a FSS, the entangled state evolves over the X lifetime and the timeaveraged fidelity to the Bell state reveals classical correlations among the emitted photons. High fidelity to the state Ψ^{+}〉 can be only observed by temporal post selection of the emitted photons that, however, results in a strong reduction of the brightness of the quantum source. Therefore, the FSS in an ELED containing QDs is the key parameter determining the quality of the entangledphoton pairs. Recent work has shown that in standard selfassembled QDs^{22}, the probability of finding QDs with a FSS smaller than the radiative linewidth of the X emission (1 μeV) is lower than 10^{−2}. This finding implies that asgrown QDs are still impractical for scalable quantum networks. For example, it was reported that only one QD per ELED shows an FSS small enough for entangledphoton generation^{16}. In this context, the real potential of ELEDs for entangledphoton generation can be harnessed only when a tight control over the FSS is achieved.
The FSS of semiconductor QDs can be suppressed or tuned to zero via the application of either a vertical electric field^{23,24} or a combination of strain and electric field^{25}. The main drawback of these approaches is the difficulty of using the electric field to control the FSS and to inject carriers simultaneously, as in ELEDs. Other techniques such as thermal annealing^{26} and inplane magnetic field^{27} would be potentially compatible with the ELEDs, but the former requires a lengthy procedure and the latter bulky setups, thus rendering a practical implementation inconvenient. Recent theoretical works (although not experimentally realized so far) suggest that the FSS can be eliminated using solely a wellcontrolled strain field^{28,29}. Using piezoelectricinduced strains to engineer the properties of ELEDs would be highly desirable, because this fully electromechanically controlled tuning knob would allow the problems related to the FSS in ELEDs to be overcome.
Here we experimentally demonstrate such a quantum device by integrating ELEDs onto a piezoelectric actuator featuring giant piezoelectric response and capable of delivering welldefined anisotropic strain fields. With this device—which we call straintunable ELED (STELED)—we show that the FSS of QDs can be tuned effectively with the elastic strain fields without affecting the electrical injection of the operation of the ELEDs. Up to 30% of the QDs are tuned to be suitable for the generation of entangledphoton pairs (more than an order of magnitude more than in previous devices^{16}) and a high operation speed for an entangledphoton source is achieved, that is 400 MHz. This set of properties paves the way towards the exploitation of ELEDs in high datarate entangledphoton applications involving a large number of quantum emitters.
Results
Selfassembled QDs in straintunable diode devices
The STELED studied in this work is schematically shown in Fig. 1a. A 440nmthick nip nanomembrane containing InGaAs QDs is integrated onto a 0.3mmthick [Pb(Mg_{1/3}Nb_{2/3})O_{3}]_{0.72}[PbTiO_{3}]_{0.28} (PMNPT) single piezoelectric crystal. The detailed fabrication process is described in Methods. Different from previous works dealing with strain tuning of QDs via PMNPTs^{30,31}, the actuator used here has pseudocubic cut directions [100], [011] and [011], denoted by x, y and z axis, respectively. When the PMNPT is poled along the z axis, inplane strain fields with normal components ɛ_{xx} along the x axis and ɛ_{yy} along the y axis with opposite sign can be transferred to the nanomembrane. Accounting for its relevant piezoelectric coefficients d_{31}∼+420 pC N^{−1} along the x axis and d_{32}∼−1,140 pC N^{−1} along the y axis^{32}, the inplane anisotropy is estimated to be ɛ_{xx}≈−0.37ɛ_{yy}. The large and wellcontrolled strain anisotropy and the broad range of attainable strain magnitudes are unique and turned out to be vital in our work.
Tunable electroluminescence under applied strain fields
Apart from the strain fields, electrical contacts are arranged in such a way that electrical fields can be independently applied across the diode and the PMNPT actuator. By biasing the diode and applying a variable electric field (F_{p}) to the PMNPT simultaneously, energytunable electroluminescence (EL) from a single QD is produced, as shown in Fig. 1b. According to the power and polarizationresolved measurements the observed EL lines are ascribed to exciton (X), biexciton (XX) and charged exciton emission (X^{+}), respectively. As the magnitude of F_{p} is varied, all the emission lines shift in energy. In a first approximation, this shift is due to the straininduced change of the energy bandgap of the material, which in turn is proportional to the volumetric strain ɛ_{tot}=ɛ_{xx}+ɛ_{yy}+ɛ_{zz} at the QD position. For inplane stress and cubic materials, ɛ_{tot} is given by which, in the present case, is (with S_{ij} the compliance coefficients of the host material, see Supplementary Note 1). As ɛ_{tot} has the same sign as d_{32}, which has a relatively large magnitude and is negative, we expect a positive F_{p} to induce a compressive strain, which results in a blue shift of the EL, whereas a negative F_{p} induces a tensile strain, which results in a red shift. We also note that a total energy shift of about 2.5 meV is achieved as F_{p} is varied from −6.7 to 20 kV cm^{−1}.
Changes in polarization and FSS with the strain fields
To control the FSS of the QDs embedded in the diode, the crystal axes [110] and [110] of the GaAs nanomembrane were carefully aligned along the x and y axes of the PMNPT actuator, respectively (see Fig. 1a). Representative plots of the FSS (s) of different QDs as a function of F_{p} are shown in Fig. 2a. Although the emission energy shift is only about 2.5 meV as F_{p} is varied from −6.7 to 28 kV cm^{−1} as a consequence of the strong strain anisotropy (and thus relatively small ɛ_{tot}), the FSS is tuned over a broad range from 30 to 0 μeV. Away from the minimum FSS, all studied QDs exhibit an approximately linear change in the FSS with F_{p} at a rate of about 2.0 μeV kV^{−1} cm^{−1}, which is about nine times larger than what has been reported for vertical electric fields^{23}. In addition to this drastic change in FSS, we also observe rotations of the exciton polarization angle θ, that is, the polarization direction of the highenergy line of the exciton with respect to the [110] direction of the GaAs nanomembrane (see Fig. 2b). At the largest available tensile (compressive) strain, θ tends to be directed along the [110] ([110]) direction for all QDs. Furthermore, we note that the above tuning behaviour is mainly determined by the exciton polarization angle at zero strain fields (θ_{0}) with respect to the predefined direction of the strain^{29,33}. Experimentally, this polarization angle can be extracted from ΔE=E(ϕ, F_{p}=0)−E_{min}, where ϕ is the polarization direction selected by our polarization analyser (which varies from 0° to 360°), E(ϕ, F_{p}=0) is the relative position between X and XX as a function of ϕ and it can be directly extracted from a polarizationresolved EL measurement, and E_{min} is the minimum energy of E(ϕ, F_{p}=0; see Supplementary Fig. 1). Figure 2c–g show ΔE(ϕ, F_{p}=0) for the five studied QDs. The initial FSS s_{0} and θ_{0} are represented by the magnitude and orientation of the lobes in each polar plot. For the dot A and B, θ_{0} are 102.0°±0.4° and 92.7°±0.2° (the numbers quoted are the mean±s.d. and the same definition is applied below), respectively, suggesting positive deviations of θ_{0} from the strain x axis. Consequently, as F_{p} is increased, the polarization angle θ rotates counterclockwise and the FSS experiences a finite lower bound s_{min}=7.2±0.2 and 2.2±0.1 μeV (the green and wine curves in Fig. 2a,b). For dot C, θ_{0} is found to be 86.1°±0.4°, which suggests a negative deviation from the strain x axis. Thus, a clockwise rotation of θ over F_{p} is observed, together with an s_{min}=4.2±0.2 μeV (the purple curve). For the QDs D and E, θ_{0} is found to be 90.4°±0.3° and 90.6°±0.3° respectively, which indicate exact alignment of θ_{0} with the strain x axis. The polarization angles for both QDs rotate clockwise as the strain is varied and this implies that their polarization angles at zero strain fields are oriented at angles slightly <90°. It should be noted that this difference from the observed values (larger than 90°) is ascribed to the limited alignment precision of the polarizer (within a few degrees)^{29}. Most importantly, owing to this exact alignment between the exciton polarization angle θ_{0} and the strain axes for dot D and E, their FSS can be reduced well below 1 μeV and s_{min} is found to be 0.30±0.25 and 0.60±0.20 μeV, respectively. By simply treating the anisotropic strain as an effective uniaxial strain^{28} (see Supplementary Note 2), the behaviour of s and θ are well fitted (solid lines in Fig. 2a,b). Noticeably, the minimum reachable FSS value, following the form s_{min}=s_{0}sin(2θ_{0}), is determined by s_{0} and θ_{0} (see Supplementary Table 1). Even more, the s_{min} predicted before varying the strain fields are 8.18±0.20, 2.34±0.21, 3.3±0.18, 0.24±0.32 and 0.76±0.15 μeV for dot A, B, C, D and E, respectively, which show excellent agreement with our experimental data. From our experimental observations and theoretical analysis, it is clear that, to cancel the FSS with our external strain fields, the strain principal axes should be as close as possible to the polarization angle of QDs at zero applied stress.
Quantum state tomography measurments
The ability to tune the FSS of the QDs to zero allows us to investigate the capability of the STELED to generate polarizationentangled photon pairs without the aid of postfiltering techniques^{34,35}. Figure 3a shows the polarization resolved co and crosspolarization correlation between the XX and X photons emitted by dot E under electrically pulsed excitation and tuned to a FSS of 0.60±0.20 μeV (at F_{p}=18.7 kV cm^{−1}). The periodic correlation peaks with wellseparated temporal distance of 5.4 ns arise from the chosen repetition rate of 185.2 MHz. Importantly, for copolarized twophoton, strong correlations are observed in linear (HV) and diagonal (DA) bases, while strong anticorrelations are observed in circular basis (RL), as expected for the photon pairs emitted in the maximally entangled Bell state Ψ^{+}〉. To quantify the degree of polarization entanglement, we have reconstructed the twophoton density matrix by performing quantum state tomography measurements, as described in ref. 36. Sixteen polarization correlation measurements were performed and the density matrix is reconstructed using a maximum likelihood estimation. The imaginary part and the real part of the density matrix are displayed in Fig. 3b,c. The outer offdiagonal elements in the real part of the density matrix reveal a high probability for a superposition of the twophoton wave function, being a clear signature of polarization entanglement^{36}. Specifically, the density matrix can be used to quantify the degree of entanglement by extracting the tangle T, the concurrence C, the largest eigenvalue λ and the Peres criterion P. We find C=0.688±0.040 (>0), T=0.474±0.055 (>0), λ=0.795 (>0.5) and P=−0.30±0.02 (<0). All these tests exceed the classical limit, proving that the quantum state obtained in our experiment is highly entangled. Using the largest eigenvalue, we are able to determine the most probable state of the system: , in which the presence of the phase φ_{0}=−0.11π is likely to be due to the reflection at the beam splitter^{37} and the residual FSS ^{38}. As a consequence, the fidelity to the maximally entangled Bell state Ψ^{+}〉 is found to be f^{+}=0.766±0.051.
High yield of QDs for entangledphoton generation
Having demonstrated generation of entangledphoton pairs from our STELED, we present one of the most important results of our work, that is, the capability of anisotropic strain fields to tune about 30% of the QDs for entangledphoton emission. A statistical study from 82 randomly selected QDs revealed that the majority of QDs in our STELED device have θ_{0} oriented close to the [110] crystal axis (see Supplementary Fig. 2). Therefore, the alignment of the strain axes parallel (or perpendicular) to the [110] crystal axis of the GaAs ensures frequent observation of QDs with low value of s_{min}. Figure 4a shows the statistical investigation of s_{min}, falling into a range of 0 to 40 μeV. Remarkably, nine QDs have s_{min} <1 μeV, which is of the order of the homogenous linewidth of the X emission. Therefore, 11% of dots have sufficiently small FSS for strong entanglement in our device (see Supplementary Note 3, Supplementary Fig. 3 and Supplementary Table 2 for the entanglement results measured for other dots at s_{min}<1 μeV). In addition, recent works have suggested that for InGaAs QDs entanglement is robust and the violation of the classical limit can be achieved for FSS smaller than 3–4 μeV (refs 37, 39). To quantify this probability in our STELEDs, we use the following approach: we study the evolution of the fidelity to the maximally entangled Bell state Ψ^{+}〉 as a function of the FSS for one single QD and we use the obtained result to estimate at which value of the FSS it is possible to overcome the classical limit. To determine the entanglement fidelity, polarization correlations were performed for each value of the FSS and entanglement was equivalently quantified by measuring the degree of correlation (see Methods). As shown in Fig. 4b, the maximum fidelity f^{+}=0.75±0.02 is achieved when the FSS is tuned close to zero. For FSS values larger than 3 μeV, the fidelity drastically decreases below the classical limit (see the dashed line). Taking into account that the exciton lifetime of the InGaAs QDs in our STELED device has typical values of about 1 ns, this FSS of about 3 μeV provides an upper limit to observe entanglement, consistent with previous reports for InGaAs QDs^{12,27,37,39}. From the statistical investigation we find that 27 QDs can be tuned below 3 μeV, which indicates a probability as high as 33% of QDs that can be exploited as entangledlight emitters in our STELEDs. Compared with the only work on ELEDs present in the literature^{16}, the yield demonstrated in our work is more than an order of magnitude higher (a factor of ∼30). This probability is higher than what was reported for highly symmetric pyramidal QDs where, however, electrical injection has not been realized yet^{40}. We note that the yield of dots tuned for entangledphoton generation in our STELED can be further improved by optimizing the alignment of the strain principal axes to the statistical mean value of the initial polarization direction. According to our statistical measurement, the mean value of the initial polarization direction is in fact 92.25° instead of 90° (see Supplementary Fig. 2).
High speed generation of entangledphoton pairs
In addition, we can increase the pulsed excitation rate to achieve fast generation rate of the entangledphoton pairs. This feature is highly desirable for high datarate quantum information processing. Figure 5 shows the results of polarization correlation measurements at 400 MHz for the dot E. Similar to the case of 185.2 MHz, we observe correlations in the HV and DA bases and anticorrelation in the RL basis for copolarized two photons. In Fig. 5b the degrees of correlation in given bases are reported. We find a state fidelity as high as 0.66±0.02, which exceeds the classical limit of 0.5 and thus proves generation of entangledphoton pairs at 400 MHz. We observe that the fidelity at 400 MHz is smaller than the fidelity at 185.2 MHz reported above. This is likely ascribed to the contribution of a small amount of uncorrelated photon pairs due to the timedependent reexcitation process, residual FSS and background emission^{16,38,39}. By temporal post selection of the emitted photons we can alleviate these effects for the entanglement degradation. The curves in Fig. 5c show the degrees of correlation for a temporal gate Δτ=0.8 ns at which ∼20% of the coincidence counts are discarded. We measure C_{HV}=0.67±0.06, C_{DA}=0.63±0.04 and C_{RL}=−0.78±0.07, corresponding to f^{+}=0.77±0.03. The degree of correlation and entanglement fidelity can be improved by further shortening Δτ^{16,13,38,39}. With the narrowest available gate width of 0.1 ns applied, ∼80% coincidence counts are discarded and the degrees of correlation increase significantly: C_{HV}=0.74±0.12, C_{DA}=0.74±0.09 and C_{RL}=−0.84±0.12, which provides the highest fidelity of 0.83±0.05. It is interesting to investigate whether such a high level of entanglement is sufficient to violate Bell’s inequality. Using the measured values of the degree of polarization correlation, it is possible to determine Bell parameters S_{RD}, S_{RC} and S_{DC}, which are related to three different planes of the Poincaré sphere (see Methods). Our results show that the Bell parameters increase as the gate width is decreased, and the Bell inequality is found to be violated starting from the gate width of 0.8 ns. From the degrees of correlation at Δτ=0.8 ns, we calculate S_{RD}=1.83±0.07, S_{RC}=2.04±0.09 and S_{DC}=2.00±0.08. Two of these values are >2 and they indicate violations of the Bell inequality. In particular, S_{RD} is found to be less than S_{RC} and S_{DC}, and this is due to the weaker degree of correlation observed in the HV and DA bases (C_{HV}, C_{DA}<C_{RL}) (refs 16, 37, 39). This common feature is usually observed for the QDs entangledphoton sources and is most probably ascribed to the weak coupling between the two bright exciton states^{41}. Therefore, for the actual entangled state S_{RD} is not optimally chosen to inspect violation of the Bell inequality. In addition, for the gate width of 0.1 ns, we find S_{RD}=2.09±0.21, S_{RC}=2.23±0.21 and S_{DC}=2.23±0.24 (see Supplementary Fig. 4). All these three parameters are above the threshold of 2, thus proving that our STELED is capable of generating nonlocal states of light in response to an electrical trigger.
Discussion
We have presented STELEDs in which anisotropic strain fields are used to tune QDs for entangledphoton generation. We have shown that up to 30% of QDs embedded in this device are capable of emitting polarization entangledphoton pairs. This practically removes the tedious search for special QDs plaguing previous ELEDs^{16}. Furthermore, we demonstrate triggered entangledphoton emission at a repetition rate of 400 MHz. Our all electrically controlled STELEDs emerge as one of the most practical entangledphoton sources with fast operation speed and great potential for largescale quantum communication and computation tasks.
Despite the considerable advances in our STELED, it should be noted that the high yield of QDs tuned for entangledphoton emission has been achieved by applying different magnitudes of strain to different QDs in the single STELED device due to the structural randomness of the QDs. To achieve scalable onchip integrative entangledphoton applications, active engineering efforts are required to fabricate welldefined microstructures on PMNPT crystal so that different strain fields can be exerted to different QDs simultaneously on one single chip. This will be of particular interest for realizing QDs arrays of independently tunable electrically triggered entangledphoton sources. Further improvements to the STELED devices, such as integration with microcavities^{42,43} or microlenses^{44}, to achieve bright entangledphoton emission, using IIInitride QDs to develop entangledphoton sources operating at room temperature^{45,46}, constitute important steps towards realizing more practical electrically driven entangledphoton sources for scalable quantum information applications.
Methods
Sample and device fabrication
The studied sample was grown on a (001) GaAs substrate by solidsource molecular beam epitaxy. It consisted of a pin heterostructure diode composed of a 178nmthick ntype GaAs layer, a 160nmthick intrinsic GaAs layer and a 96nmthick ptype GaAs layer from the bottom to the top. A layer of lowdensity (∼10^{6}–10^{7} cm^{−2}), selfassembled InGaAs QDs was embedded in the middle of the intrinsic GaAs layer. The entire diode structure was grown on a 100nmthick Al_{0.75}Ga_{0.25}As sacrificial layer. As for the device processing, first of all, standard ultraviolet photolithography and wet chemical etching were used to fabricate mesa structures with size of 120 × 160 μm^{2}. The longer edge of the GaAs membrane was processed along [110] crystal axis of GaAs and—during the transfer onto the piezoelectric actuator—was carefully aligned along the y axis of the PMNPT actuator. It is worth noting that the bonded gold layer on the bottom formed a pcontact, whereas the ntype contact was formed by depositing a gold pad with size of 50 × 50 μm^{2} on the top of the nanomembrane.
Electrically pulsed excitation and spectroscopic measurements
The EL is observed when the diode is biased with a DC voltage (V_{d}) above −1.7 V; however, it is slightly different from one device to another due to the different bonding conditions. The pulsed electrical excitation is accomplished by superimposing an ultrafast electrical pulse stream onto a −1.6 V DC bias by using a broad bandwidth biasTee. The pulse stream used in this work has nominal duration of 300 ps and amplitude of V_{pp}=−8.0 V. The large magnitude of the pulse stream used here is caused by the low pulse injection efficiency, which is probably ascribed to the imperfect electrical connections and large impedance mismatching between the device and the external electronics. Further improvements, including optimization of the electrical connections and introducing an impedance matching network^{47}, are expected to increase the pulse injection efficiency and consequently reduce the pulse magnitude.
In optical measurements, the EL emitted from the diode is collected by a × 50 microscope objective with numerical aperture of 0.42, which is placed on the top of the nanomembrane and collects the photon emission from the area close to the metal contact. By inserting a halfwave plate and a linear polarizer directly after the collection lens, polarizationresolved measurements were performed to obtain the FSS against F_{p}. The exciton polarization is determined by aligning the fast optical axis of the polarizer along [110] direction of the nanomembrane. The EL was directed to a spectrometer with 750 mm focus length and the spectrum was analysed using a nitrogencooled chargecoupled device. The FSS is determined with an accuracy of subμeV by taking the experimental procedure in refs 23, 25.
Polarizationresolved photon correlation measurements
Regarding the polarizationresolved correlation measurements, a nonpolarizing 50:50 beam splitter is placed directly after the collection objective, to divide the optical paths between two spectrometers, which are used to detect X and XX separately. After each spectrometer, a Hanbury–Brown Twiss setup consisting of a polarizing beam splitter and two highefficiency singlephoton avalanche detectors is placed. Half and quarter waves were used to select the proper polarization basis. The temporal resolution of the system is ∼400 ps. The entanglement can be equivalently quantified by measuring degree of correlation C, which is defined by
where g_{XX,X}^{(2)}(τ) and are normalized secondorder time correlations for copolarized and crosspolarized XX and X photons, respectively. The fidelity f^{+} is calculated by using the formula: f^{+}=(1+C_{HV}+C_{DA}−C_{RL}), in which C_{HV}, C_{DA} and C_{RL} are degree of correlations in HV, DA and RL bases. The Bell parameters are determined with the formulas: , and .
Additional information
How to cite this article: Zhang, J. et al. High yield and ultrafast sources of electrically triggered entangledphoton pairs based on straintunable quantum dots. Nat. Commun. 6:10067 doi: 10.1038/ncomms10067 (2015).
Change history
11 May 2016
A correction has been published and is appended to both the HTML and PDF versions of this paper. The error has not been fixed in the paper.
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Acknowledgements
The work was supported financially by BMBF QuaHLRep (contract numbers 01BQ1032 and 01BQ1034), Q.ComH (16KIS0106) and the European Union Seventh Framework Programme 209 (FP7/20072013) under grant agreement number 601126 210 (HANAS). J.X.Z. was supported by China Scholarship Council (CSC, number 2010601008). We thank B. Eichler, R. Engelhard, P. Atkinson, B. Höfer and S. Harazim for discussions and the technical support.
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Author notes
 Eugenio Zallo
Present address: PaulDrudeInstitut für Festkörperelektronik, Hausvogteiplatz 57, 10117 Berlin, Germany.
Affiliations
Institute for Integrative Nanosciences, IFW Dresden, Helmholtzstrasse 20, 01069 Dresden, Germany
 Jiaxiang Zhang
 , Fei Ding
 , Yongheng Huo
 , Eugenio Zallo
 & Oliver G. Schmidt
Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenbergerstrasse 69, 4040 Linz, Austria
 Johannes S. Wildmann
 , Rinaldo Trotta
 , Yongheng Huo
 , Daniel Huber
 & Armando Rastelli
Material Systems for Nanoelectronics, TU Chemnitz, 09107 Chemnitz, Germany
 Oliver G. Schmidt
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Contributions
The sample was grown by Y.H. and E.Z., and the device was fabricated by J.X.Z. The work was conceived and designed by J.X.Z., F.D. and R.T., and guided by A.R. and O.G.S. The optical measurements were performed by J.X.Z., J.W., R.T. and D.H. The results were discussed by all authors. J.X.Z. wrote the manuscript with help from all the other authors.
Competing interests
The authors declare no competing financial interests.
Corresponding authors
Correspondence to Jiaxiang Zhang or Fei Ding or Rinaldo Trotta.
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Supplementary Figures 14, Supplementary Tables 12, Supplementary Notes 13 and Supplementary References.
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