High yield and ultrafast sources of electrically triggered entangled-photon pairs based on strain-tunable quantum dots

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. Entangled-light-emitting-diodes based on semiconductor quantum dots are among the most promising sources that can potentially address this task. However, entangled-light-emitting-diodes 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 entangled-photon generation (∼10−2). Here we introduce strain-tunable entangled-light-emitting-diodes that exploit piezoelectric-induced strains to tune quantum dots for entangled-photon generation. We demonstrate that up to 30% of the quantum dots in strain-tunable entangled-light-emitting-diodes emit polarization-entangled photons. An entanglement fidelity as high as 0.83 is achieved with fast temporal post selection. Driven at high speed, that is 400 MHz, strain-tunable entangled-light-emitting-diodes emerge as promising devices for high data-rate quantum applications.


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The FSS can be suppressed or tuned to zero via the application of either a vertical electric field 11 or a combination of strain and electric field 12,13 .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 14,15 and in-plane magnetic field 16 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 well-controlled strain field 17,18 .Using piezoelectric-induced 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 piezo-electric response and capable of delivering welldefined anisotropic strain fields.With this novel devicewhich we call S-ELEDswe show (i) 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; (ii) that up to 30% of the QDs are tuned to be suitable for the generation of entangled-photon pairs (more than an order of magnitude more than in previous devices 5 ) and (iii) the highest operation speed ever reported so far for an entangledphoton source (400 MHz).This unique set of properties paves the way towards the real exploitation of ELEDs in high data-rate entangled-photon applications involving a large numbers of quantum emitters.axis with opposite sign can be transferred to the nanomembrane.Accounting for its relevant piezoelectric coefficients d 31 ~ +420 pC/N along the x axis and d 32 ~ -1140 pC/N along the y axis 21 , the in-plane anisotropy is estimated to be ≈ -0.37 .The large and well controlled strain anisotropy and the broad range of attainable strain magnitudes are unique and turned out to be vital in our work.

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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 PMN-PT actuator.By biasing the diode and applying a variable electric field (F p ) to the PMN-PT simultaneously, energy-tunable electroluminescence (EL) from a single QD is produced, as shown in Fig. 1b.According to the power and polarization-resolved measurements the observed EL lines are ascribed to exciton, biexciton and charged exciton emission, respectively.As the magnitude of F p is varied, all the emission lines shift in energy.The shift is expected to be mostly proportional to the opposite of the variation of the volumetric strain at the QD position, which can be estimated as (with S ij the compliance coefficients of the host material).Since 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, while 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 .In order to control the FSS of the QDs embedded in the diode, the crystal axes [1-10] and

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[110] of the GaAs nanomembrane were carefully aligned along the x and y axes of the PMN-PT actuator, respectively (see Fig. 1a).Representative plots of the FSS 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 kVcm -1 as a consequence of the strong strain anisotropy (and thus relatively small ), the FSS is tuned over a broad range from 30 ~ 0 eV.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eV·kV -1 ·cm, which is about 9 times larger than what has been reported for vertical electric fields 11 .In addition to this drastic change in FSS, we also observe rotations of 7/28 the exciton polarization angle , i.e., the polarization direction of the high-energy line of the exciton with respect to the [110] direction of the GaAs nanomembrane (see Fig. 2b).At the largest available tensile (compressive) strain, for all QDs tends to be directed along the [1-10]   ([110]) direction.Furthermore, we note that the above tuning behavior is mainly determined by the exciton polarization angle at zero strain fields ( ) with respect to the predefined direction of the strain 12,22 .Experimentally this polarization angle can be extracted from | ( ) | as a function of , where is the minimum energy of ( ). ) is ascribed to the limited alignment precision of the polarizer (within a few degrees) 12 .Most importantly, owing to this exact alignment between the exciton polarization angle and the strain axes for dot D and E, their FSS can be reduced well below 1 eV and s min is found to be 0.30 ±0.25eV and 0.60± 8/28 0.20 eV respectively.By simply treating the anisotropic strain as an effective uniaxial strain 18 , the behavior of s and are well fitted (solid lines in Fig. 2a and 2b).Noticeably, the minimum reachable FSS value, following the form s min = , is determined only by s 0 and (see Supplementary Information).The s min predicted before varying the strain fields are: 8.18±0.20 eV, 2.34±0.21eV, 3.3±0.18eV, 0.24±0.32eV and 0.76±0.15eV for dot A, B, C, D, E, which show excellent agreement with our experimental data.From our experimental observations and theoretical analysis, it is clear that, in order to cancel the FSS with our external strain fields, the polarization angle at zero applied stress should be as close as possible to the strain principal axes.being a clear signature of polarization entanglement 26 .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 10/28 eigenvalue, we are able to determine the most probable state of the system: √ , in which the presence of the phase = -0.11 is likely due to the reflection at the beam splitter 13 .As a consequence, the fidelity to the maximally entangled Bell state | is found to be f + = 0.766 ± 0.051.
Having demonstrated generation of entangled-photon pairs from our S-ELED, 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 entangled-photon emission.A statistical study from 82 randomly selected QDs revealed that the majority of QDs in our S-LED device have oriented close to the [1-10] crystal axis (see Supplementary Information).Therefore, the alignment of the strain axes parallel (or perpendicular) to the [1-10] crystal axis of the GaAs ensures frequent observation of QDs with low value of s min .Fig. 4a shows the statistical investigation of s min , falling into a range of 0 ~ 40 eV.Remarkably, 9 QDs revealed a s min less than 1 eV, 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.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 13,27 .In order to quantify this probability in our S-ELEDs, we use the following approach: we study the evolution of the fidelity to the maximally entangled Bell state | 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 eV, the fidelity drastically 11/28 decreases below the classical limit (see dashed line).Taking into account that the exciton lifetime of the InGaAs QDs in our S-ELED device has typical values of about 1 ns, this FSS of about 3 eV provides an upper limit to observe entanglement, consistent with previous reports for InGaAs QDs 13,27,28,29 .From the statistical investigation we find that 27 QDs can be tuned below 3 eV, which indicates a probability as high as 33% of QDs that can be exploited as entangled-light emitters in our S-ELEDs.Compared to the only work on ELEDs present in the literature 5 , this is more than an order of magnitude (a factor ~30) higher.This probability is even higher than what was reported for highly symmetric pyramidal QDs where, however, electrical injection has not been realized yet 30 .In addition, we can increase the pulsed excitation rate in order to enhance the generation rate of the entangled-photon pairs.This feature is highly desirable for high data-rate quantum information processing.Fig. 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 anti-correlation in the RL basis for co-polarized two photons.In the left panel of 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, for the first time, generation of entangled-photon 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 time-dependent re-excitation process, residual FSS, and background emission 5,26,27 .By temporal post-selection of the emitted photons we can alleviate these effects for the entanglement degradation.The red curves in Fig. 5b show the degrees of correlation for a temporal gate  = 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  5,26,27,29,31,32 .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±0.09and 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  5,13,31 .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 31 .Therefore, for the actual entangled state S RD is not optimally chosen to inspect violation of the Bell inequality.Additionally, for the gate width of 0.1 ns, we find S RD = 2.09± In conclusion, we have presented the first S-ELEDs in which anisotropic strain fields are used to tune QDs for entangled-photon generation.We have shown that up to 30% of QDs embedded in this device are capable of emitting polarization entangled-photon pairs.This practically removes the tedious search for special QDs plaguing previous ELEDs 5 .Furthermore, we prove for the first time triggered entangled-photon emission at the repetition rate of 400 MHz, the highest value ever reported so far.Our all electrically-controlled S-ELEDs emerge as the most practical and fastest source of entangled photons available to date, that can be exploited for large-scale quantum communication and quantum computation tasks.

Methods
The studied sample was grown on a (001) GaAs substrate by solid-source molecular beam Regarding the polarization resolved correlation measurements, a non-polarizing 50:50 beam splitter is placed directly after the collection objective in order to divide the optical paths between two spectrometers, which are used to detect X and XX separately.After each

Figure 2 |
Figure 2 | Strain-induced change of fine structure splitting and exciton polarization angle.

3 o
Fig. 2c ~ g show the dependence of on for the five QDs.The initial FSS s 0 and are represented by the magnitude and orientation of the lobes in each polar plot.For the dot A and B, are 102.0o ± 0.4 o and 92.7 o ± 0.2 o , respectively, suggesting positive deviations of from the strain x axis.Consequently, as F p is increased, the polarization angle rotates counterclockwise and the FSS experiences a finite lower bound s min = 7.2±0.2eV and 2.2±0.1eV(the green and wine curves in Fig. 2a and 2b).For dot C, is found to be 86.1 o ± 0.4 o , which suggests a negative deviation from the strain x axis.Thus a clockwise rotation of over F p is observed, together with a s min = 4.2±0.2eV (the purple curve).For the QDs D and E, is found to be 90.4 o ± 0.and 90.6 o ± 0.3 o respectively, which indicate exact alignment of and 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 less than 90 o .It should be noted that this difference from the observed values (larger than 90 o

Figure 4 |
Figure 4 | Statistical investigation of the minimum FSS and dependence of the

0. 21 , 28 Figure 5 |
Figure 5 | Polarization correlation results from the S-ELED under electrically pulsed epitaxy (MBE).It consisted of a p-i-n heterostructure diode composed of a 178 nm-thick n-typeGaAs layer, a 160 nm-thick intrinsic GaAs layer and a 96 nm-thick p-type GaAs layer from the bottom to the top.A layer of low density (10 6 ~10 7 cm -2 ) self-assembled InGaAs QDs was embedded in the middle of the intrinsic GaAs layer.The entire diode structure was grown on a 100 nm-thick Al 0.75 Ga 0.25 As sacrificial layer.As for the device processing, first of all, standard 15/28 UV photolithography and wet chemical etching were used to fabricate mesa structures with size of 120×160 m 2 .The longer edge of the GaAs membrane was processed along [110] crystal axis of GaAs andduring the transfer onto the piezoelectric actuatorwas carefully aligned along the y axis of the PMN-PT actuator.It is worth noting that the bonded gold layer on the bottom formed a p-contact, while the n-type contact was formed by depositing a gold pad with size of 50×50 m 2 on the top of the nanomembrane.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 bias-Tee.The pulse stream used in this work has nominal duration of 300 ps, and amplitude of V pp = -8.0V.For 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 half-wave plate and a linear polarizer directly after the collection lens, Polarization-resolved measurements were performed to obtain the FSS vs. 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 is analyzed using a nitrogen cooled charge-coupled device.The FSS is determined with an accuracy of sub-eV by taking the experimental procedure in ref.11 and 12.

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, a Hanbury-Brown Twiss setup, consisting of a polarizing beam splitter and two high efficiency single-photon avalanche detectors, is placed.Half-and quarter-wave were used to select the proper polarization basis.The temporal resolution of the system is about 400 ps.The entanglement can be equivalently quantified by measuring degree of correlation C, which is defined by are normalized second-order time correlations for co-polarized and cross-polarized XX and X photons, respectively.The fidelity f + is calculated by using the formula:f + = , inwhich , and are degree of correlations in HV, DA and RL bases.The Bell parameters are determined with the formulas: S RD = √ ( ); S RC = √ ( ); S DC = √ ( ).
13/28entanglement 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  = 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 larger than 2 and they indicate violations of the Bell inequality.In particular, S RD is found to be less than S RC , 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 |)