SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY MATERIAL Towards quantum dot arrays of entangled photon emitters Gediminas Juska *1, Valeria Dimastrodonato 1, Lorenzo O. Mereni 1, Agnieszka Gocalinska 1 and Emanuele Pelucchi 1 1 Tyndall National Institute, University College Cork, Lee Maltings, Cork, Ireland * Corresponding author: gediminas.juska@tyndall.ie Here we discuss in more details some issues which did not find space in the main body of our contribution, as a source of extra clarification. Linewidth The typical Lorentzian linewidth of the exciton transition was found to be 80±15 µev in our first samples. Such broadening of the natural linewidth is possibly due to patterning introduced impurities creating local electric field fluctuations by randomly trapped charges 1 and unintentional impurities generated during the MOVPE precursor decomposition. While linewidth has a minor role on the specific of this report (which concentrates on the achievement of high symmetry dots emitting entangled photons, while spectral meandering, which is not noise, is a slow process (typically a few milliseconds) and does not affect in itself entanglement nor coherence), we nevertheless anticipate, as an answer to possible readers concerns, that it is possible to reduce spectral meandering below 20 µev under non resonant excitation in our QDs, when proper reactor and processing protocols are adopted. We actually managed to obtain entangled photons from QDs exhibiting lines as narrow as ~40 µev, after our manuscript was firstly submitted 2,3. These results are a clear indication that spectral meandering can be defeated, and does not represent a limitation for pyramidal QDs incorporation in integrated photonic circuits. Significance of the excitonic pattern In the text, we stress that a particular excitonic pattern acts as a very reliable fingerprint of entangled photon emitters. The samples which we present here contain QDs with two different types of excitonic patterns which mainly differ in the order of biexciton and charged exciton (the attributed type of transitions is consistent with photon correlation, excitation power dependent, time resolved and temperature dependent measurements). The most widely spread type is presented in Fig. S1(a). It is the pattern which we almost always observed in our first samples 4 antibinding biexciton with binding energy in the range of 3-4 mev. Typically there exists a charged exciton between exciton and biexciton. In the new optimized and reproducible samples, a significant percentage of QDs (~20%) NATURE PHOTONICS 1

2 Figure S1. Significance of the excitonic pattern. (a), (b) Two different types of excitonic patterns found on the same sample. The data presented in the main text is obtained from QD with excitonic pattern (b). (c) Biexciton binding energy of QDs from dots with an excitonic pattern as in (b). (d) Fidelity of entangled state as a function of QD emission energy for dots with an excitonic pattern as in (b). had a different excitonic pattern (Fig. S1(b)). The main difference comparing to the first pattern is swapped positions of biexciton and charged exciton with biexciton being separated from exciton by mev (Fig. S1(c)). By picking these dots, entanglement tests have failed only a minority of times. It must be stressed that the fine-structure splitting (FSS) values were not reliable indicators of entangled photon emitters for the both types of excitonic patterns, as in majority of cases, no FSS was measured within the 4 µev resolution of our FSS detection procedure. By picking QDs with the first pattern, entanglement tests have failed all the times despite vanishing FSS. The reasons of such behavior are not obvious we can only confirm the observed result, and suggest that maybe a FSS was actually present, even if not detectable by us. Fig. S1(d) shows the fidelity of entangled state as a function of the exciton transition energy from the second pattern QDs. No dependence was observed, suggesting that as long as the excitonic pattern is the same, the entanglement quality is maintained. 2 NATURE PHOTONICS

3 Influence of the fine-structure splitting In the main text, we state the typical FSS detection procedure limit to be generally ~4 µev. In some individual cases, this limit could be overcome and the FSS was measured even if smaller than 4 µev. Figure S2 shows a particular QD with the FSS of 3 µev (Fig. 2S(a)). The QD is from a different sample, with a slightly thicker nominal QD layer (it is reflected in the reduced emission energy (Fig. 2S(b))). We stress that, in general, a rather small splitting is sufficient to destroy all the indications of polarizationentanglement. Fig. S2(a) presents the degree of correlation as a function of linear polarization detection angle (twice the angle between a fixed linear-polarizer and the fast axis of a half-wave plate). The degree of correlation follows the sinusoidal trend an indication of classical correlations 5. For comparison, Fig. S2(c) presents the same type of measurement when a QD does not suffer from FSS related issues. The degree of correlation barely depends on polarization angle, as expected for entangled photons. The average value of 0.56±0.04 can be only obtained if polarization correlations are nonclassical. Data points fit better with sinusoidal than linear trend possibly due to a tiny remaining FSS and (or) incoherent dephasing effects 6. Figure S2. Demonstration of the fine-structure splitting influence on polarizationentanglement indication.(a) FSS measurementand degree of correlation as a function of linear polarization detection angle showing typical behavior when only classical polarization correlations are present. (b) The spectrum of the same QD with ~3 µev FSS. (c) Degree of correlation as a function of linear polarization detection angle obtained from a different QD which does not suffer from FSS related issues. The trend and the average value of 0.56±0.04 demonstrate presence of non-classical correlations. (d) A direct example of classical polarization correlations obtained from photons emitted by the QD shown in (b). NATURE PHOTONICS 3

4 The obtained FSS and degree of correlation curves (Fig. S2(a)) are in agreement with each other. The maximum and minimum of the FSS curve indicate the polarization axes of the QD (which are expected to be random for different QDs, as the sources of the FSS are not expected to be related to crystallographic directions). The degree of correlation is expected to be highest at these angles. Fig. S2(d) directly demonstrates the presence of classical correlations. Polarization correlation is observed only in linear bases, but not in diagonal and circular. Useful QD density comparison with other QD systems In our contribution, we claimed easily finding areas containing at least 15% of entangled photon emitters. Comparing to the other QD systems, this density is typical significantly smaller (1/100 or worse). For example, Salter et al. 7 claimed finding one good dot per device with an active area of ~130k µm 2, patterned with 100 circular holes. The typical density of QDs quoted is 1 µm -2, suggests one entangled photon emitter out of 300 potential candidates (without using any FSS tuning strategy, such as magnetic, electric fields, strain), per useful area, and 1/130k per total area involved. Different figure presentation Figure presentation is often a question of taste: here we show the original Figure 1 in the text with a different labeling criteria, for the demanding reader. Figure S3. An alternative version of the Figure 1 in the main text to introduce the information on absolute QD intensity values to the concerned readers. 4 NATURE PHOTONICS

5 REFERENCES 1. Empedocles, S. A. & Bawendi, M. G. Quantum-confined stark effect in single CdSe nanocrystallite quantum dots. Science 278, (1997). 2. Mereni, L. O., Dimastrodonato, V., Young, R. J. & Pelucchi, E. A site-controlled quantum dot system offering both high uniformity and spectral purity. Appl. Phys. Lett. 94, (2009). 3. Juska, G., Dimastrodonato, V., Mereni, L. O., Gocalinska, A. & Pelucchi, E. A study of nitrogen incorporation in pyramidal site-controlled quantum dots. Nanoscale Res. Lett. 6, 567 (2011). 4.Dimastrodonato, V., Mereni, L. O., Juska, G. & Pelucchi, E. Impact of nitrogen incorporation on pseudomorphic site-controlled quantum dots grown by metalorganic vapor phase epitaxy. Appl. Phys. Lett. 97, , (2010). 5.Stevenson, R. M. et al. A semiconductor source of triggered entangled photon pairs. Nature 439, (2006). 6.Yuan, L. Q. & Das, S. Quantum correlations and violation of the Bell inequality induced by an external field in a two-photon radiative cascade. Physical Review A 83, (2011). 7. Salter, C. L. et al. An entangled-light-emitting diode. Nature 465, 594 (2010). NATURE PHOTONICS 5