Abstract
Longdistance quantum communication is one of the prime goals in the field of quantum information science. With information encoded in the quantum state of photons, existing telecommunication fibre networks can be effectively used as a transport medium. To achieve this goal, a source of robust entangled singlephoton pairs is required. Here we report the realization of a source of timebin entangled photon pairs utilizing the biexciton–exciton cascade in a III/V selfassembled quantum dot. We analyse the generated photon pairs by an inherently phasestable interferometry technique, facilitating uninterrupted long integration times. We confirm the entanglement by performing quantum state tomography of the emitted photons, which yields a fidelity of 0.69(3) and a concurrence of 0.41(6) for our realization of timeenergy entanglement from a single quantum emitter.
Introduction
A source of entangled photon pairs is essential for quantum communication^{1,2} and linear optics quantum computing^{3}. Quantum information protocols such as quantum teleportation^{4,5} and entanglement swapping^{6,7} use entangled photons to enable longdistance distribution of entanglement through quantum repeaters^{8}. Optical fibres are the medium of choice for distribution, with the existing extensive global telecommunication fibre network. Polarization entangled photons suffer from decoherence in optical fibres due to polarization mode dispersion^{9,10}. This effect results in the wavelength and timedependent splitting of the principal states of polarization with a differential group delay. Thus the arrival time of the photons carries information about their polarization state causing decoherence. Alternatively, timebin entangled photons^{11} are immune to these decoherence mechanisms and are more robust^{12,13} in optical fibres^{12}. At present, spontaneous parametric downconversion is widely used as a source of timebin entangled photons^{11}. Nevertheless, photons produced by a single quantum emitter show inherently subPoissonian statistics^{14}. Thus, in this work, we show that the photon cascade in a single semiconductor quantum dot can produce timebin entangled photon pairs.
So far, experimental efforts have been focused on utilizing the biexciton–exciton cascade of a semiconductor quantum dot as a source of polarization entangled photons^{15,16,17,18}. A major hurdle in the realization of these sources comes from the asymmetry of the selfassembled quantum dots that results in nondegenerate exciton polarization states, thereby revealing the polarization state of the emitted photons. This hurdle has been overcome by some groups with great effort^{19,20,21,22,23}, but these technologies are not generally available.
Our entanglement scheme combines the strength of a quantum dot as a singlephoton source and the robustness of timebin entanglement. We use only one exciton polarization cascade so that the emitted photons are in a welldefined polarization mode. Nevertheless, our scheme is fairly insensitive to the polarization nondegeneracy; the polarization of the detected photon does not contain any information about the creation timebin of the photon pair. Schemes to generate single pairs of timebin entangled photons using the biexciton cascade in a quantum dot have been proposed^{24,25}. While these schemes require the quantum dot to be initially prepared in a longliving metastable state, we implement timebin entanglement through resonant excitation of the biexciton from the ground state. This method can produce maximally entangled states but it does not completely suppress double excitations. In this work we show timebin entanglement generated by a single quantum emitter. Our measurement yields a fidelity of 0.69(3) and a concurrence of 0.41(6).
Results
Writing the quantum superposition
To excite the quantum dot we use a pump interferometer that transforms the incoming laser pulse into a coherent superposition of two pulses that form welldefined time bins ‘early’ and ‘late’. The delay in the pump interferometer is set such that the time difference (Δt=3.2 ns) between the early and late bins is longer than the width of the laser pulse (4 ps) and coherence time of the biexciton (211 ps) and exciton (119 ps) photons. These laser pulse pairs excite the quantum dot biexciton state through the resonant twophoton excitation process shown in Fig. 1a. Details of the excitation process and experimental setup can be found in ref. 26. The schematic of timebin entanglement generation from a quantum dot and its spectrum are shown in Fig. 1c,b, respectively. The relative phase between the pump pulses creating twophoton excitations is given by φ_{P}=E_{XX}Δt/ℏ, where E_{XX} is the energy of the biexciton photon. Resonant excitation is crucial as it coherently transfers the phase of the pump pulses and thus the coherence created by the pump interferometer to the biexciton state. The coherence of the excitation process was proved in our previous work^{26}, through coherent manipulation experiments demonstrating Ramsey interference. In contrast, other, nonresonant excitation techniques involve phonon transitions, which leak the creation time of the biexciton to the environment^{27}, thereby degrading the coherence. At sufficiently low excitation power the biexciton state is created either by the early or by the late pulse, followed by the emission of a biexciton–exciton photon cascade. The emitted photons are in the timebin entangled state
where the photon pairs are in a coherent superposition of being emitted in the early or late time bin. The subscripts X and XX refer to the exciton and biexciton recombination photon, respectively. We analyse the entanglement of the emitted photons in a timebininterference experiment^{11} as shown in Fig. 1c. The exciton and biexciton photons are fed into two separate analysing interferometers that have delays equal to the pump interferometer. Finally, we record the coincidences between the outputs of the analysing exciton and biexciton interferometers. Photon pairs produced by the early pulse and taking the long path in the analysing interferometers are indistinguishable from photon pairs produced by the late pulse and taking the short path. Thus, the probability amplitudes of the two possible indistinguishable events interfere. This interference results in a sinusoidal change of the coincidence rates while the phase of one of the interferometers is varied. The relationship between coincidence counts and interferometer phase can be approximated^{28} by
with i, j taken as +1(−1) for the XX and X outputs 1(2), respectively. Here, φ_{X(XX)} is the phase of the exciton (biexciton) analysing interferometer. The visibility (V) of the interference is connected to the quality of the timebin entanglement and it is ideally equal to unity. In order to achieve maximum visibility the phase (φ_{XX}+φ_{X}−φ_{P}) has to be stable during the experiment. This can be accomplished by active stabilization of all three interferometers with respect to a phasestable laser. In our experiment, the phase stability is achieved by realizing the pump and analysing interferometers in three different spatial modes of a single bulk interferometer as shown in Fig. 2. We take advantage of the phase relation, such that the relative phase always remains the same independent of the drift in the interferometer. The phase of both the analysing interferometers can be set independently with the phase plates PP_{X} and PP_{XX}.
Detection in postselection
In order to extract the single events and coincidences between the photons at the outputs of the two analysing interferometers we record the arrival times of the photons with respect to the pump pulse. The triggering to the laser pulse is essential because it allows us to separate distinguishable from indistinguishable events. For example, Fig. 3a shows the recorded single events for the output X_{1}. The photons created by the early (late) pulse and travelling the short (long) path form the first (third) peak. The second peak is formed by photons created by the early excitation taking the long path and the photons created by the late excitation taking the short path. For our analysis we postselect only the photons arriving within a window of 1.28 ns in each of the peaks, shaded with grey in Fig. 3a. From the postselected events we extract coincidences between the outputs of the two analysing interferometers. The resulting histogram has five peaks (see Fig. 4). The first (last) peak consists of the pairs created by the early (late) pulse and passing through the short (long) paths of the analysing interferometers. Also, the second and the fourth peaks represent distinguishable events, where the biexciton and exciton photons have travelled along opposite interferometer arms. Thus the second (fourth) peak exclusively shows coincidences created by the early (late) pulse. The third peak shows the indistinguishable events that interfere and exhibit entanglement.
Tomography measurements
We quantify the timebin entanglement of the emitted photon pairs by measuring their quantum state through quantum state tomography^{29}. With this method we reconstruct the density matrix of the generated timebin entangled photons. We record coincidence events for different projections of the individual qubits (exciton and biexciton photons) to the states 0›, 1›, +X› and +Y› (represented on the Bloch sphere shown in Fig. 3b). Projections onto the states X› and Y› (energy basis) are achieved by setting the phase in the analysing interferometer to 0 and , respectively. It takes four measurements (see Methods) to obtain all 16 projections of the entangled twoqubit state that are required for the tomographic state reconstruction^{29}. The analysing interferometers phase settings for these four measurements are . The real and imaginary parts of the reconstructed density matrix are shown in Fig. 5, from which we obtain a fidelity of 0.69(3) with respect to the Φ^{+}› state, a tangle of 0.17(5) and a concurrence of 0.41(6). In addition, the visibilities in three orthogonal bases 0/1, +X/−X and +Y/−Y were measured to be 78.94(2)%, 41.40(3)% and 37.79(3)%, respectively. The raw counts used to reconstruct the density matrix are given in Supplementary Table 1.
Discussion
The imperfect interference visibility and hence the reduced fidelity and concurrence of the entangled state can mainly be attributed to double excitation and environmentinduced dephasing. Ideally, we expect pairs to be produced in only one of the two pulses. Nevertheless, there is a finite probability that both early and late pulse generate a photon pair. For this first realization of timebin entanglement we chose a relatively high excitation power as a compromise between the quality of the entanglement and count rate. For this power we calculate from our data a 12.4% contribution of such events. The coincidences between these double excitations form an incoherent background, hence reducing the visibilities in all three orthogonal bases. For example, if we reduced the excitation pulse power by 75% we estimate visibilities of 95.11(3)%, 48.47(3)% and 51.34(3)%, for 0/1, +X/−X and +Y/−Y bases, respectively. Correspondingly we would then obtain 0.48(6) for the tangle, 0.61(6) for the concurrence and 0.79(4) for the fidelity (for details see Supplementary Note 1).
Beyond double excitations some decoherence of the entangled state originates from the pure dephasing of excitons and biexcitons in the solidstate environment due to phonon interactions and spectral diffusion. These interactions leak information about the creation time of the biexciton^{27} and energy fluctuations of the excitons reduce the visibility of twophoton interference. The dephasing in the quantum dot used for the experiment is characterized with lifetime (biexciton: 405 ps, exciton: 771 ps) and coherence length (biexciton: 211 ps, exciton: 119 ps) measurements, which are far from the ideal transform limited condition. Timebin entanglement measures the mutual coherence between the emission of the early and the late cascade, not the coherence between the individual photons. Therefore we cannot directly use these numbers to calculate the required mutual coherence without a full quantum optical model of the quantum dot and its environment.
We generate timebin entangled photons from a quantum dot using the biexciton–exciton cascade. As far as we know this is the first realization of energytime entanglement from a single quantum emitter of any type. This was made possible by our method of coherent excitation of the biexciton^{26}. Reconstructing the density matrix through quantum state tomography unambiguously confirms the entanglement of the generated photon pairs. At the same time, our source is distinguished from spontaneous parametric downconversion sources by its subPoissonian photon statistics. Because our scheme is not affected by finestructure splitting it can be applied to a much larger variety of quantum dots than polarization entanglement and it also directly provides the most robust kind of entanglement.
Higher extraction efficiencies, which can be achieved with quantum dots in coupled pillar microcavities^{19}, would immediately improve the entanglement of our source in two ways: (1) one would be able to measure at lower excitation power for the same count rate, thus reducing the unwanted double excitations, and (2) the Purcell enhancement of the microcavity would improve the indistinguishability^{30} of the emitted photons and in turn the twophoton interference. In the long run, to achieve scalability of the source we will need to eliminate the double excitations that reduce the entanglement by identifying a metastable state^{24,25} that can serve as an initialization state. We expect that such an initialization state will also reduce the dephasing during the coherent excitation process and therefore allow us to reach levels of entanglement achievable by parametric downconversion (Supplementary Tables 2 and 3).
Methods
A measurement of the arrival time of a photon at the output of the analysing interferometer with respect to the excitation laser gives rise to the three peaks shown in Fig. 3a. Here, the first and the last peak carry the information on classical correlations (between 0› and 1›) and the middle peak shows quantum correlations. For example, +Y, 0› is a projection where the biexciton photon is projected onto the energy basis and the exciton is projected onto the time basis. The joined projections onto the time basis (0, 0›, 0, 1›, 1, 0›, 1, 1›) are obtained as coincidence events in respective combination of the time intervals measured between the outputs of the analysing interferometers for biexciton and exciton. Projections onto the energy bases (Y›, X›) are obtained from respective specific phase settings by extracting coincidence events in the time of arrival of the middle peak for the exciton and biexciton signals. Projections with energy and time bases combinations (0, +Y›, +Y, 0›, +Y, 1›, 1, +Y›, 0, +X›, +X, 0›, 1, +X›, +X, 1›) are collected from coincidence events in the interval of arrival of the respective middle and side peaks. In order to obtain the measurement errors we performed a 100run Monte Carlo simulation of the data with a Poissonian noise model applied to the measured values. The single count rate in the measurements was 4k counts for both exciton and biexciton, collected and detected in a singlemode fibre. The wavelength of the entangled photons is around 920 nm (Fig. 1b). The time resolution of the avalanche photo detector is 200 ps and the quantum efficiency is 20%. We estimate the rate of entangled photon pairs to be 0.6 counts s^{−1}.
Additional information
How to cite this article: Jayakumar, H. et al. Timebin entangled photons from a quantum dot. Nat. Commun. 5:4251 doi: 10.1038/ncomms5251 (2014).
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Acknowledgements
This work was funded by the European Research Council (project EnSeNa) and the Canadian Institute for Advanced Research through its Quantum Information Processing program. G.S.S. acknowledges partial support through the Physics Frontier Center at the Joint Quantum Institute (PFC@JQI).
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The quantum dot sample was fabricated by G.S.S. H.J., A.P., and G.W. conceived the experiments. H.J.and T.K. performed the experiments and A.P. and T.H. the data analysis. Density matrix reconstruction and entanglement tests were performed by A.P.. H.J, A.P, and G.W wrote the article with inputs from all the other coauthors.
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Supplementary Information
Supplementary Tables 13, Supplementary Note 1 and Supplementary References (PDF 109 kb)
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Jayakumar, H., Predojević, A., Kauten, T. et al. Timebin entangled photons from a quantum dot. Nat Commun 5, 4251 (2014). https://doi.org/10.1038/ncomms5251
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