1GHz clocked distribution of electrically generated entangled photon pairs

Quantum networks are essential for realising distributed quantum computation and quantum communication. Entangled photons are a key resource, with applications such as quantum key distribution, quantum relays, and quantum repeaters. All components integrated in a quantum network must be synchronised and therefore comply with a certain clock frequency. In quantum key distribution, the most mature technology, clock rates have reached and exceeded 1GHz. Here we show the first electrically pulsed sub-Poissonian entangled photon source compatible with existing fiber networks operating at this clock rate. The entangled LED is based on InAs/InP quantum dots emitting in the main telecom window, with a multi-photon probability of less than 10% per emission cycle and a maximum entanglement fidelity of 89%. We use this device to demonstrate GHz clocked distribution of entangled qubits over an installed fiber network between two points 4.6km apart.


INTRODUCTION
For implementation of various kinds of advanced quantum network schemes [1][2][3][4], entanglement must be distributed between nodes [5][6][7][8]. The most widely used sources are currently based on spontaneous non-linear processes [9,10], though the efficiency of these sources is intrinsically limited if multi-photon emission is to be minimised. This limit does not apply to entangled photon sources with sub-Poissonian statistics, such as semiconductor quantum dots (QD)s [11,12], with the prospect of deterministic entangled pair generation [13].
For an entangled photon source to be embedded in a quantum network, it must further conform to the basic requirements of operating clock rate and wavelength. State-of-the art quantum key distribution (QKD) systems operate at clock frequencies of 1GHz and above [14,15], with photons in the telecom C-band most suitable for distribution over standard optical fibers.
Epitaxially grown semiconductor QDs can be readily incorporated into PIN diode structures, enabling the fabrication of light sources using standard semiconductor processing techniques [11,16]. As QDs embedded within diodes can be electrically excited [17], it is possible to create entangled photon sources that can be conveniently operated similar to other standard light sources, such as telecom laser diodes. InAs/InP QDs emit in the lowest-loss silica fiber window [18], which makes them prime candidates for transmission over standard fiber networks.
Entangled LED (ELED) telecom C-band sources have been demonstrated with DC excitation [19]. Pulsed single [16,20,21] and entangled [11,17,[22][23][24][25] photon sources based on semiconductor QDs have been developed but are either at short wavelengths, and therefore incompatible with existing fiber networks, or only operate at repetition rates too slow for current quantum network applications. Entanglement distribution experiments over installed networks have used low repetition rates [6][7][8] while GHz clock rates, necessary for synchronisation with high clock rate QKD systems, have only been demonstrated with non-2 linear sources over long fiber in a laboratory [26,27]. In this work, we show the distribution of entangled qubits from a 1GHz driven sub-Poissonian source over an installed standard telecom network.

GHZ CLOCKED SINGLE PHOTON SOURCE
The fabrication of ELED devices used in this work was developed to be simple, with only two etch steps and two metal depositions. An image of a device is shown in Fig.1(a). This design allows for fast electrical operation at GHz frequencies, with dimensions close to the limit imposed by the size of a bond ball as can be seen in Fig. 1(a). The ELED shows good electrical performance as a diode, with the resistance reaching 50Ω beyond the turn-on voltage. The wafer structure, described in the Supplemental Material, is designed for QD emission in the telecom C-band. The emission spectrum shown in Fig.1(b) comes from a QD that is located within a 5µm connected pillar, as can be seen in Fig.1(a), and so can be readily relocated. The device was mounted onto the centre of a radio-frequency compatible FR4 packaging with conductive paint before wire bonding to a Au layer on one end of 50Ω impedance matched tracks, ending with a low-profile micro-coaxial connector as illustrated in the inset of Fig.1(b).
In QDs, single photons are emitted via the radiative recombination of confined electronhole (e-h) pairs [28]. Entangled photon pairs are emitted via the biexciton cascade [11] where a QD initialised in the doubly excited biexciton (XX) state decays to the singly excited exciton (X) state via emission of the first photon. This state subsequently decays via emission of a second photon, leaving the QD in the ground state. Due to conservation of angular momentum, the two emitted photons are maximally entangled in their polarization.
To assess the sub-Poissonian photon emission from the ELED, we measure the second order autocorrelation function (g (2) ) of X photons as shown in Fig.2(a). This measurement requires isolation of the X spectral line as in Fig.1(b). Since the QD emits at telecom wavelengths, a compact spectral wavelength filtering unit can be used that is based on an optical add-drop multiplexer as shown in Fig.2 Fig.2(c) are also suppressed in a grid pattern with spacing of 1ns. This pattern occurs due to the electrical excitation pulse at the start of each 1ns cycle, when the QD is reinitialised. During this reinitialisation period, the population in the X level is depleted due to excitation to higher energy levels such as the XX. The 1ns squares containing coincidences of photons emitted in different excitation cycles appear to have an almost flat distribution. This is due to the long natural lifetime of the X state of 1.9ns and the dynamics involved in populating the X state via decay from the XX state, which has a lifetime of 0.5ns.

Coincidences in
Photon coincidences in each 1ns square were then normalised using coincidences in cycles with completely uncorrelated detection events. Fig.2(d) shows that the g (2) for X photons emitted in the same 1ns cycle is 0.097±0.002 without application of any temporal postselection. This is far below the classical limit, proving strongly sub-Poissonian emission. The g (2) (0) is limited by the non-resonant excitation scheme used here, likely due to interactions with the charge environment.

GHZ CLOCKED ENTANGLEMENT
As entangled photons are critical for quantum network applications, we now show the generation of 1GHz clocked entangled photon pairs from our ELED. The device was driven similarly to before, using pulses with a high of 1.5V and a low of 0.5V. The XX and X photons were separated with a spectral filter and each were detected with a polarization analyser comprising of an electronic polarisation controller (EPC) and a polarising beam splitter (PBS) followed by superconducting nanowire single photon detectors (SNSPD)s as in Fig.3(a). When detecting photons in a polarization basis PQ, P polarized XX photons were measured at detector 1 in Fig.3 The resulting fidelity to the maximally entangled Bell φ + state, calculated as explained in the Supplemental Material, is shown in Fig.3(c). For most of the grid in Fig.3(c), the entanglement fidelity is ∼0.25, corresponding to completely random polarization correlations.
For XX and X photons from the same 1ns cycle, the entanglement fidelity rises above the classical limit of 0.5 for X photons arriving after XX photons, before decaying with oscillations due to the fine structure splitting of the QD of 6.0µeV [29]. Each vertical column of time bins in Fig.3(c) contains photon coincidences with the same relative XX-X time delay, but different arrival times within the 1ns emission cycles. One can see that the entanglement fidelity drops for time bins at the start and end of the 1ns cycles due to reinitialisation of the emission (∼130ps). Therefore, to give an idea of the highest 7 possible value, XX and X photon arrival times were additionally gated to 0.864ns around the center of 1ns cycles (shown as a white dashed box in Fig.3(c)). The average of each column is plotted in Fig.3(d), where one can again observe the time dependent oscillation of the fidelity due to the finite fine structure splitting of the QD. The resulting maximum fidelity to the Bell φ + state is 0.89±0.02 with comparable correlation contrasts in the three principal polarisation bases (see the Supplemental Material for further information). However, this value corresponds to a bin size of 72ps, which is not compatible with post-selection free detection schemes.
Detectors used in state-of-the-art QKD systems operating at 1GHz clock rates have typical detection gate widths of <170ps [14,30]. To assess the performance of the pulsed ELED with these non-research grade detectors, we position a single 168ps integration window to give maximum entanglement fidelity, shown as a black dashed box in Fig.3(c). This results in a fidelity of 0.86±0.03, in the regime compatible with error correction in quantum key distribution applications [31]. The drop in fidelity when increasing the time window size is within the errors, showing that the QD FSS is not limiting the fidelity achievable with typical gated detectors. Analysing the X autocorrelation data from Fig.2 in a similar fashion gives a g (2) of 0.04±0.01. However, only 3.4% of the detected photon pairs originating from the same excitation cycle arrive within this 168ps time window. For future compatibility of deterministic GHz clocked entangled photon pair sources with gated detectors for post-selection-free operation, high source efficiencies are crucial. In addition, XX and X lifetimes similar to the detector gate width are necessary to increase the number of photon pairs arriving within the active gate window of the detectors. This could be achieved via Purcell enhancement, which reduces XX and X lifetimes, for example with micropillar designs [32] or circular bragg gratings [13,33].
Given the GHz clock rate, an overall efficiency of the optical system including detectors of approximately 0.6% (see the Supplemental Material), and average XX and X photon rates at each detector of 52000 and 83000 counts per second, we estimate an intrinsic efficiency of around 2% for the ELED to generate a photon per excitation pulse. Efficiencies are currently low for non-resonantly excited telecommunication wavelength QDs, which are still undergoing significant development and are not as well established as short-wavelength InAs/GaAs dots. Telecommunication wavelength QDs are larger than their short-wavelength counterparts, making them more susceptible to fluctuations in the surrounding charge environment. This typically results in the presence of multiple charged states with radiative and non-radiative decay paths. Techniques to enhance emission from the neutral XX and X states rather than charged complexes may increase the photon pair efficiency for ELEDs in the future [34]. Perhaps counter-intuitively, truncating the cascade by reinitialising the QD at a high clock rate does not intrinsically limit the photon generation rates; we have recently shown that photon generation rates can surpass those achievable with DC driving for some pulsed regimes [25].

ENTANGLEMENT DISTRIBUTION
To demonstrate network compatibility of the pulsed entangled photon pair source we distributed entanglement over 4.6km between the Toshiba Cambridge Research Laboratory (CRL) and the Physics Department of the University of Cambridge as shown in Fig.4, using installed network fiber. The source was operated at CRL where X photons were detected, and XX photons were sent to a deployed detection system over 15km of installed fiber with 6dB loss at 1550nm.
The electrical 1GHz clock signal used to drive the ELED was down-sampled to 15.6MHz and converted to an optical signal at 1570nm and multiplexed with 1Gbit/s classical communication data traffic at 1310nm. The communication channel was required for remote control of the detection system and data acquisition, both classical signals were transmitted over a separate installed fiber. At the other end, both classical signals were demultiplexed, and the clock signal was converted back to an electrical signal to be used as the synchronisation reference in the deployed detection system.
In both locations, photon arrival times in two detector channels were recorded with respect to the reference clock with TCSPCs similar to the previously discussed measurements in a laboratory. Photon arrival times were measured in the three principal detection bases in sets of 7 minutes. Polarization drifts occurring over the network fiber due to changing environmental conditions were compensated for before each measurement using a similar stabilisation system as in [35]. Photon correlations were evaluated in postprocessing.
Entangled photon pairs were distributed between East and West Cambridge for 14 consecutive hours of operation. Fig.5 (a) and (b) shows results plotted in a similar way to Fig.3  but for distribution of entanglement rather than a measurement in a laboratory. The maximum fidelity to the Bell φ + state, analysed on a 72ps grid with the reinitialisation period discarded as for the laboratory measurement, is 0.79±0.01. Using the timing characteristics of GHz clocked detectors as indicated in Fig.5(a), the maximum entanglement fidelity is 0.76±0.01.
The 10% reduction in the fidelity when transmitting XX photons over the installed fiber is attributed to an increased ratio of background events to XX photon signal at the deployed detectors from <2% to >10%. We further observe a larger drop in polarization correlation contrast for measured superposition bases (diagonal/antidiagonal and right-/left-hand circular, see the Supplemental Material). This most likely results from a larger uncertainty in calibrating the detection bases at the deployed detection system (see the Supplemental Material) which is again caused by a drop in the signal-to-background ratio rather than the performance of the ELED itself. Fig.5(c) shows the evolution of the maximum entanglement fidelity for sets of 2 hours of data. It remains around 0.79 for the entire 14 hour experiment, demonstrating the excellent stability of the 1GHz clocked ELED as a source for distributed entangled photon pairs across a real-world fiber network. CONCLUSION We have shown an electrically driven 1GHz clocked telecom ELED with strong single photon characteristic, resulting in a two-photon probability of less than 10% without any temporal post-selection. Using the ELED as a source of 1GHz clocked entangled photons yields a maximum entanglement fidelity of 89% in a 72ps post selection window. In addition, the device is suitable for operation using standard actively gated GHz clocked detector modules as are used in current QKD systems, with no additional software-based post-selection.
However, for real-world applications in quantum communication relying on high entangled photon pair rates, an enhancement of the source brightness is required and the number of photons arriving within the active gate window of such detectors must be significantly increased via the reduction of XX and X lifetimes.

FABRICATION
The device in Fig.1(a) was fabricated in 4 steps. To contact the p-layer, CrAu was thermally evaporated onto the wafer surface. The p-type contact was just large enough to fit a bond ball, 80x110µm. The mesa and the isolated area were each etched using inductively coupled plasma (ICP) with Cl 2 based process chemistry. 150nm of AuGeNi was evaporated onto the isolated area to contact the n-layer before annealing at 420 • C.

CHARACTERISATION
The device was cooled to 30K in a He vapour cryostat, with an xyz piezo nano-positioning stage enabling navigation around the device. A fibre-based confocal microscope system with NA 0.68 collected light emitted from the device. QD electroluminescence (EL) spectra were measured by sending this light via a fiber to a spectrometer with an InGaAs array.
The fine structure splitting of a QD was measured as in [18], by polarization dependent spectroscopy using a quarter wave plate and linear polarizer in front of the spectrometer.
This measurement identified XX and X lines, such as for the QD with the EL spectrum in Fig.1(b) which had a fine structure splitting of (6.0±0.3)µeV.

MEASUREMENT OF ENTANGLEMENT FIDELITY
XX and X photons emitted via the biexciton cascade are co-polarized in the horizontal/vertical basis due to conservation of angular momentum [11]. The degree of correlation in a polarization basis PQ is calculated from co-polarized, c P P , and cross-polarized, c P Q , photon correlations by The entanglement fidelity to the maximally entangled Bell φ + state is obtained [37] from measurements in the horizontal/vertical (HV), diagonal/antidiagonal (DA), and right-and left-hand circularly polarized (RL) detection bases.
Correlations in these three principal detection bases are shown for the measurement in the laboratory in Fig.S1 and for the entanglement distribution measurement in Fig.S2. In the superposition bases, DA and RL, there is an oscillation due to the 6.0µeV fine structure splitting of the QD.
The degrees of correlation in the HV, DA, and RL bases, analysed on a 72ps grid with the reinitialisation period discarded as shown in Fig.3(d) and Fig.5 In contrast to the laboratory measurement, photon coincidences for equivalent polarisation sets were combined for better statistics, such as HH and VV for (a), as all 4 polarizing beam splitter outputs were detected rather than just 3.
A free-space spectral filter was used to separate XX and X photons in the entanglement measurements in Fig.3, Fig.4, and Fig.5, followed by electronic polarization controllers and polarizing beam splitters (PBS)s before the detectors.

PHOTON-PAIR COINCIDENCE RATES
An acquisition time of 56.25 minutes was used for the measurement of entanglement in a laboratory shown in Fig.3. To show the time dependence of photon-pair emission, co-and cross-polarized photon-pair coincidences in the 3 principal detection bases were summed. Fig.S3 shows this sum with the same time bins as in Fig.3(b). Although the X lifetime is longer than 1ns, it can be seen that the cascade decays to the uncorrelated level within 1 excitation cycle due to the reinitialisation provided by electrical driving [25]. 52818 photon-pairs coincidences with both photons originating from the same excitation cycle were measured. However, only one output of the PBS for XX photons in Fig.3(a) was used for this measurement; if both outputs were used the number of coincidences would be doubled.
The overall efficiency of the optical system is approximated to be 0.6% (22.45dB loss).
The loss for coupling photons emitted by the QD into single mode fiber was 15.2dB. The 18 free space grating setup had a loss of 2.6dB. Typical EPC and PBS losses were 0.8dB and 0.4dB respectively. Equivalent photon loss due to finite detection efficiency of SNSPDS around 50% was 3dB. The experimental setup had 3 fiber-to-fiber connections for XX and X photons, with losses of 0.15dB per connection.

ENTANGLEMENT DISTRIBUTION PHOTON DETECTION
At CRL, the overall timing jitter for detection was 70ps including the superconducting nanowire single photon detectors (SNSPD)s (Single Quantum). In the deployed system, the overall timing jitter for detection was around 75ps including the avalanche photodiodes (APD)s. The combined X photon rate at the SNSPDs, detectors 1 and 2 in Fig.4, was around 228 000 counts per second and the combined XX photon rate at the APDs, detectors 3 and 4 in Fig.4, was around 15 000 counts per second.
To calibrate the detection basis, the QD emission was replaced by a polarization reference matched to the eigenbasis of emitted photon pairs (not shown in Fig.4). EPC voltages were then varied to minimise the output signal from one output mode of the PBS at a detector, aligning the detection basis to the reference.