Quantum key distribution using quantum dot single-photon emitting diodes in the red and near infrared spectral range

In 1984 Bennett and Brassard proposed a key distribution protocol (BB84) that uses the quantum mechanical properties of single-photons to detect eavesdropping attempts [1]. Due to the lack of efficient single-photon sources, almost all quantum key distribution (QKD) experiments, however, have been performed with strongly attenuated lasers [2–4]. For such sources various attacks, e.g. number splitting or beam splitting attacks, become possible. Using decoy methods [5], these attacks can be averted but significant shrinking of the sifted key is required. Provided a single-photon source (SPS) with very high efficiency, i.e. with an average number of photons per pulse 〈n〉_SPS comparable to average intensities typically used for decoy protocols (e.g. 〈n〉_dec = 0.4), the reduced protocol overhead gives a clear benefit. Moreover, in the case of a limited number of counts, as expected for future satellite links or other mobile systems, statistical effects arising from the finite key size are far less severe for systems using SPSs [6]. Currently, the maximal detection rates of commercially available single-photon detectors are limited to MHz, while the repetition rates of modern QKD systems steadily increase to the GHz range [7–9]. Therefore high-transmission QKD systems can easily be limited by the receiver. In this case using a SPS even with moderate efficiency will increase the secret key rate. To date, QKD experiments using optically pumped SPSs have been demonstrated with single-nitrogen-vacancy color centers in a diamond nanocrystal (NV-centers) in free space [10, 11] as well as with quantum dots (QDs) in free space [12, 13] or optical fibers [14–16]. These experiments affirmed their great potential for QKD. However, they have of course suffered from drawbacks of the rather inefficient and impractical optical excitation scheme.

In this paper, we report on proof of concept QKD experiments using two different electrically driven QD SPSs emitting in the near-infrared and red spectral range based on InAs and InP QDs, respectively. The infrared emitting devices generate sifted key rates of 27.2 kbit s⁻¹ (35.4 kbit s⁻¹) at a quantum bit error rate (QBER) of 3.9% (3.8%) and a g⁽²⁾(0) value of 0.35 (0.49) at moderate (high) excitation. In the case of the red emitting diodes we achieve sifted keys at a rate of 95.0 kbit s⁻¹, a QBER of 4.1% and a g⁽²⁾(0) value of 0.49.

Whereas wavelengths in the 1.3 and 1.55 μm telecommunication windows are often used for long-distance fiber-based transmission, the shorter wavelengths of our sources have the advantage of being well suited for free space communication. This is due to the fact that Earth's atmosphere has a high-transmission window around 770 nm and thus naturally provides a low-loss communication channel, which is only weakly dispersive and non-birefringent [17]. In addition, the shorter wavelengths utilized in this experiment permit the application of silicon avalanche photo diodes (Si APDs) as detectors with the InP QDs' emission (approx. 650 nm) almost perfectly matching the maximum detection efficiency at about 700 nm. Si APDs also have advantages in terms of higher efficiencies, lower dark count rates and lower afterpulsing probabilities compared to telecom-wavelength InGaAs APDs and easier handling with respect to superconducting single-photon detectors. Particularly large photon extraction efficiencies are achieved for the InAs-based SPSs by exploiting the Purcell effect in a highly optimized micropillar cavity design. Therefore the lower detection efficiency of photons compared to the InP QDs can partly be compensated for. Although both QD SPSs were used in a free space approach in this work, it is worth mentioning that the InAs QD emission (approx. 900 nm) would also allow for short-distance communication in standard telecom fiber as proposed by P D Townsend [18], a fact highlighting the flexibility of QD-based SPSs for quantum cryptography applications. Both device approaches have recently proven their potential, acting as efficient SPSs under pulsed electrical current injection featuring high single-photon emission rates and strong suppression of multiphoton emission events [19, 20] and thus provide an excellent technology platform for the implementation of QKD experiments.

QD SPSs suitable for the QKD experiments were identified using micro-electroluminescence (μEL) together with photon autocorrelation measurements at cryogenic temperatures. In the case of SPSs based on InAs QDs, described in this section, a temperature control assembly additionally allowed for resonance tuning of the single QD emission with respect to the fundamental cavity mode of the micropillar. The samples were excited by electrical pulse generators providing pulses with widths down to 100 ps (full-width at half-maximum (FWHM)) and repetition rates of up to 3.35 GHz. In addition, a DC-offset could be applied to the samples. The μEL from InAs/InP QDs was collected by a ×20/ × 50 microscope objective with a numerical aperture of 0.40/0.45 and spectrally analyzed by a grating monochromator with an attached liquid nitrogen/Peltier cooled Si charge-coupled device (CCD) camera enabling a spectral resolution of about 35 μeV/200 μeV, respectively. Single-photon emission was probed using a Hanbury Brown and Twiss (HBT) setup, which was placed behind the exit slit of the monochromator. The HBT was equipped with single-photon counting modules based on Si APDs with a temporal resolution of approximately 700 /500 ps in the case of InAs/InP QDs. g⁽²⁾(0) values in this work were evaluated by directly integrating the measured coincidences of the zero delay peak over one full pulse duration and dividing this sum by the mean value of the remaining peaks. We did not apply any corrections, such as background subtraction, to the measured data. In this way, we are giving an upper limit for the two-photon emission probability within the quantum channel.

2.1. InAs QD SPSs

The electrically driven SPS emitting in the near-infrared spectral range (see the inset of figure 1(a)) utilized in the QKD system was based on a doped planar microcavity structure grown by molecular beam epitaxy on an n-doped GaAs substrate. The microcavity consists of a 1λ thick undoped GaAs cavity embedded between a lower n-doped distributed Bragg reflector (DBR) and an upper p-doped DBR composed of λ/4 thick AlAs/GaAs mirror layers. Three-dimensional finite-difference time-domain modeling was performed in order to determine the optimum number of 13/26 mirror pairs in the upper/lower DBR for high extraction efficiency and highly directional emission away from the sample surface [19]. In the vicinity of the low-density InAs QD layer, located at the center of the GaAs cavity, an n-type (δ-doped) layer was introduced to eliminate dark-state configurations that are known to reduce the efficiency of SPSs based on neutral QDs [21]. Thus, electron–hole pair capture owing to electrical excitation predominantly created charged excitons in a singlet configuration, leading to fast recombination of the optically bright excitonic state. For details of the fabrication of electrically contacted micropillars, see [22].

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Figure 1(a) displays μEL spectra of a micropillar with a diameter of d_C = 2.0 μm operated at a repetition rate of 199 MHz. The device was biased with a dc voltage V_DC of 1.450 V, just below the onset of EL. In addition, pulses with an amplitude V_AC of 5.25 V were applied. At 30 K, a dominant single QD exciton line as well as the fundamental cavity mode C with a Q-factor of about 2100 can be identified. By decreasing the temperature to 17 K, the X⁻-line was tuned into resonance with the cavity mode, which resulted in an enhancement of the emission due to the Purcell effect. On resonance, a maximum detection rate of 1.26 × 10⁵ Hz was obtained. As can already be seen from this on-resonance spectrum, this device features a very clean emission spectrum with low background contributions from the fundamental and higher order cavity modes, which are typically fed non-resonantly by spectator QDs in high Q-factor microcavities [23–25]. The photon autocorrelation measurement shown in figure 2(b) confirms the purity of single-photon emission with g⁽²⁾(0) = 0.09, i.e. with a very low probability of multiphoton emission events, under pulsed electrical operation. It is also worth mentioning that the change in overall performance of this device was below 20% in terms of signal intensity over a period of a few months (including many cool-down and warm-up cycles), which highlights the durability of these devices.

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2.2. InP QD SPSs

The experimental setup of the QKD system is shown in figure 3. As the core of the transmitter module (Alice), the respective SPS presented in the previous section was mounted on the cold finger of a liquid He flow-type cryostat and excited by an electrical pulse generator (cf section 2). The QD emission was collected by a microscope objective, spectrally filtered by an interference bandpass filter, and coupled into a single-mode optical fiber (780HP/SM600 for InAs/InP-QDs). The use of narrow interference bandpass filters (FWHM of 0.25 /1 nm for InAs/InP-QDs) instead of a monochromator significantly simplifies the setup. Single-photon emission was probed using a fiber-coupled HBT setup with Si APDs acting as detectors. Additionally, the SPS emission could be monitored by a monochromator with an attached CCD.

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For the actual QKD experiment the fiber-coupled SPS signal was polarized and the four polarization states for the BB84 protocol were set by a fast electro-optic modulator (EOM) (here we used horizontal and vertical linear polarizations together with right and left circular polarizations). In this proof of concept experiment, we were only interested in the key parameters of our system, i.e. sifted key rate and error rate. Therefore the EOM was controlled by a waveform generator with a fixed, repeating pattern of the four polarization states. After the EOM photons left the transmitter and propagated through a short free space link to the receiver module (Bob). Two quarter wave plates were used to rotate the circular polarizations to ±45° linear polarizations and align the horizontal and vertical axes of the transmitter and the receiver. The photons then entered the polarization analyzer where the measurement basis was chosen randomly using a beam splitter. The photons were detected by four Si APDs connected to the data acquisition electronics. The whole setup was synchronized using the pulse generator's trigger output as a global clock. The detection events were transferred to a computer performing time filtering and key sifting. The maximum repetition rate f_max of the system is limited to 200 MHz by the EOMs bandwidth, but the achievable detection rate is limited to 4 MHz by the commercial APD modules. Thus, for any system for which the product f_max × 〈n〉_SPS × τ × η, where τ is the transmission of the link and η is the efficiency of the detectors, exceeds this maximum rate, SPSs have a clear advantage.

The first QKD experiment used the near-infrared emitting InAs-based SPS (λ ≈ 897 nm) described in section 2.1. Figure 4(a) shows the on-resonance μEL spectrum (T = 20 K) recorded with the spectrometer (repetition rate f = 182.6 MHz).

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For optimum performance regarding emission intensity and signal-to-background ratio, the excitation parameters V_DC = 1.400 V and V_AC = 6.0 V were chosen. In order to measure the purity of single-photon emission inside the quantum channel, the bandpass filtered μEL signal of figure 4(a) was directly coupled to the HBT setup. The resulting photon autocorrelation function is depicted in figure 4(b), revealing a g⁽²⁾(0) value of 0.35 < 0.5 as a clear signature of single-photon emission. The fact that we observed higher values of g⁽²⁾(0) compared to measurements with a monochromator is mainly due to the finite bandwidth of the interference filter, which causes increased contributions of uncorrelated background emission.

In order to perform the QKD experiment, the bandpass filtered single-photon emission was coupled into a single mode fiber connected to the transmitter module described in section 3. The excitation conditions remained unchanged except for the dc-offset V_DC which served as control parameter for the single-photon emission rate (as reported in [19]). Figure 5 summarizes the recorded sifted key rates, QBER and g⁽²⁾(0) values.

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For a low excitation at V_DC = 1.350 V we measured a sifted key rate of 8.6 kbit s⁻¹ at g⁽²⁾(0) = 0.30. The sifted key rate increased up to 27.2 kbit s⁻¹ at V_DC = 1.400 V and a slightly higher g⁽²⁾(0) value of 0.35 (cf figure 4(a)). Further increasing V_DC, the sifted key rate finally saturated due to QD saturation accompanied by a noticeable rise in the g⁽²⁾(0) value. The latter can be explained by increasing contributions of uncorrelated background emission from the cavity mode. Figure 5(b) affirms that the sifted key rates were recorded at a low level of the QBERs. In fact, the QBER drops from 5.3% at low excitation to values of roughly 4% owing to the increasing signal to background ratio, which was already close to the contrast limit of the EOM (≈3%). Increasing the excitation, even higher sifted key rates of up to 35.4 kbit s⁻¹ at g⁽²⁾(0) = 0.49 could be obtained at the cost of higher g⁽²⁾(0) values—a trend that is illustrated in figure 5(c). The corresponding QBERs were in the range of 3.8–6.7%.

The second QKD experiment was performed using the InP-based resonant cavity light-emitting diode emitting at about 650 nm. Along the lines of section 2.2 a fixed bias of 2.12 V was applied to the device just below the onset of EL and additional pulses of 250 ps pulse width and amplitudes from 2.71 up to 3.86 V accomplished the carrier injection into the active region. In order to achieve higher emission rates, the repetition rate was raised to 200 MHz, only restricted by the maximum EOM frequency. The μEL spectrum for 3.71 V pulse amplitude is shown in figure 4(c) where the red arrows display spectral filtering, and figure 4(d) shows the corresponding photon autocorrelation measurement indicating the suppression of multiphoton emission via the g⁽²⁾(0) value of 0.49.

The sifted key rates, g⁽²⁾(0) values and QBERs of the pulse amplitude series are displayed in figures 6(a) and (b). Due to the increased injection of charge carriers into the QD the sifted key rate increased from 9.2 kbit s⁻¹ up to 117 kbit s⁻¹. As an undesirable effect the background emission also increased and consequently downgraded the single-photon emission quality observable via an increase of the g⁽²⁾(0) value. The QBER dropped from 6% down to nearly 4% comparable to the results discussed above. The highest sifted rate with g⁽²⁾(0) < 0.5 was 95.0 kbit s⁻¹, achieved at an excitation pulse amplitude of 3.71 V (cf the dashed red line in figure 6(a)).

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In our experiment the detection rates of about 200 kHz are below the maximum detection rates of 4 MHz by about a factor of 20. However, improvements of the coupling of photons into single mode fibers and particularly the development of cavities containing only a single QD should make the required increase feasible, likely enabling SPS systems to outperform attenuated pulse systems. In particular, lower g⁽²⁾(0) values will lead to higher achievable communication distances (or channel losses) as outlined in [27].

For the first time, the utilization of electrically driven QD SPSs emitting in the red as well as infrared spectral range for QKD was evaluated. The main results are summarized in table 1.

Emulating a BB84 protocol we achieve a sifted key rate of 27.2 kbit s⁻¹ (35.4 kbit s⁻¹) at a QBER of 3.9% (3.8%) and a g⁽²⁾(0) value of 0.35 (0.49) with the infrared emitting device (λ ≈ 897 nm) at moderate (high) excitation. With the red emitting diode (λ ≈ 653 nm) sifted keys could be generated at a rate of 95.0 kbit s⁻¹ with a QBER of 4.1% and a g⁽²⁾(0) value of 0.49. The fact that we achieve higher sifted key rates with the InP-based SPS is mainly due to the higher detection efficiency of the Si APDs in the red spectral range. The second trend, that we observe at general lower g⁽²⁾(0) values for the InAs QD SPS results from a stronger suppression of uncorrelated background contributions in this device if compared to InP-based SPS (cf figure 4). This is especially evident for the low excitation regime where we observe g⁽²⁾(0) values as low as 0.28 for the infrared emitting device. Therefore, by following the InAs as well as InP material approach we cover the benefits of both systems in this work, which highlights the flexibility of QD-based SPSs for quantum cryptography applications. We believe that this successful QKD proof of concept of two different electrically operated semiconductor SPSs can be considered to be a major step toward practical and efficient QKD scenarios. With new technological developments like positioned single QDs inside the micropillar resonator [28, 29] and more efficient output coupling, we expect key rates outperforming attenuated pulse QKD systems.

This work was financially supported by the German Ministry of Education and Research through the projects QPENS and EPHQUAM. Expert sample preparation by M Emmerling and A Wolf is gratefully acknowledged.