Oscillating photonic Bell state from a semiconductor quantum dot for quantum key distribution

The development of bright, entangled photon sources is crucial for advancements in quantum key distribution (QKD), quantum repeaters, and quantum information processing. Spontaneous parametric down-conversion (SPDC) in nonlinear crystals is a leading method, but suffers from low pair extraction efficiency at high fidelity due to multiphoton emission. Semiconductor quantum dots (QDs) in photonic nanostructures offer a potential solution, but existing high-fidelity devices often have low extraction efficiency. This research addresses this challenge by focusing on InAsP quantum dots embedded in InP nanowires. A key challenge with using quantum dots is the exciton fine-structure splitting (FSS), which causes oscillations between Bell states, potentially reducing entanglement fidelity. Existing approaches to mitigate FSS involve external magnetic fields or low-jitter detection systems with time-gating, but these methods either limit practicality or discard useful photon pairs. This paper investigates a novel approach using time-resolved QKD to utilize photon pairs despite the presence of FSS. The goal is to demonstrate a bright, high-fidelity entangled photon source suitable for practical QKD applications, overcoming limitations of existing technologies.

Previous research has explored the use of III-V semiconductor quantum dots in photonic nanostructures as sources of entangled photon pairs. While deterministic polarization-entangled photon pair emission via the biexciton-exciton cascade has been demonstrated, challenges remain. Depolarization of exciton spin due to interactions with nuclear spins and free/trapped charges is a concern, particularly in indium-based QDs with larger nuclear spins. Exciton fine-structure splitting (FSS) causes oscillations between Bell states, impacting entanglement fidelity. Attempts to overcome FSS have involved external magnetic fields or time-gated coincidence detection, each with limitations. This work builds upon these efforts by exploring a time-resolved QKD approach to leverage the oscillating Bell states for key generation.

The study utilizes an InAsP quantum dot embedded in a site-selected tapered InP nanowire waveguide. Two-photon resonant excitation (TPRE) is employed to generate biexciton-exciton cascades, leading to entangled photon pair emission. Time-resolved quantum state tomography (QST) is performed using superconducting nanowire single-photon detectors (SNSPDs) and single-photon avalanche diodes (SPADs) to characterize the generated entangled states. The temporal evolution of the entangled state is analyzed, revealing oscillations between Bell states due to FSS. A Hanbury-Brown-Twiss experiment is conducted to quantify the multi-photon emission probability. The measured concurrence and fidelity are determined from the reconstructed density matrices. A time-resolved QKD protocol is implemented, and the key rate is estimated based on the experimentally obtained data. The methodology involves detailed characterization of the quantum dot source, precise control of the excitation pulses, high-resolution time-resolved measurements, and careful analysis of the quantum states generated. Specific details on the experimental setup, including the cryogenic micro-photoluminescence apparatus, optical components (beamsplitters, filters, waveplates), and detectors, are provided. The excitation pulses are precisely shaped to achieve optimal TPRE. The detection system's timing resolution is carefully considered to account for the effects of FSS.

The study achieves a peak entanglement fidelity of 97.5% ± 0.8% and a pair extraction efficiency of 0.65% from the InAsP quantum dot. The time-resolved QKD protocol successfully utilizes the oscillating Bell states to generate a secure key, demonstrating the viability of this approach. Two-photon resonant excitation significantly reduces the multi-photon emission probability compared to quasi-resonant excitation. A comparison between SNSPDs and SPADs highlights the impact of detector timing jitter on the measured concurrence, with SNSPDs showing significantly improved results. The experimental data is compared with a dephasing-free model to identify sources of discrepancy, including laser photon leakage, phonon interactions, AC Stark shift, and nanowire asymmetry. The time-resolved key rate is analyzed, showing that photon pairs emitted over a significant time window contribute to secure key generation. The lifetime-weighted key rate is calculated as 0.64 under experimental conditions.

The findings demonstrate that the low concurrence observed in previous studies using similar sources were not primarily due to spin dephasing, but rather to experimental limitations. By implementing TPRE and utilizing SNSPDs, this work demonstrates the feasibility of creating a bright, high-fidelity entangled photon source suitable for practical QKD. The time-resolved QKD protocol effectively addresses the challenge posed by FSS, eliminating the need to discard useful photon pairs. The results show that the challenges associated with FSS can be overcome using this approach. This work paves the way for developing large arrays of deterministically positioned NW-QDs for QKD networks and suggests that the stringent synchronization requirements for previous resource-QKD schemes might be relaxed.

This research successfully demonstrates a high-fidelity and efficient source of entangled photon pairs from an InAsP quantum dot in an InP nanowire, suitable for QKD. A novel time-resolved QKD protocol overcomes the limitations imposed by FSS, allowing for the utilization of all emitted photon pairs. The achieved performance significantly advances the state-of-the-art in semiconductor-based entangled photon sources. Future work could focus on improving pair extraction efficiency by addressing luminescence blinking and optimizing TPRE, as well as exploring the scalability of this approach for larger QKD networks.

The study acknowledges the presence of luminescence blinking, impacting the overall efficiency. The dephasing-free model used for comparison does not fully capture all aspects of the experimental system, leading to small discrepancies between the model and the experimental results. The analysis assumes a perfect channel for the QKD protocol, which would be affected by channel loss and error in a real-world scenario. Future improvements in the nanowire growth and fabrication could further enhance the performance of this source.