The development of a large-scale quantum internet is a crucial step towards achieving quantum advantage. Current quantum networks distribute entanglement over significant distances but face the challenge of mitigating signal loss during transmission. Entanglement swapping, facilitated by quantum repeaters (QRs), offers a solution. Quantum memories (QMs) are essential components of QRs, temporarily storing qubits to coordinate their arrival at Bell-state measurement (BSM) stations, improving entanglement swapping success probability. Room-temperature atomic ensembles are a promising platform for scalable photonic quantum repeaters. There are two main types of QR implementations. Type I relies on the DLCZ protocol, generating entanglement with inherently low rates. Type II generates entanglement independently, storing photons in multiple QMs before heralded entanglement swapping via BSM. Type II repeaters, by interfacing fast entanglement sources and fast quantum memories, can achieve rates orders of magnitude higher than Type I. For successful entanglement swapping, retrieved qubits must maintain their quantum states and be indistinguishable. HOM interference measurement provides a method to verify this indistinguishability. This work demonstrates HOM interference between few-photon-level polarization states and single-photon-level pulses stored and retrieved from independent Type II absorptive QMs, a key step towards demonstrating Type II memory-assisted entanglement swapping. The experiments investigate phase stability, single-photon-level performance, and the effect of background noise on HOM visibility, using both dual-rail and single-rail memory configurations. A model is presented to quantify the effect of background noise on visibility. The aim is to establish the viability of room-temperature QMs for memory-assisted quantum operations.

The paper reviews existing quantum repeater network implementations, highlighting the advantages and limitations of Type I (DLCZ protocol) and Type II repeaters. It emphasizes the importance of room-temperature atomic ensembles as a scalable platform for photonic quantum repeaters and cites recent advancements in integrating high-duty-cycle room-temperature atomic quantum memories with fast entanglement sources. The authors discuss the significance of Hong-Ou-Mandel (HOM) interference as a method for verifying the indistinguishability of qubits retrieved from quantum memories in the context of entanglement swapping, particularly for Type II repeaters. Previous work focusing on Type I repeaters is acknowledged, and the need for experimental demonstration of HOM interference between pulses retrieved from Type II absorptive quantum memory systems is highlighted as a crucial step towards practical entanglement swapping.

The experiments utilize two generations of quantum memories (Gen I and Gen II) based on electromagnetically induced transparency (EIT) in warm ⁸⁷Rb vapor. Gen I memories employ a dual-rail configuration for polarization state storage, while Gen II memories are optimized for noise reduction. The experimental setup involves two independent sources (Alice and Bob) generating polarization states, which are then stored and retrieved from the quantum memories. The retrieved pulses are made to interfere at a 50:50 beamsplitter, and coincidence counts are measured to determine HOM visibility. Three sets of experiments are performed: 1. HOM interference with few-photon-level polarization states (Gen I, dual-rail): Investigates phase stability and memory compatibility by storing diagonal polarization states. 2. HOM interference at single-photon-level (Gen I, single-rail): Investigates single-photon level operation and the effect of noise on visibility. 3. HOM interference at single-photon-level (Gen II, single-rail): Employs noise reduction techniques to improve signal-to-background ratio (SBR) and assesses the relationship between HOM visibility and SBR. Various parameters are varied, including pulse width, storage time, and region of interest (ROI) for coincidence counting, enabling the estimation of SBR. The experimental setup is calibrated by measuring HOM interference without memories to establish a baseline visibility. A model is developed to quantify the effect of background noise on HOM visibility, considering signal-background and background-background coincidences. The model uses the equation V = Vo(1 - R + R²)⁻¹, where V is the measured visibility, Vo is the visibility with no background, and R is the signal-to-background ratio.

The key findings are: 1. In the dual-rail configuration with few-photon-level inputs, storage and retrieval of diagonal polarization states do not significantly affect HOM visibility (41.9% with memories vs. 42.1% without). This indicates good phase stability and memory compatibility. 2. At single-photon-level with Gen I memories (single-rail configuration), a reduced HOM visibility (25.9%) is observed due to lower SBR (2.6). The background noise itself does not exhibit HOM interference. 3. With Gen II memories (single-rail), noise reduction techniques improve SBR (1.7-11.9) and HOM visibility (up to 42.9%). The experimental results validate the model relating HOM visibility and SBR, indicating a maximum achievable visibility of 45.5%. Analysis suggests a predicted 33% visibility for polarization qubits in a dual-rail configuration using Gen II memories. The paper also presents data showing the relationship between HOM visibility and SBR. Different ROIs were used to vary the SBR, showing that higher SBR leads to higher HOM visibility. In the high-SBR limit the visibility approaches the limit obtained without the memories.

The results demonstrate the feasibility of using room-temperature atomic vapor quantum memories for memory-assisted operations requiring high indistinguishability, such as entanglement swapping for continuous variable qubits and polarization qubits, quantum gates, memory-assisted Bell-state measurements, and memory-assisted measurement-device-independent quantum-key-distribution (MA-MDI-QKD). The high SBR achieved at single-photon levels is crucial for these applications. The paper discusses the limitations on HOM visibility due to background noise and the potential for improvement through further background reduction techniques such as cavity mode selection, optical pumping, and active manipulation of the EIT Hamiltonian. The authors also discuss using shorter signal pulses to increase the SBR. The successful demonstration of interoperability between four room-temperature atomic quantum memories lays the groundwork for Type II quantum repeaters.

This study demonstrates successful HOM interference with single-photon-level pulses stored and retrieved from independent room-temperature quantum memories. The findings highlight the viability of these memories for memory-assisted quantum operations. Future research directions include further background noise reduction, using shorter pulses, and implementing real-time single-photon heralding to achieve higher HOM visibilities and realize practical Type II quantum repeater networks. Potential applications include variable-delay MDI-QKD and Bell-state measurements.

The study acknowledges limitations in achieving higher HOM visibility, primarily due to background noise associated with the control field in the EIT scheme and imperfections in the quantum memories, including slight mismatches in memory efficiencies, variations in mean photon numbers, and polarization drifts in the memory output fibers. The model relating HOM visibility to SBR is a simplification, and other factors may influence the results. The current memory systems have not yet reached the levels of performance needed for efficient entanglement swapping experiments.