在基於光纖傳輸的量子網路架構，通訊頻段對於量子節點間的長距離量子資訊傳輸至關重要。然而，近紅外波段是透過鹼金族原子進行量子資訊儲存和處理的最佳波段。考慮到需要高效率地彌合原子量子設備和通訊光纖間的頻率間隙，同時保持光子攜帶的量子資訊，量子頻率轉換是應對這種挑戰的一種關鍵的量子介面。在這項研究中，我們探索了一種高效的通訊頻段量子轉頻機制，該轉頻機制是基於銣原子鑽石型能階的四波混頻，使光子能夠在795奈米的近紅外波長和1367或1529奈米的通訊頻段間進行轉換。我們使用海森堡-朗之萬方法來最佳化在各種光學深度下的轉換效率並提供對應的實驗參數，同時我們的模型考慮量子雜訊的影響。與先前忽略應用光場吸收損耗的工作不同，我們的理論模型更符合現實世界的情況。此外，我們採用約化密度算符理論建構理論框架，並利用該理論證明鑽石型四波混頻方案可以高保真度地維持輸入光子的量子特性，例如正交方差和光子統計。重要的是，這些量子特性不會受到真空場雜訊的干擾，使系統能夠實現高純度的量子轉頻。另一個重要貢獻在於研究此量子轉頻方案如何影響以光子數、路徑和偏振自由度編碼的量子資訊。這些編碼的量子位元在足夠高的轉換效率下表現出顯著的糾纏保留。對於完美的轉換效率，此方案可以達到完美保真度。這項綜合探索為基於原子系綜的鑽石型量子轉頻方案在量子網路的應用奠定了必要的理論基礎，是推進此量子轉頻方案在分散式量子計算和長距離量子通訊中使用的關鍵基礎研究。

在量子資訊科學領域，量子態的高效儲存與檢索對於某些關鍵應用是不可或缺的，包括但不限於量子中繼器、確定性單光子或多光子源以及線性光量子計算。因此，量子記憶體的實現一直是關鍵的研究熱點。在這項研究中，我們探索了一種高效的量子儲存方案，該方案利用原子系綜中的Λ型電磁波誘發透明機制實現量子記憶體。此儲存機制使我們能夠透過操縱外部的同調光場來對量子光脈衝的傳播進行相干控制。利用暗態極激子描述，我們推導了在絕熱極限之下，量子記憶體操作週期內任意給定時間的旋波原子算符和光場算符。我們的模型考慮基態間的去同調，使我們的模型更接近現實世界的條件。此外，我們採用約化密度算符理論建立多模態理論框架，並利用該理論證明Λ型量子儲存方案可以高保真度地保持輸入光子的量子特性，包括光子統計和量子糾纏。我們研究的另一個關鍵在於分析此方案如何影響各種自由度中編碼的量子資訊，包括光子數、路徑和偏振自由度。當儲存效率足夠高時，N個量子位元的糾纏態將得到良好的保存。對於完美的儲存效率，檢索的量子態將達到完美保真度。我們的深入研究為在量子計算和量子網路中實現基於原子系綜的Λ型量子儲存方案提供了必要的理論基礎。這項基礎研究對於此方案在量子資訊處理和長距離量子通訊的未來發展至關重要。

In a fiber-based quantum network, the utilization of the telecom band is crucial for long-distance quantum information (QI) transmission between quantum nodes. However, the near-infrared wavelength is identified as optimal for storing and processing QI through alkaline atoms. Recognizing the challenge of efficiently bridging the frequency gap between atomic quantum devices and telecom fibers while maintaining the QI carried by photons, quantum frequency conversion (QFC) serves as a pivotal quantum interface. In this study, we explore an efficient telecom-band QFC mechanism based on diamond-type four-wave mixing (FWM) with rubidium energy levels. The mechanism enables the conversion of photons between the near-infrared wavelength of 795 nm and the telecom band of 1367 or 1529 nm. Using the Heisenberg-Langevin approach, we optimize conversion efficiency (CE) across varying optical depths while considering quantum noises and present corresponding experimental parameters. Unlike previous works neglecting the applied field absorption loss, our results are more relevant to practical scenarios. Moreover, by employing the reduced-density-operator theory to construct a theoretical framework, we demonstrate that this diamond-type FWM scheme can maintain the quantum characteristics of input photons with high fidelity, such as quadrature variances and photon statistics. Importantly, these properties remain unaffected by vacuum field noise, enabling the system to achieve high-purity QFC. Another significant contribution lies in examining how this scheme impacts QI encoded in photon-number, path, and polarization degrees of freedom (DOFs). These encoded qubits exhibit remarkable entanglement retention under sufficiently high CE. In the case of perfect CE, the scheme can achieve unity fidelity. This comprehensive exploration establishes a theoretical foundation for the application of the diamond-type QFC scheme based on atomic ensembles in quantum networks, laying essential groundwork for advancing the scheme in distributed quantum computing and long-distance quantum communication. The content in this paragraph is adapted from [Po-Han Tseng, et. al., Phys. Rev. A 109, 043716 (2024)] and [Po-Han Tseng, et. al., arXiv:2401.09768 (2024)].

In the realm of QI science, the efficient storage and retrieval of quantum states are indispensable for crucial applications, including but not limited to quantum repeaters, deterministic single-photon or multi-photon generation, and linear optical quantum computing. As a result, the realization of quantum memories constitutes a pivotal research focus. In this study, we explore an efficient quantum memory scheme using the Λ-type electromagnetically induced transparency in atomic ensembles. The storage mechanism enables the coherent control of quantum light pulse propagation through the manipulation of an external coherent field. Using the dark-state polariton description, we derived the spin-wave atomic operator and the field operator at any given time within the quantum memory operation cycle in the adiabatic limit. The consideration of ground state decoherence brings our model closer to real-world conditions. Moreover, through employing the reduced-density-operator theory to establish a multimode framework, we demonstrate that the Λ-type quantum memory scheme can preserve the quantum characteristic of input photons with high fidelity, including photon statistics and quantum entanglement. A key aspect of our research involves analyzing how this scheme affects QI encoded in various DOFs, including photon-number, path, and polarization. The N-qubit entangled state is well-preserved when storage efficiencies are adequately high, reaching unity fidelity for perfect storage efficiencies. Our thorough investigation provides a theoretical foundation for implementing the Λ-type quantum memory scheme based on atomic ensembles in quantum computing and quantum networks. This groundwork is crucial for the future development of this scheme in QI processing and long-distance quantum communication. The content in this paragraph is being prepared for submission to a journal, and the manuscript is currently in preparation [Po-Han Tseng and Yong-Fan Chen, Entanglement preserving quantum memory based on Λ-type electromagnetically induced transparency, Manuscript in preparation (2024)].

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