For the realization of long-distance quantum communication and distributed quantum computing through the quantum repeater network, a key requirement is the development of multiplexed quantum storage using atoms, N-V centers, or solid-state systems [1–10]. The photonic multi-dimensional storage capabilities, storage time, and high storage efficiency of multiplexed quantum storage devices are critical factors that directly influence entanglement distribution efficiency, and facilitate the implementation of long-distance quantum communication and optical quantum computing [11–17].

Polarization, a well-established photonic degree of freedom, has been extensively utilized for quantum storage, achieving over 50% storage efficiency in cold rubidium [18] and cesium atomic media [19]. However, the polarization degree of freedom is inherently limited to two-dimensional coding within quantum storage operations. In contrast, photonic orbital angular momentum (OAM) provides the ability to construct an infinite-dimensional Hilbert space, serving as an effective carrier for high-dimensional photonic quantum states [20]. To date, OAM-based storage has been successfully implemented across a wide range of systems utilizing various storage protocols. For instance, the electromagnetically induced transparency (EIT) scheme has been employed to achieve storage of high-dimensional states [21–25]. Additionally, off-resonant Raman protocols, harnessing the properties of cold atomic ensembles, have been utilized to realize quantum storage [26]. Furthermore, solid-state systems have demonstrated their potential as platforms for implementing OAM-based storage [27–29]. To increase the mode number within storage systems, a perfect optical vortex (POV) beam, with beam size independent of the topological charge, has been employed to encode photons. This feature has been effectively harnessed in quantum storage applications, facilitating high-dimensional state encoding and achieving a storage efficiency of nearly 60% for a 25-dimensional state [30]. However, the transmission of POV exhibits non-stationary behavior, presenting significant challenges for the practical application of quantum information transfer across free space or through optical fibers.

The vector beam (VB), which serves as a mode in which photon polarization and OAM are intricately coupled [31], represents an eigen-solution of the vector Helmholtz equation. This characteristic endows VBs with the capability for stable transmission and presents potential advantages in applications such as optical imaging [32], precision measurement [33], optical trapping [34], and drilling [35]. Additionally, due to their unique polarization structure, VBs demonstrate considerable potential for investigating new effects and phenomena in the interaction between light and matter [36], such as spatially dependent electromagnetically induced transparency [37], detecting 3D magnetic fields [38], and measuring optical concurrence [39]. Furthermore, the unique properties of VBs have also been utilized in quantum information processing, including quantum steering, quantum hyper-entanglement, and quantum information transfer [40–49]. In addition to these applications, VBs, owing to their capabilities for high-dimensional photonic encoding, have also been utilized in quantum storage systems involving both cold and hot atomic ensembles [50–52]. However, the storage efficiency in all these experiments is below 50% and cannot beat the quantum non-cloning limit without post-selection. Achieving efficient storage of VBs has remained an elusive milestone.

To date, most quantum storage utilizing high-dimensional states based on photon polarization and OAM has focused on single-path configurations. However, the advent of photonic path-multiplexing techniques offers a promising avenue for advancing efficient quantum repeaters [2,5,53,54]. Multi-path photonic high-dimensional storage provides a straightforward option for facilitating multi-path quantum entanglement in quantum memories [55–57]. It facilitates the simultaneous storage of multiple flying qudits transmitted by multi-terminal users, making it ideal for quantum networks with several quantum nodes. To our knowledge, there have been no reports on the multi-path efficient optical storage of VBs using any storage protocol or storage medium.

In this paper, we demonstrate an experimental realization of high-efficiency multi-dimensional optical storage using a laser-cooled ${}^{87}\mathrm{Rb}$ atom ensemble with a cigar shape. We achieve a large optical depth and a low ground state decoherence rate in the cold atomic cloud by utilizing a spatial dark line, compressed magneto-optical trap (MOT), Zeeman optical pumping, and microwave spectroscopy techniques (the details are outlined in Appendix A) [58–60]. Additionally, we have developed a compact structure for generating two-channel VBs, with each channel carrying a vector mode of a specific order. These beams are coherently decomposed into four paths via a beam displacer and subsequently converted into the spatial frequency domain through a Fourier-transform optical lens. This configuration enables complete mapping of the optical field into the cold atoms while significantly enhancing the effective light-matter interaction strength, which is critical for achieving high storage efficiency. By utilizing this technology, we obtain storage efficiency exceeding 70% and storage fidelity above 89% for two-channel VBs. And then we achieve a storage time of approximately 7 μs for two-channel VBs, and the spatial structure and phase information are preserved during storage through performed projection measurements. Furthermore, single-photon level storage and quantum state tomography demonstrate that our storage system can work in the quantum region. Our work has the potential to play a crucial role in the development of large-scale quantum networks utilizing repeaters, as well as in the field of distributed quantum computing.

The experimental setup is illustrated in Fig. 1(a) and is divided into three parts: state preparation, storage, and measurement. The first part consists of two-channel probe beams from an external cavity diode laser (ECDL) in free space. Two q-plates with topological charges of $m=1$ and $m=2$, which are birefringent optical devices characterized by a spatially varying orientation of their optic axes [61], are inserted for each channel to convert Gaussian modes to the VBs. These two VBs serve as probe beams and are transformed into hybrid VBs using a quarter-wave plate (QWP) before being injected into the optical storage section via two pairs of mirrors. A semi-circular half-wave plate (HWP) and a beam displacer (BD) convert two hybrid VBs into four beams with the same polarization state [as shown in Fig. 1(a)]. The four probe beams through the QWP are transformed into the spatial frequency domain by a lens (L1), ensuring that all channels are fully encompassed by the atomic ensemble to achieve a high optical depth (OD). A control beam with a waist of 4 mm is injected into the MOT with an angle of 1° relative to the four probe beams. After the MOT, the four probe beams are collimated by another lens (L2) with the same focal length, and through the other QWP and a semi-circular HWP. A second BD is inserted to combine these four polarization components into the hybrid VBs, ensuring that their polarization matches the initial polarization before storage. The measurement part is composed of a QWP, an HWP, a polarizing beam splitter (PBS), and a spatial light modulator (SLM) positioned at the focal plane of the lens (L2).Finally, we utilize an HWP and a PBS to couple the two channels into single-mode fiber separately, allowing for the analysis of the output states. The retrieved photons are detected using a single-photon counting module (SPCM). To ensure high storage efficiency, we first adjust the two pairs of mirrors in the “state preparation” part to guarantee that the four-channel probe beams possess a high OD. The OD measurement results are presented in Appendix B, demonstrating similar OD values of approximately 200 across all four channels (as shown in Fig. 6 of Appendix B). This consistency ensures high storage efficiency across all channels.

In the following, we implement a multi-VB optical storage based on the EIT protocol, which enables the conversion of the probe photon into atomic collective excitation through quantum interference effects. Due to the space-variant polarization in the transverse plane, the two-channel VBs are divided into four basis vectors. This division allows for the adjustment of the two polarized components of each VB, ensuring that all basis vectors are uniformly polarized for optical storage, as illustrated in Fig. 1(a). The intensity and phase of four basis vectors for multi-VB are depicted in Figs. 2(a1) and 2(b1). The frequency of the probe beam consisting of these four basis vectors is locked to the $|5{\mathrm{S}}_{1/2},F=1,m_F=1⟩\to |5{\mathrm{P}}_{1/2},F^{\prime }=2,m_F=2⟩$ transition. The control beam is phased-locked to the probe beam and resonates with the $|5{\mathrm{S}}_{1/2},F=2,m_F=1⟩\to |5{\mathrm{P}}_{1/2},F^{\prime }=2,m_F=2⟩$ transition to eliminate the photon switching effect. The control beam with an angle of 1° relative to the four probe beams can prevent the four-wave mixing noise and reduce the decoherence rate of the ground state. To minimize probe photon leakage during the storage process, the power of the control beam is optimized to 60 mW. The probe pulse is shaped into a Gaussian waveform with a temporal duration of 500 ns to align with the spectral-temporal characteristics of the EIT storage system. The control beam is turned on 600 μs after the magnetic coil is turned off to reduce the decoherence rate induced by the inhomogeneous magnetic field. It is adiabatically turned off once the probe pulse fully enters the atomic ensemble, ensuring that all of the probe pulse is converted into long-lived atomic collective excitations. After a delay of 500 ns, the control beam is switched on again to convert the collective excitations into photonic modes.

In front of storage, the input pulse is attenuated to contain three photons per pulse, with an accumulation time of 1000 s for each measurement. The temporal waveforms of the input probe pulses and the released signals after a storage time of 500 ns are shown in Figs. 2(a2) and 2(b2) for four basis vectors ($|H⟩|l=1⟩$, $|V⟩|l=-1⟩$ and $|H⟩|l=2⟩$, $|V⟩|l=-2⟩$; $l$ is topological charge) of two-channel VBs. The blue and the red dots indicate the input and retrieval signal counts after 500 ns storage time. The measured storage efficiencies, calculated using the ratio of the input pulse areas to the corresponding output pulse areas, are $74.4\%\pm 2.5\%$, $79.6\%\pm 2.6\%$, $72.3\%\pm 2.6\%$, $72.1\%\pm 3.0\%$ for the four basis vectors.

Storage time is a critical factor in the performance of multiplexed storage devices. Next, we measure the storage efficiency of the four basis vectors as a function of storage time delay. The results presented in Figs. 3(a1) and 3(a2) indicate that storage efficiency decreases exponentially with the storage time. The blue and red dots, along with the corresponding lines, represent the experimental results and theoretical simulations. [The fitting line is given by the equation of ${\eta }_0\exp (-\frac{t}{\tau })$, and ${\eta }_0$ and $\tau$ are initial storage efficiency and storage time.] To achieve prolonged storage time, the ground-state decoherence rate must be reduced to a lower level. In this paper, we utilize microwave spectroscopy technology to reduce the residual magnetic field by adjusting three pairs of Helmholtz coils. Through continuous optimization of the coil currents, we achieve a storage time of approximately 7 μs for each channel, as illustrated in Fig. 3.

Before quantum state tomography, we perform projection measurements to demonstrate that both the spatial structure and the phase information of two-channel VBs are preserved during multiplexed storage. As shown in the measurement part of Fig. 1, a QWP, an HWP, a PBS, and an SLM are employed for projection measurements. First, we position an HWP with its fast axis at an angle of 22.5° to project the OAM mode under the $|H⟩+|V⟩$ polarization state. Then, two holographic gratings on the SLM are configured as $|l=1⟩+e^{il\phi }|l=-1⟩$ for channel 1 and $|l=2⟩+e^{il\phi }|l=-2⟩$ for channel 2 based on split screen technology, where $\phi$ is the relative azimuthal angle between $|l=1⟩$ and $|l=-1⟩$ for channel 1, or relative azimuthal angle between $|l=2⟩$ and $|l=-2⟩$ for channel 2. By adjusting the HWP and QWP to specific angles, we obtain four interference curves after storage based on four basis vectors ($|H⟩+|V⟩$, $|H⟩-|V⟩$, $|H⟩+i|V⟩$, $|H⟩-i|V⟩$) as shown in Fig. 3. The average interference visibility values of channel 1 are 0.98, 0.80, 0.99, and 0.91, while for channel 2, they are 0.76, 0.88, 0.83, and 0.85, respectively. The blue, dark, purple, and red dots, along with the lines, represent the experimental results and theoretical simulations.

In summary, we realize high-efficiency optical storage of two VBs in laser-cooled ${}^{87}\mathrm{Rb}$ atom ensembles with a cigar shape. We achieve a large optical depth and a low ground state decoherence rate in the cold atomic cloud. Additionally, we have developed two-channel multiplexed VBs, each carrying a polarization topological charge of a different order. These VBs are stored in cold atom ensembles through the EIT storage protocol. Finally, we obtain storage efficiency above 70% and storage fidelity above 89% for two-channel VBs. We further verify the properties of our storage, particularly its storage time and optical mode invariance concerning polarization and OAM degrees of freedom. We measure interference curves across different polarizing basis vectors and coherence storage times, confirming that our system can function as a storage for photon spin and orbital angular momentum qubits. Additionally, single-photon quantum state tomography demonstrates that our storage system operates effectively within the quantum regime. The storage efficiency reported here has promising applications in constructing large-scale, repeater-based quantum networks and distributed quantum computing.

In our scheme, the input state is $|{\psi }_{\text{input}}⟩=|H⟩|l⟩+|V⟩|-l⟩$ ($l=1$ for channel 1 and $l=2$ for channel 2) while the output state after storage can be expressed as $|{\psi }_{\text{output}}⟩=1\sqrt{{\sum }_{j=1}^2{\eta }_j^2}({\eta }_1|H⟩|l⟩+{\eta }_2|V⟩|-l⟩$. To achieve a high storage fidelity, the storage efficiency $\eta$ for different basis vectors of VBs should be similar to guarantee that the weight of each component in the superposition state does not change upon retrieval. As observed in Figs. 3(a) and 3(b), the storage efficiencies for $|H⟩$ and $|V⟩$ remain similar across different storage time. Currently, we have only achieved high-efficiency storage of VBs with topological charges of 1 and 2 for two individual channels. To achieve efficient storage of higher-order VBs, it is essential to enhance light-atom interaction strength by increasing the transverse size of cold atomic ensembles [62], and optimizing the transverse profile of the probe beam [63] through the utilization of high-resolution spatial light modulators [64], digital micromirror devices [65], and compact optical micro-nano devices (such as metasurfaces [66]) for multiplexed storage of VBs.

Notably, the crosstalk between the two VBs is negligible due to their large separation distance. Additionally, the cold atomic ensemble’s exceptional coherence properties and low thermal velocity effectively suppress crosstalk between orthogonal spatial modes within each channel. It is feasible to further advance the information capacity of such quantum memories by optimizing the beam waist and the divergence angle in the multiplexed configuration, as well as the transverse dimension and the OD of the atomic ensemble.