Multiplexed storage and real-time manipulation based on a multiple degree-of-freedom quantum memory


The faithful storage and coherent manipulation of quantum states with matter-systems would enable the realization of large-scale quantum networks based on quantum repeaters. To achieve useful communication rates, highly multimode quantum memories are required to construct a multiplexed quantum repeater. Here, we present a demonstration of on-demand storage of orbital-angular-momentum states with weak coherent pulses at the single-photon-level in a rare-earth-ion-doped crystal. Through the combination of this spatial degree-of-freedom (DOF) with temporal and spectral degrees of freedom, we create a multiple-DOF memory with high multimode capacity. This device can serve as a quantum mode converter with high fidelity, which is a fundamental requirement for the construction of a multiplexed quantum repeater. This device further enables essentially arbitrary spectral and temporal manipulations of spatial-qutrit-encoded photonic pulses in real time. Therefore, the developed quantum memory can serve as a building block for scalable photonic quantum information processing architectures.


Large-scale quantum networks would enable long-distance quantum communication and optical quantum computing1,2,3. Due to the exponential photon loss in optical fibers4, quantum communication via ground-based optical fibers is currently limited to distances of hundred of kilometers. To overcome this problem, the idea of quantum repeater5,6 has been proposed to establish quantum entanglement over long distances based on quantum memories and entanglement swapping. It has been shown that to reach practical data rates using this approach, the most significant improvements can be achieved through the use of multiplexed quantum memories7,8,9.

The multiplexing of quantum memories can be implemented using any degree-of-freedom (DOF) of the photons, such as those in the temporal10, spectral11, and spatial12 domains. Rare-earth-ion-doped crystals (REIC) offer interesting possibilities as multiple-DOF quantum memories for photons by virtue of their large inhomogeneous bandwidths11,13,14 and long coherence time15 at cryogenic temperatures. Recently, there have been several important demonstrations using REIC, such as the simultaneous storage of 100 temporal modes16 by atomic frequency comb (AFC)17 featuring preprogrammed delays, the storage of tens of temporal modes by spin-wave AFC with on-demand readout18,19,20,21,22 and the storage of 26 frequency modes with feed-forward controlled readout11. The orbital-angular-momentum (OAM) of a photon receives much attention because of the high capacity of OAM states for information transmission and spatial multimode operations23. Tremendous developments have recently been achieved in quantum memories for OAM states24,25,26, paving the way to quantum networks and scalable communication architectures based on this DOF.

To date, most experiments with quantum memories have been confined to the storage of multiple modes using only one DOF, e.g., temporal, spectral, or spatial. To significantly improve the communication capacity of quantum memories and quantum channels, we consider a quantum memory using more than one DOF simultaneously11,27,28,29.

Here, we report on the experimental realization of an on-demand quantum memory storing single photons encoded with three-dimensional OAM states in a REIC. We present the results of a multiplexed spin-wave memory operating simultaneously in temporal, spectral and spatial DOF. In addition to expanding the number of modes in the memory through parallel multiplexing, a quantum mode converter (QMC)30 can also be realized that can perform mode conversion in the temporal and spectral domains simultaneously and independently. Indeed, our quantum memory enables arbitrary temporal and spectral manipulations of spatial-qutrit-encoded photonic pulses, and thus can serve as a real-time sequencer14, a real-time multiplexer/demultiplexer31, a real-time beam splitter32, a real-time frequency shifter33, a real-time temporal/spectral filter31, among other functionalities.


Experimental setup

A scheme of our experimental setup and relevant atomic level structure of Pr3+ ions is presented in Fig. 1. The memory crystal (MC) and filter crystal (FC) used in this setup are 3 × 6 × 3 mm crystals of 0.05% doped Pr3+ :Y2SiO5, which are cooled to 3.2 K using a cryogen-free cryostat (Montana Instruments Cryostation). In order to maximize absorption, the polarization of input light is close to the D2-axis of Y2SiO5 crystal. To realize reliable quantum storage with high multimode capacity, we created a high-contrast AFC in MC (the AFC structure is shown in Supplementary Note 1). Spin-wave storage is employed to enable on-demand retrieval and extend storage time17. The control and input light are steered towards the MC in opposite directions with an angular offset ~4° to reject the strong control field and avoid the detection of free induction decay noise34. To achieve a low noise floor, we increase the absorption depth of the FC by employing a double-pass configuration. Figure 2a presents the time histograms of the input photons (blue) and the photons retrieved at 12.68 μs (green) with a spin-wave storage efficiency ηSW = 5.51%. For an input with a mean photon number μ = 1.12 per pulse, we have measured a signal-to-noise ratio (SNR) ~39.7 ± 6.7 with the input photons in the Gaussian mode.

Fig. 1

Experimental setup and atomic levels. a Schematic illustrations of the experiment. The AFC is prepared in a memory crystal (MC) and a narrow spectral filter has been prepared in a filter crystal (FC)49. The beam waist of the input light is 65 μm at the middle of the MC. The pump/control light has a beam waist of 300 μm inside the MC to ensure good overlap with the high-dimensional input light. The input pulses are attenuated to single-photon level by neutral density filters (NDF). The spatial modes of these photons are converted into OAM superposition states by a spatial light modulator (SLM1). After storage in the MC, the retrieved signal passes through two consecutive acousto-optical modulators (AOM)42, which act as a temporal gate and a frequency shifter. The AOM are used in double-pass configuration to ensure the photons’ spatial mode unchanged when the frequency of photons is swept over tens of MHz. The SLM2 and a single-mode fiber (SMF) are employed to analyze the OAM states of the retrieved photons. The FC is double-passed with help of a polarization beam splitter (PBS), a half-wave plate (HWP) and a Faraday rotator (FR). Two bandpass filters (BPF) centered at 606 nm are employed to further suppress noises before the final detection of signal photons using single-photon detector (SPD). QWP quarter-wave plate. b Hyperfine states of the first sublevels of the ground and the excited states of Pr3+ in Y2SiO5. The input field is resonant with 1/2g–3/2e, and the control field is resonant with 3/2g–3/2e (see Methods section for details)

Fig. 2

Time histograms and the reconstructed process matrix of quantum storage process in three-dimensional OAM space. a Time histograms of the input photons (blue), the photons retrieved at 12.68 μs for μ = 1.12 (green) and the unconditional noise for μ = 0 (black). b Graphical representation of the process matrix χ of memory process as estimated via quantum process tomography. Details of operators λi are shown in Section Methods. Only the real part of the experimentally reconstructed process matrix is shown. All values are in the imaginary part are smaller than 0.090

Quantum process tomography

The ability to realize the on-demand storage of photonic OAM superposition states in solid-state systems is crucial for the construction of OAM-based high-dimensional quantum networks24. Quantum process tomography for qutrit operations35 benchmarks the storage performance for OAM qutrit in our solid-state quantum memory. The qutrit states are prepared in the following basis of OAM states: \(\left| {{\mathrm{LG}}_{p = 0}^{l = - 1}} \right\rangle\), \(\left| {{\mathrm{LG}}_{p = 0}^{l = 0}} \right\rangle\), \(\left| {{\mathrm{LG}}_{p = 0}^{l = 1}} \right\rangle\). Here, \(\left| {{\mathrm{LG}}_p^l} \right\rangle\) corresponds to OAM states defined as Laguerre-Gaussian (LG) modes, where l and p are the azimuthal and radial indices, respectively. In the following, we use the kets |L〉, |G〉, and |R〉 to denote the OAM states \(\left| {{\mathrm{LG}}_{p = 0}^{l = 1}} \right\rangle\), \(\left| {{\mathrm{LG}}_{p = 0}^{l = 0}} \right\rangle\), and \(\left| {{\mathrm{LG}}_{p = 0}^{l = - 1}} \right\rangle\), respectively. For μ = 1.12, we first characterized the input states before the quantum memory using quantum state tomography (see Methods section for details). The reconstructed density matrices of input are not ideal because of imperfect preparation and measurements based on spatial light modulators and single-mode fibers26. We then characterized the memory operation using quantum process tomography. Figure 2b presents the real part of the experimentally reconstructed process matrix χ. It is found to have a fidelity of 0.909 ± 0.010 with respect to the Identity operation. This fidelity exceeds the classical bound of 0.831 (see Supplementary Note 4 for details), thereby confirming the quantum nature of the memory operation. The nonunity value of the memory fidelity may be caused by the limited beam waist of the pump/control light, which may result in imperfect overlap with different OAM modes. Moreover, we noted that the memory performance for superposition states of |L〉 and |R〉 is much better than that achieved here (as detailed in Supplementary Note 2). The visibility of such two-dimensional superposition states is higher than the fidelity of the memory process in all three dimensions. This result indicates that the storage efficiency is balanced for the symmetrical LG modes but is not balanced for all the three considered spatial modes.

Multiplexing storage in multiple DOF

Carrying information in multiple DOF on photons can expand the channel capacity of quantum communication protocols11,36. Here, we show that our solid-state memory can be simultaneously multiplexed in temporal, spectral, and spatial DOF. As shown in Fig. 3a, two AFC are created in the MC with an interval of 80 MHz between them to achieve spectral multiplexing. The two AFC have the same peak spacing of Δ = 200 kHz and the same bandwidth of ΓAFC = 2 MHz. The spin-wave storage efficiencies are 5.05% and 5.13%, for the first AFC and the second AFC, respectively. The temporal multimode capacity of an AFC is limited by ΓAFC17. However, increasing the number of modes, the time interval between the last control pulse and the first output signal pulse will be reduced. Therefore, we employed only two temporal modes to reduce the noise caused by the last control pulse. The spatial multiplexing is realized by using three independent paths as input as shown in Fig. 3b. These paths, s1, s2, and s3, correspond to the OAM states as |L〉, |R〉, and |G〉 defined above. By combining all three DOF together, we obtain 2 × 2 × 3 = 12 modes in total. The FC is employed to select out the desired spectral modes. Figure 3c illustrates the results of multimode storage over these three DOF for μ = 1.04. The minimum crosstalk as obtained from mode crosstalk for each mode is 19.7 ± 3.41, which is calculated as one takes the counts in the diagonal term as the signal and then locates the large peaks over the range of output modes as the noise.

Fig. 3

Multiplexed spin-wave storage in three degrees of freedom at the single-photon level. a The double AFC structure (red) in the MC and the double filter structure (black) in the FC. b Three independent spatial modes carrying different OAM states are employed for spatial multiplexing. The spatial mode s1 is converted into |L〉 state in SLM1. The spatial mode s2 is converted into |R〉 state in a spiral phase plate (SSP); the spatial mode s3 is a Gaussian mode which is used as |G〉 state. They are combined by two pellicle beam splitters (BS). c A demonstration of temporal, spectral and spatial multiplexed storage for single-photon level inputs

Here, the temporal, spectral and spatial DOF are employed as classical DOF for multiplexing. One can choose any DOF to carry quantum information. As a typical example, now we use the temporal and spectral DOF for multiplexing and each channel is encoded with spatial-qutrit state of \(\left| {\psi _1} \right\rangle = \left( {\left| L \right\rangle + \left| G \right\rangle + \left| R \right\rangle } \right)/\sqrt 3\). Each channel is labeled as fitj, where fi represent spectral modes i and tj similarly represent temporal modes j. Figure 4a shows the experimental results for μ = 1.04. The minimum crosstalk as obtained from the mode crosstalk is approximately 15.2. We measured the fidelities of the spatial-qutrit state for each channel as shown in Fig. 4b.

Fig. 4

Multiplexed storage and quantum mode conversion for spatial encoded qutrit state using four temporal and spectral channels. a The multiplexed storage for spatial-qutrit state of |ψ1〉 in the temporal and spectral DOF. b Fidelities for the qutrit states after storage. c The performance of the QMC with an encoded state of |ψ1〉. d Fidelities for the qutrit state after mode conversion. The error bars for the fidelities correspond to one standard deviation caused by the statistical uncertainty of photon counts

A QMC can transfer photonic pulses to a target temporal or spectral mode without distorting the photonic quantum states. A real-time QMC that can operate on many DOF is essential for linking the components of a quantum network30,37. By adjusting the timing of the control pulse, one can specify the recall time in an on-demand manner to realize the temporal mode conversion. The two-AOM gate in our system can be used as a high-speed frequency shifter by tuning its driving frequency. Therefore, spectral and temporal mode conversion can be realized independently and simultaneously. Figure 4c presents the results of QMC operation for μ = 1.04. We can convert from fi to fj and from ti to tj, where these notations represent all different spectral modes and temporal modes. The noise level is significantly weaker than the strength of the converted signal, which indicates that the QMC operates quietly enough to avoid introducing any mode crosstalk. All these modes are encoded with OAM spatial-qutrit of |ψ1〉. To demonstrate that the qutrit state coherence is well preserved after QMC operation, we measured the fidelities (see Methods for details) between the input and converted states. The results, presented in Fig. 4d, indicate that the QMC can convert arbitrary temporal and spectral modes in real-time while preserving their quantum properties. Our device is expected to find applications in quantum networks comprising two quantum memories, in which mismatched spectral or temporal photon modes may need to be converted30. This device can ensure the indistinguishability of the photons which are retrieved from any quantum memory. This device could find application in many photonic information processing protocols, e.g., a Bell-state measurement11, and quantum memory-assisted multiphoton generation9.

Arbitrary manipulations in real time

The precise and arbitrary manipulation of photonic pulses while preserving photonic coherence is an important requirement for many proposed photonic technologies31. In addition to the QMC functionality demonstrated above, the developed quantum memory can enable arbitrary manipulations of photonic pulses in the temporal and spectral domains in real time. As an example, we prepared the OAM qutrit state |ψ1〉 in the f1t1 and f2t2 modes (Fig. 5a) as the input. Four typical operations were demonstrated, i.e., exchange of the readout times for the f1 and f2 photons, the simultaneous retrieval of the f1 and f2 photons at t1, shifting the frequency of f1 photons to f2 but keeping the frequency of f2 photons unchanged and temporal beam splitting the f1 photons but filtering out the f2 photons. These operations correspond to output of \(\left| {\psi _1} \right\rangle _{f_1t_2,f_2t_1}\), \(\left| {\psi _1} \right\rangle _{f_1t_1,f_2t_1}\), \(\left| {\psi _1} \right\rangle _{f_2t_1,f_2t_2}\), and \(\left| {\psi _1} \right\rangle _{f_1t_1,f_1t_2}\), respectively. Another example was implemented with the OAM qutrit state \(\left| {\psi _2} \right\rangle = \left( {\left| L \right\rangle + \left| G \right\rangle - {\mathrm{i}}\left| R \right\rangle } \right)/\sqrt 3\) encoded in the f1t2 and f2t2 modes as the input, as shown in Fig. 5b with same output. The retrieved states were then characterized via quantum state tomography as usual (see Methods). Table 1 shows the fidelities between output states and input states.

Fig. 5

Arbitrary temporal and spectral manipulations in real time. Four typical operations are presented for two different input states. a The OAM qutrit state |ψ1〉 is encoded on the f1t1 and f2t2 modes. The f1 photons are marked as red color and the f2 photons are marked as blue color. These operations, from up to down, correspond to a pulses sequencer, a multiplexer, a selective spectral shifter and a configurable beam splitter (the f2 photons are filtered out), respectively. The little “×2” indicates that the integration time of temporal beam splitting is two times of the other operations. b The OAM qutrit state |ψ2〉 is encoded on the f1t2 and f2t2 modes. These operations, from up to down, correspond to a demultiplexer, a pulses sequencer, a selective spectral shifter (the f1 photons is frequency shifted to f2 and retrieved at t1, while the f2 photons are retrieved at t2) and a configurable beam splitter (the f2 photons are filtered out), respectively. All of these operations can be determined after the photons have been absorbed into the quantum memory. The inputs are shifted earlier by 3 μs in the histograms for visual effects

Table 1 Fidelities of qutrit states after temporal and spectral manipulations


In conclusion, we have experimentally demonstrated a multiplexed solid-state quantum memory that operates simultaneously in three DOF. The currently achieved multimode capacity is certainly not the fundamental limit for the physical system. Pr3+ :Y2SiO5 has an inhomogeneous linewidth of 5 GHz, which can support more than 60 independent spectral modes. The number of temporal modes that can be achieved using the AFC protocol17 is proportional to the number of absorption in the comb, which has already been improved to 50 in Eu3+ :Y2SiO522. There is no fundamental limit on the multimode capacity in the OAM DOF since it is independent on the AFC bandwidth. The capacity in this DOF is simply determined by the useful size of the memory in practice. We have recently demonstrated the faithful storage of 51 OAM spatial modes in a Nd3+ :YVO4 crystal26. The combination of these state-of-the-art technologies could result in a multimode capacity of 60 × 50 × 51 = 1,53,000 modes. This large capacity could greatly enhance the data rate in memory-based quantum networks and in portable quantum hard drives with extremely long lifetimes15.

The developed multiple-DOF quantum memory can serve as a QMC, which is a fundamental requirement for the construction of scalable networks based on multiplexed quantum repeaters. Although it is not demonstrated in the current work, mode conversion in the spatial domain should also be feasible using a high-speed digital micromirror device38. QMC can also find applications in linear optical quantum computations. One typical example is to solve the mode mismatch caused by fiber-loop length effects and the time jitter of the photon sources in a boson sampling protocol39,40.

Quantum communication and quantum computation in a large-scale quantum network rely on the ability to faithfully store and manipulate photonic pulses carrying quantum information. The presented quantum memory can apply arbitrary temporal and spectral manipulations to photonic pulses in real time, which indicates that this single device can serve as a variable temporal beam splitter32,41 and a relative phase shifter42 that enables arbitrary control of splitting ratio and phase for each output. Therefore, this device can perform arbitrary single-qubit operations43. Combining with the recent achievements on generation of heralded single photons44,45, this device should provide the sufficient set of operations to allow for universal quantum computing in the Knill–Laflamme–Milburn scheme46. Our results are expected to find applications in large-scale memory-based quantum networks and advanced photonic information processing architectures.


AFC preparation

We tailored the absorption spectrum of Pr3+ ions to prepare the AFC using spectral hole burning42. The frequency of the pump light was first scanned over 16 MHz to create a wide transparent window in the Pr3+ absorption line. Then, a 1.6 MHz sweep was performed outside the pit to prepare the atoms into the 1/2g state. The burn-back procedure created an absorbing feature of 2 MHz in width resonant with the 1/2g–3/2e transition, but simultaneously populated the 3/2g state, which, in principle, must be empty for spin-wave storage. Thus, a clean pulse was applied at the 3/2g–3/2e transition to empty this ground state. After the successful preparation of absorbing band in the 1/2g state, a stream of hole-burning pulses was applied on the 1/2g–3/2e transition. An AFC structure with a periodicity of Δ = 200 kHz is prepared in this step. These pulses burned the desired spectral comb of ions on the 1/2g–3/2e transition and antiholes at the 3/2g–3/2e transition; thus, a short burst of clean pulses was applied to maintain the emptiness of the 3/2g state. For AFC preparation, the remaining 5/2g ground state is used as an auxiliary state, which stores those atoms which do not contribute to the AFC components. To reduce the noise generated by the control pulses during spin-wave storage, we applied 100 control pulses separated by 25 μs and another 50 control pulses with a separation of 100 μs after the preparation of the comb21. An example of the AFC with a periodicity Δ = 200 kHz is illustrated in Fig. 3a. A detailed estimation of the structure and storage efficiency of the AFC memory is presented in Supplementary Note 1. The signal photons are mapped onto the AFC, leading to an AFC echo after a time 1/Δ. Spin-wave storage is achieved by applying two on-resonance control pulses to induce reversible transfer between the 3/2e state and 3/2g state before the AFC echo emission. The complete storage time is 12.68 μs in our experiment which includes an AFC storage time of 5 μs and a spin-wave storage time of 7.68 μs.

Filtering the noise

In order to achieve a low noise floor, temporal, spectral, and spatial filter methods are employed. The input and control beams are sent to the MC in opposite directions with a small angular offset for spatial filtering. Temporal filtering is achieved by means of a temporal gate implemented with two AOM. This AOM gate temporally blocked the strong control pulses. This is important to avoid burning a spectral hole in the FC and to avoid blinding the single-photon detector. We used two 2-nm bandpass filters at 606 nm to filter out incoherent fluorescence noise. The spectral of the filter mode was achieved by narrow-band spectral filter in the FC (shown by the dashed black line in Fig. 3a), which is created by 0.8 MHz sweep around the input light frequency, leading to a transparent window of approximately 1.84 MHz due to the power broadening effect. Furthermore, the FC is implemented in a double-pass configuration to achieve high absorption.

Quantum tomography

To characterize the memory performance for three-dimensional OAM states, quantum process tomography for the quantum memory operation is performed. Reconstructing the process matrix χ of any three-dimensional state requires nine linearly independent measurements. We chose three OAM eigenstates and six OAM superposition states as our nine input states, which are listed as follows: \(\left| L \right\rangle ,\left| G \right\rangle ,\left| R \right\rangle ,\left( {\left| L \right\rangle + \left| G \right\rangle } \right)/\sqrt 2\), \(\left( {\left| R \right\rangle + \left| G \right\rangle } \right)/\sqrt 2\), \(\left( {i\left| L \right\rangle + \left| G \right\rangle } \right)/\sqrt 2\), \(\left( { - i\left| R \right\rangle + \left| G \right\rangle } \right)/\sqrt 2\), \(\left( {\left| L \right\rangle + \left| R \right\rangle } \right)/\sqrt 2\), and \(\left( {\left| L \right\rangle - i\left| R \right\rangle } \right)/\sqrt 2\)26. The complete operators for the reconstruction of the matrix χ are as follows:26,47

$$\lambda _1 = \left[ {\begin{array}{*{20}{l}} 1 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 1 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 1 \hfill \end{array}} \right]$$
$$\lambda _2 = \left[ {\begin{array}{*{20}{l}} 0 \hfill & 1 \hfill & 0 \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill \end{array}} \right]$$
$$\lambda _3 = \left[ {\begin{array}{*{20}{l}} 0 \hfill & { - i} \hfill & 0 \hfill \\ i \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill \end{array}} \right]$$
$$\lambda _4 = \left[ {\begin{array}{*{20}{l}} 1 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & { - 1} \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill \end{array}} \right]$$
$$\lambda _5 = \left[ {\begin{array}{*{20}{l}} 0 \hfill & 0 \hfill & 1 \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill \\ 1 \hfill & 0 \hfill & 0 \hfill \end{array}} \right]$$
$$\lambda _6 = \left[ {\begin{array}{*{20}{l}} 0 \hfill & 0 \hfill & { - i} \hfill \\ 0 \hfill & 0 \hfill & 0 \hfill \\ i \hfill & 0 \hfill & 0 \hfill \end{array}} \right]$$
$$\lambda _7 = \left[ {\begin{array}{*{20}{l}} 0 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & 1 \hfill \\ 0 \hfill & 1 \hfill & 0 \hfill \end{array}} \right]$$
$$\lambda _8 = \left[ {\begin{array}{*{20}{l}} 0 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & { - i} \hfill \\ 0 \hfill & i \hfill & 0 \hfill \end{array}} \right]$$
$$\lambda _9 = \frac{1}{{\sqrt 3 }}\left[ {\begin{array}{*{20}{l}} 1 \hfill & 0 \hfill & 0 \hfill \\ 0 \hfill & 1 \hfill & 0 \hfill \\ 0 \hfill & 0 \hfill & { - 2} \hfill \end{array}} \right]$$

Here, λ1 is the identity operation. The process matrix χ can be expressed on the basis of λi and maps an input matrix ρin onto the output matrix ρout47,48. Density matrices of the input states ρin and density matrices of the output states ρout are reconstructed using quantum state tomography47,48. For a given qutrit state (|ψ〉), we used ρ=|ψ〉〈ψ| to reconstruct the density matrix ρ from the measurement results. As examples, we presented graphical representations of the reconstructed density matrices for the OAM qutrit states |ψ1〉 and |ψ2〉 in Supplementary Note 3.The fidelities of the output states with respect to the input states can be calculated based on the reconstructed density matrices using the formula \(Tr\left( {\sqrt {\sqrt {\rho _{{\mathrm{out}}}} \rho _{{\mathrm{in}}}\sqrt {\rho _{{\mathrm{out}}}} } } \right)^2\).

Data availability

The data that support the findings of this study are available from the corresponding authors on request.


  1. 1.

    Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

    ADS  Article  PubMed  CAS  Google Scholar 

  2. 2.

    Sangouard, M., Simon, C., de Riedmatten, H. & Gisin, N. Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83, 33–80 (2011).

    ADS  Article  Google Scholar 

  3. 3.

    Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007).

    ADS  Article  CAS  Google Scholar 

  4. 4.

    Gisin, N. How far can one send a photon? Front. Phys. 10, 100307 (2015).

    Article  Google Scholar 

  5. 5.

    Briegel, H. J., Dur, W., Cirac, J. I. & Zoller, P. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932–5935 (1998).

    ADS  Article  CAS  Google Scholar 

  6. 6.

    Duan, L.-M., Lukin, M. D., Cirac, J. I. & Zoller, P. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001).

    ADS  Article  PubMed  CAS  Google Scholar 

  7. 7.

    Collins, O. A., Jenkins, S. D., Kuzmich, A. & Kennedy, T. A. B. Multiplexed memory-insensitive quantum repeaters. Phys. Rev. Lett. 98, 060502 (2007).

    ADS  Article  PubMed  CAS  Google Scholar 

  8. 8.

    Simon, C. et al. Quantum repeaters with photon pair sources and multimode memories. Phys. Rev. Lett. 98, 190503 (2007).

    ADS  Article  PubMed  CAS  Google Scholar 

  9. 9.

    Nunn, J. et al. Enhancing multiphoton rates with quantum memories. Phys. Rev. Lett. 110, 133601 (2013).

    ADS  Article  PubMed  CAS  Google Scholar 

  10. 10.

    Usmani, I., Afzelius, M., de Riedmatten, H. & Gisin, N. Mapping multiple photonic qubits into and out of one solid-state atomic ensemble. Nat. Commun. 1, 12 (2010).

    Article  PubMed  CAS  Google Scholar 

  11. 11.

    Sinclair, N. et al. Spectral multiplexing for scalable quantum photonics using an atomic frequency comb quantum memory and feed-forward control. Phys. Rev. Lett. 113, 053603 (2014).

    ADS  Article  PubMed  CAS  Google Scholar 

  12. 12.

    Lan, S.-Y. et al. A multiplexed quantum memory. Opt. Express 17, 13639 (2009).

    ADS  Article  PubMed  CAS  Google Scholar 

  13. 13.

    Stoneham, A. M. Shapes of inhomogeneously broadened resonance lines in solids. Rev. Mod. Phys. 41, 82–108 (1969).

    ADS  Article  Google Scholar 

  14. 14.

    Saglamyurek, E. et al. An integrated processor for photonic quantum states using a broadband light–matter interface. New J. Phys. 16, 065019 (2014).

    ADS  Article  CAS  Google Scholar 

  15. 15.

    Zhong, M. et al. Optically addressable nuclear spins in a solid with a 6-h coherence time. Nature 517, 177–180 (2015).

    ADS  Article  PubMed  CAS  Google Scholar 

  16. 16.

    Tang, J.-S. et al. Storage of multiple single-photon pulses emitted from a quantum dot in a solid-state quantum memory. Nat. Commun. 6, 8652 (2015).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  17. 17.

    Afzelius, M., Simon, C., de Riedmatten, H. & Gisin, N. Multimode quantum memory based on atomic frequency combs. Phys. Rev. A 79, 052329 (2009).

    ADS  Article  CAS  Google Scholar 

  18. 18.

    Afzelius, M. et al. Demonstration of atomic frequency comb memory for light with spin-wave storage. Phys. Rev. Lett. 104, 040503 (2010).

    ADS  Article  PubMed  CAS  Google Scholar 

  19. 19.

    Gündoğan, M. et al. Coherent storage of temporally multimode light using a spin-wave atomic frequency comb memory. New J. Phys. 15, 045012 (2013).

    Article  ADS  CAS  Google Scholar 

  20. 20.

    Jobez, P. et al. Coherent spin control at the quantum level in an ensemble-based optical memory. Phys. Rev. Lett. 114, 230502 (2015).

    ADS  Article  PubMed  CAS  Google Scholar 

  21. 21.

    Seri, A. et al. Quantum correlations between single telecom photons and a multimode on-demand solid-state quantum memory. Phys. Rev. X 7, 021028 (2017).

    Google Scholar 

  22. 22.

    Jobez, P. et al. Towards highly multimode optical quantum memory for quantum repeaters. Phys. Rev. A 93, 032327 (2016).

    ADS  Article  Google Scholar 

  23. 23.

    Erhard, M., Fickler, R., Krenn, M. & Zeilinger, A. Twisted photons: new quantum perspectives in high dimensions. Light Sci. Appl. 7, 17146 (2018).

    Article  CAS  PubMed Central  Google Scholar 

  24. 24.

    Nicolas, A. et al. A quantum memory for orbital-angular momentum photonic qubits. Nat. Photon. 8, 234–238 (2014).

    ADS  Article  CAS  Google Scholar 

  25. 25.

    Ding, D.-S. et al. Quantum storage of orbital-angular momentum entanglement in an atomic ensemble. Phys. Rev. Lett. 114, 050502 (2015).

    ADS  Article  PubMed  CAS  Google Scholar 

  26. 26.

    Zhou, Z.-Q. et al. Quantum storage of three-dimensional orbital-angular-momentum entanglement in a crystal. Phys. Rev. Lett. 115, 070502 (2015).

    ADS  Article  PubMed  CAS  Google Scholar 

  27. 27.

    Humphreys, P. C. et al. Continuous-variable quantum computing in optical time-frequency modes using quantum memories. Phys. Rev. Lett. 113, 130502 (2014).

    ADS  Article  PubMed  CAS  Google Scholar 

  28. 28.

    Parigi, V. et al. Storage and retrieval of vector beams of light in a multiple degree-of-freedom quantum memory. Nat. Commun. 6, 7706 (2015).

    MathSciNet  Article  PubMed  PubMed Central  CAS  Google Scholar 

  29. 29.

    Zhang, W. et al. Experimental realization of entanglement in multiple degrees of freedom between two quantum memories. Nat. Commun. 7, 13514 (2016).

    ADS  Article  PubMed  PubMed Central  CAS  Google Scholar 

  30. 30.

    Heshami, K. et al. Quantum memories: emerging applications and recent advances. J. Mod. Opt. 63, 2005–2028 (2016).

    ADS  Article  PubMed  PubMed Central  Google Scholar 

  31. 31.

    Hosseini, M. et al. Coherent optical pulse sequencer for quantum applications. Nature 461, 241–245 (2009).

    ADS  Article  PubMed  CAS  Google Scholar 

  32. 32.

    Reim, K. F. et al. Multipulse addressing of a Raman quantum memory: configurable beam splitting and efficient readout. Phys. Rev. Lett. 108, 263602 (2012).

    ADS  Article  PubMed  CAS  Google Scholar 

  33. 33.

    Saglamyurek, E. et al. A multiplexed light–matter interface for fibre-based quantum networks. Nat. Commun. 7, 11202 (2016).

    ADS  Article  PubMed  PubMed Central  CAS  Google Scholar 

  34. 34.

    Hashimoto, D. & Shimizu, K. Coherent Raman beat analysis of the hyperfine sublevel coherence properties of 167Er3 + ions doped in an Y2SiO5 crystal. J. Lumin. 171, 183–190 (2016).

    Article  CAS  Google Scholar 

  35. 35.

    O’Brien, J. L. et al. Quantum process tomography of a controlled-NOT gate. Phys. Rev. Lett. 93, 080502 (2004).

    Article  PubMed  ADS  CAS  Google Scholar 

  36. 36.

    Barreiro, J. T., Wei, T. C. & Kwiat, P. G. Beating the channel capacity of linear photonic superdense coding. Nat. Phys. 4, 282–286 (2008).

    Article  CAS  Google Scholar 

  37. 37.

    Andrews, R. W., Reed, A. P., Cicak, K., Teufel, J. D. & Lehnert, K. W. Quantum-enabled temporal and spectral mode conversion of microwave signals. Nat. Commun. 6, 10021 (2015).

    ADS  Article  PubMed  PubMed Central  CAS  Google Scholar 

  38. 38.

    Mitchell, K. J. et al. High-speed spatial control of the intensity, phase and polarisation of vector beams using a digital micromirror device. Opt. Express 20, 29269–29282 (2016).

    ADS  Article  Google Scholar 

  39. 39.

    Motes, K. R., Gilchrist, A., Dowling, J. P. & Rohde, P. P. Scalable boson sampling with time-bin encoding using a loop-based architecture. Phys. Rev. Lett. 113, 120501 (2014).

    ADS  Article  PubMed  CAS  Google Scholar 

  40. 40.

    Motes, K. R., Dowling, J. P., Gilchrist, A. & Rohde, P. P. Implementing Boson sampling with time-bin encoding: analysis of loss, mode mismatch, and time jitter. Phys. Rev. A 92, 052319 (2015).

    ADS  Article  CAS  Google Scholar 

  41. 41.

    Timoney, N., Usmani, I., Jobez, P., Afzelius, M. & Gisin, N. Single-photon-level optical storage in a solid-state spin-wave memory. Phys. Rev. A 88, 022324 (2013).

    ADS  Article  CAS  Google Scholar 

  42. 42.

    Gündoğan, M., Ledingham, P. M., Kutluer, K., Mazzera, M. & de Riedmatten, H. Solid-state spin-wave quantum memory for time-bin qubits. Phys. Rev. Lett. 114, 230501 (2015).

    Article  PubMed  ADS  CAS  Google Scholar 

  43. 43.

    Humphrey, P. C. et al. Linear optical quantum computing in a single spatial mode. Phys. Rev. Lett. 111, 150501 (2013).

    ADS  Article  CAS  Google Scholar 

  44. 44.

    Kutluer, K., Mazzera, M. & de Riedmatten, H. Solid-state source of nonclassical photon pairs with embedded multimode quantum memory. Phys. Rev. Lett. 118, 210502 (2017).

    ADS  Article  PubMed  Google Scholar 

  45. 45.

    Laplane, C., Jobez, P., Etesse, J., Gisin, N. & Afzelius, M. Multimode and long-lived quantum correlations between photons and spins in a crystal. Phys. Rev. Lett. 118, 210501 (2017).

    ADS  Article  PubMed  Google Scholar 

  46. 46.

    Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).

    ADS  Article  PubMed  CAS  Google Scholar 

  47. 47.

    Thew, R. T., Nemoto, K., White, A. G. & Munro, W. J. Qudit quantum state tomography. Phys. Rev. A 66, 012303 (2002).

    ADS  MathSciNet  Article  CAS  Google Scholar 

  48. 48.

    Lvovsky, A. I., Sanders, B. C. & Tittel, W. Optical quantum memory. Nat. Photon 3, 706–714 (2009).

    ADS  Article  CAS  Google Scholar 

  49. 49.

    Beavan, S. et al. Demonstration of a dynamic bandpass frequency filter in a rare-earth ion-doped crystal. J. Opt. Soc. Am. B 30, 1173 (2013).

    ADS  Article  CAS  Google Scholar 

Download references


This work was supported by the National Key R&D Program of China (No. 2017YFA0304100), the National Natural Science Foundation of China (Nos. 61327901, 11774331, 11774335, 61490711, 11504362, and 11654002), Anhui Initiative in Quantum Information Technologies (No. AHY020100), Key Research Program of Frontier Sciences, CAS (No. QYZDY-SSW-SLH003), the Fundamental Research Funds for the Central Universities (Nos. WK2470000023 and WK2470000026).

Author information




Z.Q.Z. and C.F.L. designed experiment. T.S.Y. and Z.Q.Z. carried out the experiment assisted by Y.L.H., X.L., Z.F.L., P.Y.L., Y.M., C.L., P.J.L., Y.X.X., J.H., and X.L., T.S.Y. and Z.Q.Z. wrote the paper with input from other authors. C.F.L. and G.C.G supervised the project. All authors discussed the experimental procedures and results.

Corresponding authors

Correspondence to Zong-Quan Zhou or Chuan-Feng Li.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yang, T., Zhou, Z., Hua, Y. et al. Multiplexed storage and real-time manipulation based on a multiple degree-of-freedom quantum memory. Nat Commun 9, 3407 (2018).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.