As a technology that exploits the interference of light to record and reconstruct objects with their full information^[1], holography has achieved great success in the diverse areas of data storage^[2–4], microscopy^[5–7], three-dimensional (3D) display^[8–10], nanofabrication^[11–13], and optical security^[14,15]. One of the main advantages of holography is that rich 3D information about objects can be recorded and truly restored, especially with the growth of computer-generated holograms^[16,17]. In recent years, holography has been combined with nonlinear crystals, leading to cross-band holographic information processing. In the frequency up-conversion field, the design of the 3D nonlinear crystals makes it possible for implementing multiplexing holography and 3D holography at the second-harmonic band through marvelous quasi-phase-matching conditions^[18,19]. In the frequency down-conversion field, the feature of visualized information reproduction of holography is found to be useful in quantum information^[20–24] for two main applications. The first one serves as an efficient method for the characterization of the single-photon and two-photon states (wavefunction), overcoming the issue of time consumption with massive projective measurements^[21,25]. Another direction is the holographic imaging of objects with the quantum correlation between the twin photons at the single-photon level with improved imaging quality, so-called quantum holography^[20,22,23].

Coincidence imaging is the main approach for implementing quantum holography, in which interference between two remote but correlated photons plays a leading role in the holographic reconstruction process. Holography through quantum illumination^[26,27] is a typical example that exhibits great shielding ability against classical noises. In the years of 2019 and 2021, quantum holography assisted by high-dimensional spatial entanglement^[22] and polarization-spatial hyperentanglement^[23] of twin photons is demonstrated separately. Both of them use two intensified CCDs to record the twin images by illuminating the hologram either by twin photons or one-side photons (another image serves as a reference image). The image reconstruction is then realized by spatial intensity cross-correlation calculation (usually points by points) of the twin images. Induced coherence^[28,29] is another approach to implementing quantum holography^[30], which combines the induced-coherence quantum imaging protocol with digital phase-shifting holography^[31]. Similarly, both phase and amplitude information of objects should be figured out from several holographic images with different phase steps.

In the above-mentioned quantum holography, the object’s information is all hidden in the original obtained images, which are inaccessible directly; thus the post-processing of the images is an essential step for retrieval of the information. Last year, by combining high-capacity orbital-angular-momentum (OAM) holography^[32–35] with a quantum entangled light source, high-dimensional entanglement-enabled holography was realized for breaking the information channel limit of polarization-entanglement-assisted holography and enhancing quantum information security^[36]. However, point-by-point scanning for the coincidence measurement between two single-photon detectors was adopted, making the imaging process quite time-consuming. Moreover, detailed information of pixels is removed because of the natural spatial filtering of the single-pixel detector. This makes it difficult to examine the OAM status of each image constituent unit, although it is at the heart of OAM holography. Moreover, the scanning method makes it challenging to present 3D OAM holography in the quantum version from both aspects of experimental difficulty and long measurement time.

Here, we implement visualized 3D holography using a direct coincidental imaging protocol assisted by OAM entanglement of photon pairs. A single intensified CMOS (ICMOS) camera is used to directly display the desired holographic images with OAM encoding, free of additional post-processing or scanning. As shown in Fig. 1(a), the OAM multiplexing hologram is loaded on the signal path with three information channels’ encoded OAM values equal to 3, 1, and −2, respectively, and each information channel possesses two Fourier-transform holograms at different imaging planes. The decoding of the hologram for displaying the desired images relies on switching the OAM state of the idler photons based on the entanglement, as well as adjusting the position of the ICMOS camera. Therefore, we realize visualized OAM-multiplexing 3D holography in the quantum regime. Owing to the visualized display, both OAM preserving holography and OAM selective holography can be implemented in a short duration, meanwhile reserving all the detailed information of pixels that make up an image, which directly verifies the OAM conservation law in the quantum OAM holography. The extension of two-dimensional (2D) holography to 3D holography proves the ability of holographic manipulation of the 3D wavefront in the quantum regime, promoting future ultrahigh-capacity OAM information processing, such as 3D displays^[37], holographic microscopy^[7], and virtual and augmented reality^[38], to work at the single photon level.

The key to OAM holography is preserving the OAM property for all image constituent units so that each OAM value can serve as an individual information channel, which is also crucial in quantum OAM holography. The main difference in quantum OAM holography is that the incident helical wavefront illuminating the hologram is controlled by the OAM entanglement shared by the photon pairs. The principle of our protocol is illustrated in the experimental setup described in Fig. 1(b). A wide collimated pump light with a wavelength of 405 nm passes through the periodic-poled KTP (PPKTP) crystals for generating OAM entangled photon pairs with a wide spiral (OAM) bandwidth^[39–41] under a type II degenerate quasi-phase matching condition. The continuous wave (CW) pump light has a beam width of approximately 1 mm and a power of 20 mW to ensure a sufficient coincidence rate meanwhile suppressing the multiphoton events (the power density inside the nonlinear crystal is relatively low). The OAM entangled state can be expressed as |Ψ⟩=∑l=−∞l=+∞cl|l⟩s|−l⟩i,(1)when only the angular dimension is considered^[42,43]. It indicates the existence of the probability amplitude of cl to produce a signal photon with an OAM of lℏ and an idler photon with an OAM of −lℏ (see Sec. 1 in the Supplementary Material for revealing the entangled two-photon state). The filter after the crystal rejects the pump light and restricts the bandwidth of photon pairs to approximately 10 nm. Signal and idler photons with the same central wavelength of 810 nm are commonly expanded 3 times and then separated by polarization. For both signal photons and idler photons, a spatial light modulator (SLM) is placed on the imaging plane of the nonlinear crystal for maximum OAM correlation of the twin photons. A forked grating function with an order of −li is loaded on SLM-A on the idler path for selective projection of photons with a state of |li⟩i into a single-mode fiber that is connected to a silicon-based single-photon avalanche diode (SPAD). The post-selection of the idler photons can lead to a post-selection operator of A^=|0⟩i⟨li|i on the idler arm. The effect of the post-selection operator for achieving an OAM carrying beam on the signal arm can be found in Sec. 2 in the Supplementary Material.

In our quantum holography configuration, the joint measurement is realized by triggering the ICMOS camera with idler photon events. To compensate for the inherent time delay of the camera and the SPAD, a 35 m delay line consisting of multiple image-transmission 4f systems is used for ensuring SLM-B at the imaging plane of the nonlinear crystal. This delay line achieves synchronism for detecting each photon by the ICMOS camera and its sibling photon recorded by the SPAD. The OAM preserving, selective, and multiplexing hologram is loaded on SLM-B. Detailed information on generating these holograms and realizing quantum OAM holography can be found in Sec. 3 in the Supplementary Material.

Different from the scanning approach^[34] using the single SPAD with which only the basic Gaussian modes of the image composition unit can be detected, all the pixel features in our system can be faithfully recorded by the ICMOS camera to directly research the OAM conversion and conservation situations so that our system provides an efficient way to fully characterize quantum OAM holography. The OAM preservation property is the prerequisite for implementing an OAM holography since it determines whether an individual OAM can serve as an information carrier. For OAM preserving holography as demonstrated in Fig. 2(a), post-selection of the idler OAM states of li=|1⟩ and the OAM superposition state of li=12(|2⟩+|−2⟩) [not shown in Fig. 2(a)] is adopted for providing an OAM carrying illumination for the OAM-preserved holograms (the letters “I” and “P,” respectively) in the signal arm through coincidental measurement while OAM encoding in the hologram is absent (lsn=0). The generation process of the OAM preserved hologram is also displayed under SLM-B in Fig. 2(a) with its sampling array period exceeding the maximum required spacing of the encoding OAM value^[32]. The reconstructed images of the letters “I” and “P” are recorded by the ICMOS camera, in which each pixel inherits the distribution of the corresponding signal photon’s state, as can be found in Fig. 2(b). The single OAM state of the pixel of the letter “I” can be further verified by an astigmatic transformation pattern [as can be seen in the enlarged illustration in Fig. 2(b)], in which the number of dark stripes represents the order of l and the direction of stripes represents the sign of l (more detailed information can be found in Sec. 4 in the Supplementary Material)^[32]. In our case, we can judge that these pixels inherit the signal photon’s OAM with ls=−li=−1. The superposition state of the pixels that compose the letter “P” can be directly observed by the image itself since the petal shape of pixels is unrotated compared to the amplitude distribution of the signal state of ls=12(|−2⟩+|2⟩). The projection measurement results of the superposition state indicated by coincidence rates under multiple projection measurements on SLM-B also prove the statement (see Sec. 2 in the Supplementary Material for detailed information).

The implementation of OAM selective holography is shown in Fig. 2(c), which is the most convenient approach to utilizing the OAM preservation feature. The main difference between Figs. 2(c) and 2(b) is that OAM values of lsn=|1⟩ and lsn=12(|2⟩+|−2⟩) are separately encoded in the holograms; thus, a reconstructed image composed of pixels with the basic Gaussian mode emerges on the camera [as can be found in Fig. 2(c)] according to Eq. S(4.4) in the Supplementary Material. The OAM preserving and selective results commonly indicate that the OAM conservation law is also satisfied in quantum OAM holography in an indisputable way. The reconstruction progress of both the OAM preserved holography and OAM selective holography is recorded by the ICMOS in an accumulated exposure mode with an external trigger. For each trigger by an idler photon event, the ICMOS has a gate width of 3 ns to ensure that only the correlated single photon event is registered, which greatly protects the signal from environmental noise during the measurement time, and each image is acquired with a 30 s integral time. For a simple comparison, observing the detailed information of each pixel in OAM preserved holography using the fiber scanning method takes approximately 20.8 h^[36], which is thousands of times longer than the protocol we used. Besides, the OAM value of each pixel in the scanning configuration is unable to be intuitively known since most OAM values cannot be inferred only from the donut-shaped intensity. The superposition state used here can not only reveal the capability of intuitively displaying the complex OAM structure of each pixel in our system but can also greatly improve the security of holographic imaging encryption since only by mastering all the information of this superposition state (the precise amplitude and phase of its basis states) can one decode the corresponding image by applying the correct heralding superposition state.

The OAM selectivity in quantum OAM holography can be easily extended to implement OAM multiplexing holography, in which only a clear image can stand out from a multiplexed hologram under the correct post-selection of the idler photons. As can be found in Fig. 3(a), three letters of “I,” “P,” and “C” are encoded with different OAM values of lsn=3, 1, and −2, respectively, to form an OAM multiplexing hologram. The principles of choosing the OAM values to be multiplexed in quantum OAM holography are similar to classical OAM holography. However, the spiral bandwidth of the quantum light source limited the available OAM values. This is because only a sufficient triggering rate of an OAM state can ensure fast imaging, and the image can stand out from the background environment. In our system, an OAM value of |lsn|≤4(|li|≤4) is suitable for efficient holographic imaging. In this situation, for high-capacity multiplexing in quantum OAM holography, superposition states may be considered since they possess larger freedom in both relative phase and amplitude. Without loss of generality, we display the performance of the holographic reconstruction of the letter “C” with post-selection of the heralding idler photon with the OAM states of li=−2. We can find that only the letter “C” is reconstructed with basic Gaussian modes, and the other two letters present a distinct donut structure, which indicates that they inherit the remaining OAM values (lsn−li). It is worth noting that the result in Fig. 2(a) is an original image without subtracting any background noise, in which the pixel feature of the three letters is clearly distinguishable. Heralding the holographic reconstruction of images with the other two OAM states (li=3 and li=1) of idler photons similarly gives prominence to the other two letters with the basic Gaussian mode. An aperture array^[32] can be further applied to these results in post-processing to uniquely extract the three images independently, where donut structures are rejected by the aperture array, as can be seen from Fig. 3(b). The integral time for reconstructing an image from an OAM multiplexing hologram is 100 s.

True-to-life recreation of 3D objects is the significant advantage of holography that distinguishes it from conventional 2D display technologies. Implementing quantum holography in a 3D architecture will provide an additional information-encoding freedom to expand the information capacity and pave a new way of holographic manipulation of the 3D wavefront in the quantum regime. Meanwhile, displaying 3D images through quantum holography may promote virtual reality and augmented reality scenes toward the single-photon level. On this basis, 3D OAM holography is first demonstrated for the quantum version. An OAM multiplexing hologram with three OAM channels and two imaging planes is prepared^[44], which can be described as $$\begin{gathered} H3d(x,y)=∑n=12∑sn=13F{0sn,n(u,v)} \\ ·exp(jlsnφ1)exp[−jπλzn(x2+y2)], \end{gathered}$$(2)in which H3d(x,y) is a 3D hologram. F is a discrete Fourier transform, and the subscripts sn and n stand for the serial number of the encoded OAM value and imaging plane. The parabolic phase with a parameter of zn is additionally encoded on the hologram to ensure that the desired images are retrieved at a specific distance (zn) away from the focal plane of lens FL by compensating this parabolic phase term through Fresnel holography^[45].

In our experiment, three letters of “I,” “P,” and “C” are encoded with OAM values of lsn=3, 1, and −2, respectively, with z1=0. Three digits of “5,” “2,” and “0” are encoded with the same OAM values (lsn=3, 1, and −2) separately but another z2 of 0.3 m. On-demand readout of these six images can be realized by switching the post-selection of the photon’s OAM state with li=3, 1, and −2, respectively, and simultaneously adjusting the position of the ICMOS camera. Figure 4(a) displays the 3D reconstruction results of the six images, in which an aperture array is adopted to improve the imaging quality. These images are all reconstructed with an integral time of approximately 200 s. The accumulation time for acquiring a clear image in our coincidental imaging system mainly depends on the overall brightness of the quantum light source and the amounts of the multiplexed images in a hologram. The former determines the whole effective trigger events per second, and the latter determines the proportion of these effective triggers assigned to each image. This is the reason that the accumulation time increases from a single OAM-selective hologram to a 2D multiplexing hologram and then to the 3D multiplexing hologram with an increase in the image capacity. Meanwhile, different heralding OAM states also affect the holographic imaging speed to a certain extent due to the different components they occupy in the entangled state, leading to different trigger rates for these images. In our experiment, the heralding OAM states of li=3, 1, and −2 are selected to ensure they all have considerable trigger rates. For 3D OAM multiplexing holography in which the image capacity is fixed, the imaging speed can be accelerated by improving the overall brightness of the quantum light source, e.g.,  replacing the pump CW light source with a high-repetition-rate pulsed laser. The distinguishable depth of 3D images is also explored in our system. As can be seen from Fig. 4(b), when the axial distance of the second imaging plane z2(compared to the first imaging plane of z1=0) is shortened, crosstalk emerges as a hindrance to extracting the desired image. The crosstalk between the two imaging planes is measured by detecting the imaging performance with a series of axial distances using the signal-to-noise ratio (SNR)^[32]. We can find the SNR drops quickly until the axial distance is shortened to approximately 20 mm. Therefore, in the distance of 0.3 m we selected, there are at least 15 planes to encode information, which further improves the information capacity of quantum OAM holography.

In this work, a visualized quantum OAM holography is demonstrated for both comprehensively revealing all the details of the quantum version of the OAM holography and proving the 3D holographic imaging function. In contrast to the previous experiment that reconstructs the image in a scanning configuration, visualized holography greatly accelerates the holographic reconstruction process, meanwhile retaining the spatial distribution information for each image composition unit, which is the key to encoding information with each individual OAM value. Moreover, simplification of the setup makes 3D holography with single-photon heralding possible; after all, 3D projection of objects using the scanning method is extremely complicated and challenging for massive alignment requirements. Compared to other quantum holography protocols, directly utilizing OAM correlation of photon pairs instead of retrieving second-order correlation information between many original images makes the holographic imaging process more efficient and convenient with a great reduction of computational complexity.

It is promising to involve our quantum OAM holography in the regime of secured communication. On one hand, long-distance transmission of OAM states^[46,47] makes remote control of the information in the holographic display terminal possible. On the other hand, the improved security level verified in Ref. [36] using the quantum superposition states and excellent noise resistance performance (as can be verified in Sec. 5 in the Supplementary Material) makes the communication process more secure and robust. The combination of these two terms with our fast visualization imaging even in a 3D scene may lead to a high-capacity data exchange.

In conclusion, we demonstrate a scanning-free quantum OAM holography using a coincident imaging technique based on the OAM correlation characteristic of twin photons. The visualized imaging at the single-photon level paves the way for direct observation of OAM preserving and conservation features in quantum OAM holography. An extension of quantum OAM holography to the 3D scene is also demonstrated with three OAM information channels and two axial positions. As an integration between holography and quantum optics, our approach can both offer secure solutions in quantum communication and promote OAM information processing technologies^[48–51] to work at the single-photon level.