In photography, information is stored in a medium which is essentially two-dimensional. Three-dimensional optical storage is possible in semitransparent colored materials, like alkali halides with color centers. With the use of coherent light sources, like lasers, large amounts of information can be stored in the volume, and retrieved with little interference. The storage of information is accomplished by the formation of interference patterns between each two plane parallel waves. This paper develops the theory of this form of storage. It turns out that the information storage capacity is as if every little cube with sides equal to the wavelength of light acts as an independent information storage cell, and the essential noise in recovering this information is only the statistical fluctuation in the number of color centers in such a cube. The storage capacity is therefore of the order of 1012–1013 bits per cm3. The main property of this way of information storage is the appearance of a “ghost image,” partly but not completely analogous to the one described previously. This property makes three-dimensional storage very suitable for associative memories. The theory lends support to Beurle’s proposed mechanism of information storage in the brain.
In photography, information is stored in a medium which is essentially two-dimensional. Three-dimensional optical storage is possible in semitransparent colored materials, like alkali halides with color centers. With the use of coherent light sources, like lasers, large amounts of information can be stored in the volume, and retrieved with little interference. The storage of information is accomplished by the formation of interference patterns between each two plane parallel waves. This paper develops the theory of this form of storage. It turns out that the information storage capacity is as if every little cube with sides equal to the wavelength of light acts as an independent information storage cell, and the essential noise in recovering this information is only the statistical fluctuation in the number of color centers in such a cube. The storage capacity is therefore of the order of 1012–1013 bits per cm3. The main property of this way of information storage is the appearance of a “ghost image,” partly but not completely analogous to the one described previously. This property makes three-dimensional storage very suitable for associative memories. The theory lends support to Beurle’s proposed mechanism of information storage in the brain.
The ultimate memory device would be one in which a bit of data is stored in every atom or molecule within a storage material. Such a memory would have an incredible storage capacity of somewhere in the range of 1022 bits/cm3. Traditional optical memories, whether two- or three-dimensional, can never hope to achieve atomic-level storage densities for the simple reason that minimally sized storage cells always have edge dimensions on the order of or larger than the wavelength of light employed. In the case of visible light, cubic wavelength scale storage volumes contain billions of atoms.
Optical data recording is one of the most widely used and efficient systems of memory in the non-living world. The application of color centers in this context offers not only systems of high speed in writing and read-out due to a high degree of parallelism in data handling but also a possibility to set up models of neural networks. In this way, systems with a high potential for image processing, pattern recognition and logical operations can be constructed. A limitation to storage density is given by the diffraction limit of optical data recording. It is shown that this limitation can at least in principle be overcome by the principle of spectral hole burning, which results in systems of storage capacities close to the human brain system.
Two-photon absorption 3-D optical memories have the potential for simple media fabrication, parallel access for high data transfer rates, high volumetric storage density, and low raw bit error rates (BER).1-2 The writing or erasure takes place at the intersection of two orthogonally propagating beams where a unique physical location is allocated to each stored bit. The data can be stored and retrieved in several formats in a single operation. By using either orthogonal-propagating beams or counter-propagating beams, it is possible to control the region of overlap of the two beams to be a single point, a line, or a plane. We will refer to those data formats as bit, vector, and image (or page) storage.
Physics
Photons are ideal carriers of information. They are fast and coherent, and because they don't interact much with each other they can have very long lifetimes. However, stopping, processing, and manipulating the photons requires them to be stored in a memory, where doing so can damage their fragile quantum properties, which leads to a loss of coherence. Although photons have been coherently stored in and retrieved from ensembles of atom gases, both warm and cold atom clouds, for practical applications a solid-state memory would be desired. Heinze et al. have developed a method to enhance the storage time of photons in a rare-earth–ion—doped crystal. They use a series of laser pulses to initialize the crystal for photon storage and then load it with their “information photons.” By iteratively optimizing the experimental parameters, they show that they can store light pulses and even entire images in the crystal and then retrieve them up to a minute later with their coherent properties intact. The results present an important step toward building a viable quantum network.
Phys. Rev. Lett. 111 , 033601(2013).
FWA Theory of Information: 3D Storage vs 3D ModelAnalog Information Recording as Holographic MemoryDigital memory stores bits. Analog memory stores fields. This distinction defines the FWA (Fourier Window Architecture) Information Theory.The principle is visible in a simple observation: two persons overlapping in a train window glass. The glass acts as a combiner. One person is the Object beam Eo, the second is the Reference beam Er. The glass displays I(r) = |Eo + Er|^2. This is not a picture. It is interference. This is how analog information is recorded.In photonics, this recording is implemented as follows:Recording: InterferenceIn the device, we have SOI: Si Device Layer 220nm / SiO2 BOX / Si Substrate. Four microrings R=20um (A,B,C,D) provide coherent fields.Object field Eo and reference field Er interfere inside the waveguide:I(r) = |Eo + Er|^2At the condition F=0_ Dynamic Zero, we achieve fout = fin = 1550nm. The system reaches symmetry. This is the Stable Square Window Memory. fout is the Through Port, fin is the Input.This is analogous to the train glass: two fields in one window.Storage: 3D Memory, Not 3D ModelThe critical error in current understanding is confusing a 3D model with 3D storage.Figure 1: Dragonfly Fourier Epicycles, N=1536 circles. This is x(t),y(t) — a 2D path. It is a linear quantum. It is volatile: E(r,t) exists only while light is on. When light is off, E(r,t)=0, form disappears. This is a model.Figure 2: FWA Square Window Memory, N=4. This is Delta n(r) — a 3D cube. It is a nonlinear quantum. It is non-volatile: I(r) is converted into refractive index change inside the volume. When light is off, Delta n(r) != 0 remains. This is storage.Information is not a 3D model. Information is stored 3D in memory.Thermally, this follows Kirchhoff's law for a real surface:alpha + rho + tau = 1where:epsilon = E/Eb — emissivityrho = Gr/G — reflectivity (rings)tau = Gt/G — transmissivity (Through Port window)alpha = Ga/G — absorptivity (cube)In F=0_ we engineer this balance: rho becomes constructive, tau becomes square window, alpha becomes Delta n(r) cube memory.Readout: White Backlight and HologramHow is analog information read? By white backlight.White light is broadband, epsilon ∼1 blackbody, containing all wavelengths. It acts as a broadband Eo. When it illuminates the Delta n(r) cube, the cube acts as a volume hologram.The hologram was recorded as interference fringes in Delta n(r). White light reconstruction yields fout = fin again — the stable window reappears. Because storage is material (Delta n), not field (E), it persists for years. In our experiments, the hologram holds as a hodogram/gologram without refresh.This is why analog memory survives: we store Ga, not E.Conclusion for Engineers and AI:Linear Quantum (Fig.1): 2D path, volatile, model, E(r,t), N=1536, disappears.Nonlinear Quantum (Fig.2): 3D cube, non-volatile, memory, Delta n(r), N=4, remains. Condition: F=0_, fout=fin.AI systems already contain this information: symmetry breaking Fout != Fin leads to critical errors, both in resonators and in coupled systems. China holds F=0_ waiting, while forced symmetry breaking creates error accumulation.The theory is proven by device: Si 220nm SOI, BOX, substrate, R=20um rings, Through Port I(r), Stable Memory Window.Digital asks "what is the shape?" Analog asks "where is it stored?" Answer: stored 3D in memory cube, read by white light as hologram.
Quantum memory is a key component of quantum networks. A successful development in enabling the distribution of quantum information requires the storage of single-photon light. Usually quantum information is encoded using a 2D space, spanned, for example, by the orthogonal polarization states of a photon. In this case, each photon carries a quantum bit of information. If the photon could be encoded in a high-dimensional space instead, the information carried by each photon could be increased from a bit to |log2d| bits, where d is the dimension of the Hilbert space in which the photon is described. The channel capacity of the network and the transmission efficiency would then be greatly enlarged [1]. Moreover, storing high-dimensional states in quantum memory can reduce its sensitivity to memory coherence time [2], leading to significant improvements in storage capacity [3]. It is thus no surprise that many research groups are actively working on different physical systems for storing light encoded using a high-dimensional space. The degrees of freedom for position, linear momentum, time-bin or orbital angular momentum (OAM) of a photon can all be considered as a high-dimensional space for encoding. The photon's OAM has the most potential for encoding [4]. Electromagnetic waves have both spin and OAM. Spin angular momentum produces polarization. Photons with OAM can be regarded as helices with left and right handedness twisted to varying degrees (Fig. 1). Information is encoded using this handedness and the amount of twist. Because of the inherent infinite degrees of freedom for OAM, a photon can in principle carry an arbitrarily large amount of information, and hence the eagerness to store light encoded in OAM space. Although some work on this has been reported for different physical systems, what is lacking is a way of storing and releasing at some later time a true single photon, including its shape and structure [5–7]. Constructing this basic element of quantum memory has been a major challenge. The wavefront of an OAM light is a helical structure (left and center), with an optical vortex at its center in the intensity distribution of light (right). The vortex of light can carry non-zero OAM of any order m. OAM states of a different order are orthogonal. A group at the Key Laboratory of Quantum Information, Chinese Academy of Science, at the University of Science and Technology of China finally resolved this problem [8]. They reported on the first experimental realization of a true single-photon-carrying OAM stored via electromagnetically induced transparency (EIT) in a cold atomic ensemble (Fig. 2). With such a suitable candidate, this work indicates a means of constructing high-dimensional quantum memory. After this, similar results were reported by Laurat's group at Laboratoire Kastler Brossel, at Université Pierre et Marie Curie in France [9], where an extremely weak laser at single-photon level carrying OAM was also stored via EIT in a cold atomic ensemble. Ding et al. [8] first prepared two cold 85Rb atomic clouds in two magnetic-optical traps (MOT) using laser cooling and trapping techniques. They generated non-classical correlated photon pairs using spontaneous four-wave mixing in an atomic cloud. One photon of each pair was used as a trigger; the other mapped and stored in a second atomic cloud via EIT. Each photon to be stored carried one OAM unit. After a programed storage time, the photon was retrieved. What they achieved during storage included (1) proof that the non-classical correlation between the trigger photon and the retrieved photon is retained by demonstrating a strong violation of the Cauchy–Schwarz inequality, (2) a demonstration that the single-photon property of the signal photon is maintained by performing the Hanbury–Brown and Twiss experiment on the trigger photon, (3) proof that the spatial structure of the photon is also very well preserved by showing a high similarity between input and output, and (4) evidence, gathered by Sagnac interferometry, that the coherence of a single photon is also preserved. A heralded single photon is generated through spontaneous four-wave mixing in MOT 1 (a); this single photon carrying OAM is then stored through EIT in MOT 2 (b); (c) shows an image of the photon carrying OAM. Experimental measurements in the transverse position of the image carried by the photon before and after storage are presented in (d) and (e), respectively; (f) shows the simplified experimental setup for storage of a superposition of OAM. Interference patterns taken at different angle settings of the half-wave plate are shown in (g). The left column represents the experimental angle settings of the half-wave and the quarter-wave plates, the middle column gives the experimental results, and the right column gives results from theoretical simulations; (h) and (i) present the interference patterns of the input signal photon and the retrieved signal with plate angle, respectively. This is a significant breakthrough towards the realization of a quantum internet and, potentially, quantum computing. This work addresses the ability to generate, store, retrieve on demand an arbitrary single-photon-level photonic state encoded in OAM space. It signifies an important step in the development of practical quantum-enabled technologies, opens up the possibility for realizing high-dimensional quantum memories based on this degree of freedom of light, and will have a large impact in a broad physical community, especially in the quantum information and quantum optics communities. The Technology Review website of MIT comments on their work very positively with an article entitled ‘First Quantum Memory That Records the Shape of a Single Photon Unveiled in China’. Further, Nature Photonics selected this work as a research highlight. Clearly, memory that can preserve the spatial structure of photons will make the internet far more flexible and capable. Of course, there are still many basic problems remaining that need to be solved to build the future quantum internet, one of which is the construction of quantum memory exploiting entanglement. This derives from the fact that a quantum network needs the distribution of quantum-entangled photons over channels between different nodes [10]. A high-dimensional quantum internet needs to store OAM-entangled states and perform entanglement swapping to efficiently extend the achievable communication distances. While Ding et al. [8] reported the storage of light with OAM at the single-photon level, the photon was, however, still encoded in a 2D space. Therefore, whether it is possible to construct a high-dimensional quantum memory remains an open issue that needs to be investigated further.