High-Dimensional Entanglement-Enabled Holography

As an important imaging technique, holography has been realized with different physical dimensions of light, including polarization, wavelength, and time. Recently, quantum holography has been demonstrated by utilizing polarization entangled state with the advantages of high robustness and enhanced spatial resolution, comparing with classical holography. However, the polarization is only a two-dimensional degree of freedom, which greatly limits the capacity of quantum holography. Here, we propose a method to realize high-dimensional quantum holography by using high-dimensional orbital angular momentum (OAM) entanglement. A high-capacity OAM-encoded quantum holographic system can be obtained by multiplexing a wide range of OAM-dependent holographic images. Proof-of-principle experiments with four- and six-dimensional OAM entangled states have been implemented and verify the feasibility of our idea. Our experimental results also demonstrate that the high-dimensional quantum holography shows a high robustness to classical noise. What is more, the level of security of the holographic imaging encryption system can be greatly improved in our high-dimensional quantum holography.

Figure 1

OAM entanglement-enabled quantum holography. (a) The schematic of setup. IF, interference filter centred at $810\pm 3\mathrm{nm}$; SLM-$A/B$, spatial light modulator; SMF, single mode fiber; MMF, multimode fiber with core diameter $25\mathrm{\mu }\mathrm{m}$. $D\text{−}A/B$ single photon detectors; $Lc/Lf$, lens. Top side shows the design of the OAM preserved and OAM-selective hologram (see Sec. 2 in Supplemental Material [43] for details). (b) Quantum OAM-selective holographic images reconstructed with coincidence measurement by implementing the OAM decoding operators ${\widehat{P}}_A={|0⟩}_A{⟨3|}_A$, ${|0⟩}_A{⟨2|}_A$, ${|0⟩}_A{⟨1|}_A$, ${|0⟩}_A{⟨-1|}_A$, ${|0⟩}_A{⟨-2|}_A$, and ${|0⟩}_A{⟨-3|}_A$. There are $15\times 5=75\mathrm{pixels}$ in each reconstructed holographic image. Coincidence measurement for each pixel takes 15 s.

Figure 2

Principle of quantum OAM-multiplexing holography. (a) Generation of an OAM-multiplexing hologram. (b) Experimental reconstructions of holographic images based on the OAM projective measurement operators ${\widehat{P}}_A={|0⟩}_A{⟨3|}_A$, ${|0⟩}_A{⟨2|}_A$, ${|0⟩}_A{⟨1|}_A$, ${|0⟩}_A{⟨-1|}_A$, ${|0⟩}_A{⟨-2|}_A$, and ${|0⟩}_A{⟨-3|}_A$. There are $5\times 5=25\mathrm{pixels}$ and the coincidence measurement of each pixel takes 10 s.

Figure 3

Quantum OAM-selective holography in the presence of classical noise. (a) OAM-selective holographic images measured with quantum OAM holographic systems. (b) OAM-selective holographic images measured with classical OAM holographic systems.

Figure 4

Entanglement-enabled holography for high-security holographic imaging encryption. (a) Poincaré sphere composed of OAM states $|1⟩$ and $|-1⟩$. Its north and south poles represent the $|1⟩$ and $|-1⟩$. Any superposition state of $|1⟩$ and $|-1⟩$ can be represented by a point on the Poincaré sphere. (b) Design of multiplexing hologram based on OAM superposition states and its corresponding OAM-multiplexing hologram displaying on SLM-$B$. (c) Experimental OAM-selective holographic images for different decoding operators implemented with SLM-$A$.