Fig. 1. Quantum holograms based on metasurface-enabled polarization–hologram entanglement. (a) Two holographic states generated with LCP/RCP light incidence. The two holographic fields share the same amplitude distribution but have tailored relative phase relationships. (b) Schematic for polarization–hologram entanglement generation with an entangled photon pair and a geometric-phase metasurface. A pair of entangled photons (idler and signal) is generated through a nonlinear crystal. The signal photon goes through a metasurface, generating the polarization–hologram entangled state. Inserting and rotating the polarizer in the idler arm reveals different quantum holographic contents of the signal photon.

Fig. 2. Metasurface design. (a) The modified GS algorithm to design two phase profiles that generate two holograms with a designed phase relationship. The inputs are the target hologram amplitude |ψL/R| and the phase relationship Arg(ψL/ψR). The outputs are two phase mask profiles, φL and φR. (b) The metasurface profile for a geometric-phase metasurface. The metasurface profile is obtained by combining φL and φR from the modified GS algorithm with converging lens and diverging lens profiles, respectively. (c) The SEM image of the metasurface. The metasurface uses a geometric phase design. The period of the unit cell is 0.7μm, and the rotation angle of the grating is half of the phase profile from Eq. (2).

Fig. 3. Experimental setup and results. (a) The experimental setup. A 405-nm laser shines on a type-II β-barium borate (BBO) to generate polarization-entangled photon pairs, i.e., idler photon in the upper arm and signal photon in the lower arm. The signal photon interacts with the metasurface, and the generated hologram is imaged on the camera, which is correlated with the idler photon detection. (b) The signal photon’s hologram shown without a polarizer (eraser) in the idler arm. (c)–(f) The holograms with different polarizers in the idler arm. The polarizer configured in horizontal (H), diagonal (D), vertical (V), and antidiagonal (A) positions erases the corresponding letter in the holographic results.

Fig. 4. Quantum hologram interference with erasing effect. (a) The interfered holographic image with different polarization projections in the signal arm when an H eraser is inserted in the idler arm. (b) Average intensity variation for individual letters with changing signal polarization angles when the eraser is inserted (on) and removed (off).