Experimental Observation of Quantum Talbot Effects

We report the first experimental observation of quantum Talbot effects with single photons and entangled photon pairs. Both the first- and second-order quantum Talbot self-images are observed experimentally. They exhibit unique properties, which are different from those produced by coherent and incoherent classical light sources. In particular, our experiments show that the revival distance of two-photon Talbot imaging is twice the usual classical Talbot length and there is no net improvement in the resolution, due to the near-field effect of Fresnel diffraction, which is different from the case of previous proof-of-principle quantum lithography experiments in the far field.

Figure 1

Top: Experimental setup for first-order single-photon Talbot self-imaging. (a) Theoretical plot of the single-photon Talbot imaging carpet where $x$ is the transverse position across the beam and $z_2$ the longitudinal position. The color bar denotes the relative intensity. (b)–(d) present the experimental results (open circles) of CCs for effective diffraction lengths: (b) $Z_a=z_T$ ($z_2=20\mathrm{cm}$), (c) $Z_a=(1/2)z_T$ ($z_2=6.6\mathrm{cm}$), and (d) $Z_a=(1/4)z_T$ ($z_2=2.85\mathrm{cm}$). The solid lines are theoretical curves. The red filled circles in (a) indicate the self-imaging positions corresponding to the experimental observations.

Figure 2

Top: Experimental setup for two-photon second-order Talbot self-imaging in the ghost interference scheme. The open circles in (a)–(c) are the coincidence counts for effective diffraction lengths of (a) $Z_b=(1/4)z_T$ ($z_i=12\mathrm{cm}$, $z_{s1}=8\mathrm{cm}$, $z_{s2}=20\mathrm{cm}$), (b) $Z_b=(1/2)z_T$ ($z_i=25\mathrm{cm}$, $z_{s1}=15\mathrm{cm}$, $z_{s2}=40\mathrm{cm}$), and (c) $Z_b=z_T$ ($z_i=25\mathrm{cm}$, $z_{s1}=55\mathrm{cm}$, $z_{s2}=80\mathrm{cm}$). The solid lines are theoretical curves.

Figure 3

Top: Experimental setup for two-photon second-order Talbot self-imaging in the quantum lithography scheme. The open circles are experimental data observed for effective diffraction lengths of (a) $Z_c=(1/2)z_T=11.25\mathrm{cm}$, (b) $Z_c=z_T=22.5\mathrm{cm}$, and (c) $Z_c=2z_T=45\mathrm{cm}$. Left and right parts correspond to the entangled two-photon source and the coherent light source, respectively. The solid lines are theoretical curves.

Figure 4

Talbot self-imaging carpets plotted for a grating illuminated by (left) a two-photon entangled source and (right) a classical plane wave source. The red filled circles indicate the three self-imaging positions of Fig. 3.