Symmetry Protection of Photonic Entanglement in the Interaction with a Single Nanoaperture

In this work, we experimentally show that quantum entanglement can be symmetry protected in the interaction with a single subwavelength plasmonic nanoaperture, with a total volume of $V\sim 0.2{\lambda }^3$. In particular, we experimentally demonstrate that two-photon entanglement can be either completely preserved or completely lost after the interaction with the nanoaperture, solely depending on the relative phase between the quantum states. We achieve this effect by using specially engineered two-photon states to match the properties of the nanoaperture. In this way we can access a symmetry protected state, i.e., a state constrained by the geometry of the interaction to retain its entanglement. In spite of the small volume of interaction, we show that the symmetry protected entangled state retains its main properties. This connection between nanophotonics and quantum optics probes the fundamental limits of the phenomenon of quantum interference.

Figure 1

(a) Schematic of the experimental set-up for transmission of protected quantum states through the nanoaperture. (b) Scanning electron microscope image of our target structure: a circular aperture of 750 nm diameter. Scale bar of length 500 nm. (c) Variation of the set-up to directly measure the quantum interference signature. Details of the set-up can be found in the text.

Figure 2

Reconstructed real part of the post-selected density matrices. (a) and (c) $|{\mathrm{\Psi }}_{-}⟩$ and (b) and (d) $|{\mathrm{\Psi }}_{+}⟩$ incident states. (a)–(b) no nanoaperture present, (c)–(d) after interaction with the nanoaperture. The basis is given in terms of the modes arriving at the two detectors. Labels on the axis represent the following states: RR $|RR⟩$, LL $|LL⟩$, PL $|{\mathrm{\Psi }}_0⟩$, MN $(1/\sqrt{2})(|RL⟩-|LR⟩)$. The imaginary parts are consistent with being zero within experimental uncertainty.

Figure 3

(a) Normalized coincidence count rates for plus (red) and minus (blue) states as a function of the time delay between the two photons. Open markers represent the states going through the glass only, not interacting with the nanoaperture, while solid markers represent the effect after transmission through a particular nanoaperture. (b) Shows coincidences at zero delay for six different apertures (A1–A6) with nominally the same diameter and also when the states go through glass (gl). Each coincidence rate has been measured 10 times and the error bars span 1 standard deviation of the resulting distribution. The coincidences are normalized to the coincidences at very long delays (not shown in the figures).