The protective effect of symmetry in entangled photonic states

One of the most mysterious features of quantum mechanics is that if two particles (or photons) interact at some point in time then the properties of these particles will remain connected at future times. A consequence of this is that determining the quantum state of one of the particles simultaneously determines the quantum state of the other, even isf the two particles are very far apart.

This connectedness between particles was called entanglement by Erwin Schrödinger in a paper published in 1935 in which he emphasized that it is a key feature of quantum mechanics that distinguishes it from classical physics.

For many years quantum entanglement was a purely theoretical topic of interest to people concerned with the philosophical foundations of quantum mechanics. This situation changed dramatically in 1964 when John Bell showed theoretically that experimental tests could be carried out to see whether the idea of quantum entanglement was correct. The first experiments to investigate quantum entanglement were performed by Alain Aspect and his colleagues in the 1980s. They showed that quantum entanglement is a real phenomenon.

The quantum properties of light can be used as a resource in applications such as communication, computation, and sensing. However, most of the achievements in quantum photonics are hindered by the same limitations as the classical processing of light: weak interactions with matter, which impede efficient nonlinear processes, and large devices with dimensions many times the wavelength of light (λ).

Plasmonic devices may hold the key to overcome these hurdles due to strong interaction with light, small volumes of interaction, and the possibility to engineer and fabricate suitable nanostructures to address particular tasks. It has been shown that quantum correlations of propagating photons can survive the interaction with plasmonic structures with a total size much larger than λ. But the fundamental question of whether photonic quantum entanglement can be processed or even survive the interaction in the sub-wavelength regime is still unanswered.

Now, a team of researchers, including Ikerbasque Research Professor Gabriel Molina-Terriza (CFM & DIPC), has shown 1 experimentally (see Figure 1) that symmetry protected quantum entangled photonic states can interact with a single nanostructure with a total volume of V ∼ 0.2λ3 without being affected.

FIG. 1. (a) The experiment uses specially engineered two-photon states to match the properties of the nanoaperture. The two-photon generation is performed through spontaneous parametric down conversion in a collinear configuration. The maximum Hong-Ou-Mandel interference visibility, attesting the two-photon indistinguishability, was limited by the frequency spectrum of the photons. The temporal overlap of the two generated photons was precisely controlled using a birefringent delay. A critical step in order to access the symmetry protected subspace for interaction with the nanoaperture is to transform the modes of the photons to those with total angular momentum zero. This step is achieved with a “q plate” that transforms the photons to the required modes. A half-wave plate placed before the q plate allows to select either the preferred state. The prepared two-photon state is then strongly focused with a microscope objective and subsequently collected with a second microscope objective to be finally analyzed. (b) Scanning electron microscope image of the 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.

The researchers work with a simple nanostructure consisting of an isolated circular aperture (Figure 1, b). This kind of structure is versatile and has been used for nanotrapping experiments and classical sensing of molecules, and is essential in near field optical microscopy experiments. Their choice of the nanostructure was motivated by its high symmetry and the fact that it has been thoroughly studied. Even though there is no analytical solution of the Maxwell equations for this structure, many interesting properties have been found both theoretically and experimentally. In summary, a circular nanoaperture can simply be described as a (lossy) beam splitter where the modes are mixed in polarization—the two helicities—instead of being mixed into two different propagation directions.

The researchers demonstrate that, despite the extreme changes the electromagnetic modes undergo through strong focusing and the interaction with the nanostructure, by exploiting the symmetries of the system it is possible to engineer entangled states that are protected against decoherence and unwanted transformations in the absence of losses. Also that this interaction strongly depends on the quantum phase between the entangled modes in such a way that a π phase shift between the relative amplitudes of the states can be distinguished through the interaction with the nanostructures. From a fundamental point of view, this is a result of the important impact that this quantum phase has on the symmetry of the two-photon state. Such a difference survives in the sub-wavelength regime, opening a promising approach to study the intricate interplay between plasmonics and quantum optics.

This work should help in finding ways to keep delicate quantum information from being destroyed in future nanoscale chips.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance.

References

  1. Alexander Büse, Mathieu L. Juan, Nora Tischler, Vincenzo D’Ambrosio, Fabio Sciarrino, Lorenzo Marrucci, and Gabriel Molina-Terriza (2018) Symmetry Protection of Photonic Entanglement in the Interaction with a Single Nanoaperture Phys. Rev. Lett. doi: 10.1103/PhysRevLett.121.173901

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