Wave-Particle duality of single surface plasmon polaritons Marie-Christine Dheur1, Jean-Jacques Greffet1, Gaétan Messin1, Eloise Devaux2, Philippe Lalanne3, Thomas Ebbesen2, François Marquier1 1

Institut d’Optique Graduate School, CNRS, Université Paris-Sud, Laboratoire Charles Fabry, Palaiseau, France 2 Institut de Science et d’Ingénierie Supramoléculaire, Université de Strasbourg, Strasbourg, France 3 Institut d’Optique Graduate School, CNRS, Laboratoire de Photonique, Numérique et Nanosciences, Bordeaux, France [email protected]

Abstract: We use a plasmonic beamsplitter in an interferometer to demonstrate the wave-particle duality of surface plasmon polaritons lying on a plane gold surface. The particle or wave behavior is chosen with the orientation of a half waveplate. OCIS codes: (240.6680) Surface plasmons; (270.5290) Photon Statistics

Surface plasmon-polaritons (SPPs) result from collective oscillations of free electrons coupled to an electromagnetic field at a plane interface between the metal and a dielectric medium. As well as photons, SPPs can be considered either as waves or as particles [1,2] and they can experience striking quantum,effects such as Hong-Ou-Mandel effect [3], entanglement [4] and one of the most remarkable one: wave-particle duality. Although demonstrated for guided plasmons supported by a nanorod [5], to our knowledge, wave-particle duality has not been tested yet on SPPs propagating on a simple plane metallic interface. We reproduce here for SPPs the well-known experiment from Grangier and co-workers [6] showing this dual behavior. The SPPs are created and detected by coupling single photons to nanostructured couplers etched on an optically thick gold film. A SEM top view of the device supporting surface plasmons is shown in Fig. 1. On the left and bottom of the picture are two surface plasmons launchers. When illuminated by a beam at normal incidence, surface plasmons are created and propagate toward a plasmonic beamsplitter, consisting in two grooves. After separating the surface waves, two diffracting slits allow the coupling back to photons on the backside of the sample through a solid immersion lens.. Two detectors (avalanche photodiodes APD A and B) collect the signal from these slits.

Fig. 1. SEM image of the plasmonic device. On the left and bottom, surface plasmons launchers. In the center, a plasmonic beamsplitter. On the right and top, two diffracting slits which allow the coupling of surface plasmons to photons in the glass on the backside of the sample.

A parametric down-converted photon pair source is used as a heralded single photon source. The heralded single photon is sent in a Mach-Zehnder interferometer in which we can choose at the entrance to follow a single path or both arm’s paths by changing the orientation of a half waveplate. The last beamsplitter of the interferometer is the plasmonic device shown in Fig. 1. The particle-like behavior is tested with Hanbury-Brown-Twiss experiment by sending a single heralded photon on one single path of the interferometer. A single SPP is excited and illuminates the splitter. We measure in Fig. 2 the intensity correlations between the two output ports while increasing the pump power on the parametric crystal. A clear anti-correlation is observed, demonstrating the particle behavior: the SPP is either on one output port or on the other. Following ref.[7], we find a linear fit with respect to the photon pair creation rate in our time resolution, in excellent agreement with the theory.

0.6 0.5 PAB/PAPB

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Fig. 2. Intensity autocorrelation 𝑔 ! 0 for the single photon source with respect to the collected photons pairs rate. A clear anti correlation behavior of single surface plasmons is observed (PAB tends to zero when the probability to have double pairs into the time resolution decreases). The dashed line is a linear fit corresponding to the theory developed in [7].

The wave-like behavior of the SPP is tested when we choose to follow both paths in the interferometer. We observe in Fig. 3 fringes with a visibility of 77%, demonstrating the wave behavior of the single SPP. In these experiments, the plasmonic interferometer layout is similar to the usual free-space experiments with single photons, which makes it easy to compare the results with the fundamental wave-particle duality of photons experiments [6].

APD+A+rate+(counts/s)

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Fig. 3. Individual count rate detected on APD A for a single SPP source with respect to the path difference introduced by the observer between the two arms of the Mach-Zehnder interferometer.

Experimental demonstration of this quantum property is essential to further validate the quantum description of SPPs and for future applications in quantum communication mediated by SPP. The research was supported by a DGA-MRIS and scholarship. [1] JM Elson and R.H. Ritchie, Phys. Rev. B 4, 4129 (1971) [2] A. Archambault et al., Phys. Rev. B 82, 035411 (2010) [3] J.S. Fakonas et al., Nat. Phot. 8, 317 (2014) [4] E. Altewischer et al., Nature 418, 304 (2002), Chang, Nature Phy., (2007) [5] R. Kolesov et al. , Nat. Phys. 5, 470 (2009) [6] P. Grangier et al., EuroPhys. Lett. 1, 173 (1986) [7] O. Alibart et al., Opt. Lett. 30, 1539 (2005)