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Physical Review Applied

Control of Geometric Phase by Dynamic Phase

Aleksi Leinonen, Taco D. Visser, Ari T. Friberg, Tommi K. Hakala

Published Jan 18, 2024• 2 citations
Publisher

Abstract

The geometric and dynamic phases are generally treated as independent and together give rise to the total phase of a system. Here, we present a scenario in which these two phases become strongly interdependent. We achieve this by introducing a modified Young's double-slit configuration that supports surface plasmon polaritons (SPPs) propagating between the slits. Remarkably, by varying the slit separation distance, and hence the dynamic SPP phase, by just a single plasmon wavelength, the geometric phase can be significantly modified.

DOI
10.1103/physrevapplied.21.014033

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The geometric and dynamic phases are generally treated as independent and together give rise to the total phase of a system. Here, we present a scenario in which these two phases become strongly interdependent. We achieve this by introducing a modified Young's double-slit configuration that supports surface plasmon polaritons (SPPs) propagating between the slits. Remarkably, by varying the slit separation distance, and hence the dynamic SPP phase, by just a single plasmon wavelength, the geometric phase can be significantly modified.
Surface plasmon polaritons (SPPs) result from collective oscillations of free electrons coupled to an electromagnetic field at a plane interface between a metal and a dielectric medium. As photons, SPPs can be considered either as waves or as bosonic particles [1] and they can experience striking quantum interferences such as Hong-Ou-Mandel (HOM) effect [2]. We use in this paper a plasmonic platform (Fig.1) that can convert photons into plasmons, and separate or recombine them on a plasmonic beamsplitter [3]. Single SPPs are excited using single photons created by parametric down conversion into a periodically-poled KTP crystal. The platform is placed in a Mach-Zehnder interferometer in order to vary the path difference between SPPs before impinging on the beamsplitter. The setup allows us to revisit quantum optics experiments using SPP as carriers of the quantum of energy. Using the same device, we can test the wave-particle duality, two-particle (HOM) interference and non-local control of single plasmon interference using the entanglement between a photon and a SPP [4]. In the case of the HOM experiment, we demonstrate that the losses can be used as a new degree of freedom [5]. Playing with the dephasing between transmission and reflection coefficient of the beamsplitter, we can observe a peak instead of the usually expected dip in the HOM interference (Fig.2), i.e. an anti-coalescence effect of SPP. In this talk, we will introduce the plasmonic device main features as well as the different quantum plasmonics experiments that have been performed thanks to the SPP beamsplitter. These results are essential to understand the SPP quantum behavior or to develop hybrid plasmon-photon systems for potential future applications in quantum communication mediated by SPP. [1] JM Elson and R.H. Ritchie, Phys. Rev. B 4, 4129 (1971) [2] J.S. Fakonas et al., Nat. Phot. 8, 317 (2014) [3] M.C. Dheur et al. , Sc. Advances 2, e151574 (2016) [4] M.C. Dheur et al. ArXiv 1610.07493, B. Vest et al. ArXiv 1610.07479 [5] S. Barnett et al., Phys. Rev. A 57, 2134 (1998) Fig.1: Plasmonic platform used for the quantum optics experiment (B). It consists in two SPP launchers (A), a plasmonic beamsplitter, and two slits to convert SPP to photons in the glass substrate. The plasmonic interference can thus be probed using single photon counting modules. Fig2: HOM experiment on a lossy plasmonic beamsplitter, whose complex amplitude reflection and transmission factors are denoted r and t respectively. The usual HOM dip is observed when r = it (left), a peak in the coincidence rate is shown when r = t.
In this paper, we study a dielectric under a squeezed vacuum state, a thermal field and a normal vacuum state. The dielectric atoms are considered to be in a three-level lambda type configuration, where a weak probe field induces and generates surface plasmon polaritons (SPPs) at the silver and dielectric interface. Therefore, to get deeper insights into the dispersion and absorption spectra, the propagation length as well as the skin depth, we investigate the coherence of the system. Hence, we demonstrate thatthe strong laser used to couple the intermediate level to the upper excited state, has a drastic effect on the generated SPPs wavelength at the interface. Additionally, the system properties are fully controlled by the average photon number, the thermal field, the normal vacuum and the squeezed vacuum state. Finally, in an attempt to elaborate a straightforward technique that manipulates the Lsp ( surface plasmon length ) distance we control the system by simultaneously tuning the phase and the control field in a very specific detuning region. This might be of interest to the engineering of miniature nano-photonic devices and circuits where the sub-wavelength property is required.
Previous experiments have shown that surface plasmon polaritons (SPPs) preserve their entangled state and do not cause measurable decoherence. However, essentially all of them were done using SPPs whose dispersion was in the linear “photon-like” regime. We report in this presentation on experiments showing how transition to “true-plasmon” non-linear dispersion regime, which occurs near SPP resonance frequency, will affect quantum coherent properties of light. To generate a polarization-entangled state we utilize type-I parametric down-conversion, occurring in a pair of non-linear crystals (BiBO), glued together and rotated by 90 degrees with respect to each other. For state projection measurements, we use a pair of polarizers and single-photon avalanche diode coincidence count detectors. We interpose a plasmonic hole array in the path of down-converted light before the polarizer. Without the hole array, we measure visibility V=99-100% and Bell’s number S=2.81±0.03. To study geometrical effects we fabricated plasmonic hole arrays (gold on optically polished glass) with elliptical holes (axes are 190nm and 240nm) using focused ion beam. When we put this sample in our system we measured the reduction of visibility V=86±5% using entangled light. However, measurement using classical light gave exactly the same visibility; hence, this reduction is caused only by the difference in transmission coefficients of different polarizations. As samples with non-linear dispersion we fabricated two-layer (a-Si - Au) and three-layer (a-Si – Au – a-Si) structures on optically polished glass with different pitches and circular holes. The results of measurements with these samples will be discussed along with the theoretical investigations.
Enabling the confinement of light to a scale far below the one of conventional optics, surface plasmon polaritons (SPPs) induced by an electromagnetic field in a metal-dielectric interface supply an ideal system to explore strong quantized light-matter coupling. The fast matter-SPP population exchange reported in previous works makes it a candidate for spin manipulation, but such reversible dynamics asymptotically vanishes accompanying the quantum matter relaxing completely to its ground state. Here, we study the exact dissipative dynamics of a quantum emitter (QE) coupled to SPPs. It is interesting to find that, qualitatively different from conventional findings, the QE can be partially stabilized in its excited state even in the presence of the lossy metal. Our analysis reveals that it is the formation of a QE-SPP bound state which results in such suppressed dissipation. Enriching the decoherence dynamics of the QE in the lossy medium, our result is helpful to understand QE-SPP interactions and apply plasmonic nanostructures in quantum devices.