Conflict-free collective stochastic decision making by orbital angular momentum of photons through quantum interference.

In recent cross-disciplinary studies involving both optics and computing, single-photon-based decision-making has been demonstrated by utilizing the wave-particle duality of light to solve multi-armed bandit problems. Furthermore, entangled-photon-based decision-making has managed to solve a competitive multi-armed bandit problem in such a way that conflicts of decisions among players are avoided while ensuring equality. However, as these studies are based on the polarization of light, the number of available choices is limited to two, corresponding to two orthogonal polarization states. Here we propose a scalable principle to solve competitive decision-making situations by using the orbital angular momentum of photons based on its high dimensionality, which theoretically allows an unlimited number of arms. Moreover, by extending the Hong-Ou-Mandel effect to more than two states, we theoretically establish an experimental configuration able to generate multi-photon states with orbital angular momentum and conditions that provide conflict-free selections at every turn. We numerically examine total rewards regarding three-armed bandit problems, for which the proposed strategy accomplishes almost the theoretical maximum, which is greater than a conventional mixed strategy intending to realize Nash equilibrium. This is thanks to the quantum interference effect that achieves no-conflict selections, even in the exploring phase to find the best arms.

Entangled and correlated photon mixed strategy for social decision making.

Collective decision making is important for maximizing total benefits while preserving equality among individuals in the competitive multi-armed bandit (CMAB) problem, wherein multiple players try to gain higher rewards from multiple slot machines. The CMAB problem represents an essential aspect of applications such as resource management in social infrastructure. In a previous study, we theoretically and experimentally demonstrated that entangled photons can physically resolve the difficulty of the CMAB problem. This decision-making strategy completely avoids decision conflicts while ensuring equality. However, decision conflicts can sometimes be beneficial if they yield greater rewards than non-conflicting decisions, indicating that greedy actions may provide positive effects depending on the given environment. In this study, we demonstrate a mixed strategy of entangled- and correlated-photon-based decision-making so that total rewards can be enhanced when compared to the entangled-photon-only decision strategy. We show that an optimal mixture of entangled- and correlated-photon-based strategies exists depending on the dynamics of the reward environment as well as the difficulty of the given problem. This study paves the way for utilizing both quantum and classical aspects of photons in a mixed manner for decision making and provides yet another example of the supremacy of mixed strategies known in game theory, especially in evolutionary game theory.

Entangled N-photon states for fair and optimal social decision making.

Situations involving competition for resources among entities can be modeled by the competitive multi-armed bandit (CMAB) problem, which relates to social issues such as maximizing the total outcome and achieving the fairest resource repartition among individuals. In these respects, the intrinsic randomness and global properties of quantum states provide ideal tools for obtaining optimal solutions to this problem. Based on the previous study of the CMAB problem in the two-arm, two-player case, this paper presents the theoretical principles necessary to find polarization-entangled N-photon states that can optimize the total resource output while ensuring equality among players. These principles were applied to two-, three-, four-, and five-player cases by using numerical simulations to reproduce realistic configurations and find the best strategies to overcome potential misalignment between the polarization measurement systems of the players. Although a general formula for the N-player case is not presented here, general derivation rules and a verification algorithm are proposed. This report demonstrates the potential usability of quantum states in collective decision making with limited, probabilistic resources, which could serve as a first step toward quantum-based resource allocation systems.

Entangled-photon decision maker.

The competitive multi-armed bandit (CMAB) problem is related to social issues such as maximizing total social benefits while preserving equality among individuals by overcoming conflicts between individual decisions, which could seriously decrease social benefits. The study described herein provides experimental evidence that entangled photons physically resolve the CMAB in the 2-arms 2-players case, maximizing the social rewards while ensuring equality. Moreover, we demonstrated that deception, or outperforming the other player by receiving a greater reward, cannot be accomplished in a polarization-entangled-photon-based system, while deception is achievable in systems based on classical polarization-correlated photons with fixed polarizations. Besides, random polarization-correlated photons have been studied numerically and shown to ensure equality between players and deception prevention as well, although the CMAB maximum performance is reduced as compared with entangled photon experiments. Autonomous alignment schemes for polarization bases were also experimentally demonstrated based only on decision conflict information observed by an individual without communications between players. This study paves a way for collective decision making in uncertain dynamically changing environments based on entangled quantum states, a crucial step toward utilizing quantum systems for intelligent functionalities.

Directional light beams by design from electrically driven elliptical slit antennas.

We report on the low-energy, electrical generation of light beams in specific directions from planar elliptical microstructures. The emission direction of the beam is determined by the microstructure eccentricity. A very simple, broadband, optical antenna design is used, which consists of a single elliptical slit etched into a gold film. The light beam source is driven by an electrical nanosource of surface plasmon polaritons (SPP) that is located at one focus of the ellipse. In this study, SPPs are generated through inelastic electron tunneling between a gold surface and the tip of a scanning tunneling microscope.

On the origins of transport inefficiencies in mesoscopic networks.

A counter-intuitive behavior analogous to the Braess paradox is encountered in a two-terminal mesoscopic network patterned in a two-dimensional electron system (2DES). Decreasing locally the electron density of one channel of the network paradoxically leads to an increased network electrical conductance. Our low temperature scanning gate microscopy experiments reveal different occurrences of such puzzling conductance variations, thanks to tip-induced localized modifications of electron flow throughout the network's channels in the ballistic and coherent regime of transport. The robustness of the puzzling behavior is inspected by varying the global 2DES density, magnetic field and the tip-surface distance. Depending on the overall 2DES density, we show that either Coulomb Blockade resonances due to disorder-induced localized states or Fabry-Perot interferences tuned by the tip-induced electrostatic perturbation are at the origin of transport inefficiencies in the network, which are lifted when gradually closing one channel of the network with the tip.

Local density of electromagnetic states in plasmonic nanotapers: spatial resolution limits with nitrogen-vacancy centers in diamond nanospheres.

One of the most explored single quantum emitters for the development of nanoscale fluorescence lifetime imaging is the nitrogen-vacancy (NV) color center in diamond. An NV center does not experience fluorescence bleaching or blinking at room temperature. Furthermore, its optical properties are preserved when embedded into nanodiamond hosts. This paper focuses on the modeling of the local density of states (LDOS) in a plasmonic nanofocusing structure with an NV center acting as local illumination sources. Numerical calculations of the LDOS near such a nanostructure were done with a classical electric dipole radiation placed inside a diamond sphere as well as near-field optical fluorescence lifetime imaging of the structure. We found that Purcell factors higher than ten can be reached with diamond nanospheres of radius less than 5 nm and at a distance of less than 20 nm from the surface of the structure. Although the spatial resolution of the experiment is limited by the size of the nanodiamond, our work supports the analysis and interpretation of a single NV color center in a nanodiamond as a probe for scanning near-field optical microscopy.

Highly efficient singular surface plasmon generation by achiral apertures.

We report a highly efficient generation of singular surface plasmon (SP) fields by an achiral plasmonic structure consisting of Λ-shaped apertures. Our quantitative analysis, based on leakage radiation microscopy (LRM), demonstrates that the induced spin-orbit coupling can be tuned by adjusting the apex angle of the Λ-shaped aperture. Specifically, the array of Λ-shaped apertures with the apex angle 60° is shown to give rise to the directional coupling efficiency. The ring of Λ-shaped apertures with the apex angle 60° was found to generate the maximum extinction ratio (ER=11) for the SP singularities between two different polarization states. This result provides a more efficient way for developing an SP focusing and an SP vortex in the field of nanophotonics such as optical tweezers.

Luminescent nanoparticle trapping with far-field optical fiber-tip tweezers.

We report stable and reproducible trapping of luminescent dielectric YAG:Ce(3+) nanoparticles with sizes down to 60 nm using far-field dual fiber tip optical tweezers. The particles are synthesized by a specific glycothermal route followed by an original protected annealing step, resulting in significantly enhanced photostability. The tweezers properties are analyzed by studying the trapped particles residual Brownian motion using video or reflected signal records. The trapping potential is harmonic in the transverse direction to the fiber axis, but reveals interference fringes in the axial direction. Large trapping stiffness of 35 and 2 pN µm(-1) W(-1) is measured for a fiber tip-to-tip distance of 3 µm and 300 nm and 60 nm particles, respectively. The forces acting on the nanoparticles are discussed within the dipolar approximation (gradient and scattering force contributions) or exact calculations using the Maxwell Stress Tensor formalism. Prospects for trapping even smaller particles are discussed.

Spatio-temporal second-order quantum correlations of surface plasmon polaritons.

We present an experimental methodology to observe spatio-temporal second-order quantum coherence of surface plasmon polaritons which are emitted by nitrogen vacancy color centers attached at the apex of an optical tip. The approach relies on leakage radiation microscopy in the Fourier space, and we use this approach to test wave-particle duality for surface plasmon polaritons.

Coherence and aberration effects in surface plasmon polariton imaging.

We study theoretically and experimentally coherent imaging of surface plasmon polaritons using either leakage radiation microscopy through a thin metal film or interference microscopy through a thick metal film. Using a rigorous modal formalism based on scalar Whittaker potentials, we develop a systematic analytical and vectorial method adapted to the analysis of coherent imaging involving surface plasmon polaritons. The study includes geometrical aberrations due index mismatch which played an important role in the interpretation of recent experiments using leakage radiation microscopy. We compare our theory with experiments using classical or quantum near-field scanning optical microscopy probes and show that the approach leads to a full interpretation of the recorded optical images.

Single-photon decision maker.

Decision making is critical in our daily lives and for society in general and is finding evermore practical applications in information and communication technologies. Herein, we demonstrate experimentally that single photons can be used to make decisions in uncertain, dynamically changing environments. Using a nitrogen-vacancy in a nanodiamond as a single-photon source, we demonstrate the decision-making capability by solving the multi-armed bandit problem. This capability is directly and immediately associated with single-photon detection in the proposed architecture, leading to adequate and adaptive autonomous decision making. This study makes it possible to create systems that benefit from the quantum nature of light to perform practical and vital intelligent functions.

Temporal coherence of propagating surface plasmons.

The temporal coherence of propagating surface plasmons is investigated using a local, broadband plasmon source consisting of a scanning tunneling microscope. A variant of Young's experiment is performed using a sample consisting of a 200-nm-thick gold film perforated by two 1-µm-diameter holes (separated by 4 or 6 µm). The resulting interference fringes are studied as a function of hole separation and source bandwidth. From these experiments, we conclude that apart from plasmon decay in the metal, there is no further loss of plasmon coherence from propagation, scattering at holes, or other dephasing processes. As a result, the plasmon coherence time may be estimated from its spectral bandwidth.

Optical near-field-mediated polarization asymmetry induced by two-layer nanostructures.

We demonstrate that a two-layer shape-engineered nanostructure exhibits asymmetric polarization conversion efficiency thanks to near-field interactions. We present a rigorous theoretical foundation based on an angular-spectrum representation of optical near-fields that takes account of the geometrical features of the proposed device architecture and gives results that agree well with electromagnetic numerical simulations. The principle used here exploits the unique intrinsic optical near-field processes associated with nanostructured matter, while eliminating the need for conventional scanning optical fiber probing tips, paving the way to novel nanophotonic devices and systems.

Transmission and reflection characteristics of metal-coated optical fiber tip pairs.

The optical transmission and reflection in between two metalized optical fiber tips is studied in the optical near-field and far-field domains. In addition to aluminum-coated tips for near-field scanning optical microscopy (NSOM), specifically developed gold-coated fiber tips cut by focused ion beam are investigated. Transverse transmission maps of subwavelength width clearly indicate optical near-field coupling between the tips for short tip distances and become essentially Gaussian-shaped for larger distances in the far-field regime. Moreover, concentric reflection fringes observed for NSOM-type tips illustrate the influence of the receiving fiber tip on the emission pattern of the source tip.

Single and dual fiber nano-tip optical tweezers: trapping and analysis.

An original optical tweezers using one or two chemically etched fiber nano-tips is developed. We demonstrate optical trapping of 1 micrometer polystyrene spheres at optical powers down to 2 mW. Harmonic trap potentials were found in the case of dual fiber tweezers by analyzing the trapped particle position fluctuations. The trap stiffness was deduced using three different models. Consistent values of up to 1 fN/nm were found. The stiffness linearly decreases with decreasing light intensity and increasing fiber tip-to-tip distance.

Scanning plasmonic microscopy by image reconstruction from the Fourier space.

We demonstrate a simple scheme for high-resolution imaging of nanoplasmonic structures that basically removes most of the resolution limiting allowed light usually transmitted to the far field. This is achieved by implementing a Fourier lens in a near-field scanning optical microscope (NSOM) operating in the leakage-radiation microscopy (LRM) mode. The method consists of reconstructing optical images solely from the plasmonic 'forbidden' light collected in the Fourier space. It is demonstrated by using a point-like nanodiamond-based tip that illuminates a thin gold film patterned with a sub-wavelength annular slit. The reconstructed image of the slit shows a spatial resolution enhanced by a factor ~/= 4 compared to NSOM images acquired directly in the real space.

A new transport phenomenon in nanostructures: a mesoscopic analog of the Braess paradox encountered in road networks.

The Braess paradox, known for traffic and other classical networks, lies in the fact that adding a new route to a congested network in an attempt to relieve congestion can degrade counterintuitively the overall network performance. Recently, we have extended the concept of the Braess paradox to semiconductor mesoscopic networks, whose transport properties are governed by quantum physics. In this paper, we demonstrate theoretically that, alike in classical systems, congestion plays a key role in the occurrence of a Braess paradox in mesoscopic networks.

Living cell imaging by far-field fibered interference scanning optical microscopy.

We report on the imaging of biological cells including living neurons by a dedicated fibered interferometric scanning optical microscope. The topography and surface roughness of mouse fibroblasts and hippocampal neurons are clearly revealed. This straightforward far-field technique allows fast, high resolution observation of samples in liquids without lengthy alignment procedures or costly components.

"Deterministic" quantum plasmonics.

We demonstrate "deterministic" launching of propagative quantum surface-plasmon polaritons at freely chosen positions on gold plasmonic receptacles. This is achieved by using as a plasmon launcher a near-field scanning optical source made of a diamond nanocrystal with two nitrogen-vacancy color-center occupancy. Our demonstration relies on leakage-radiation microscopy of a thin homogeneous gold film and on near-field optical microscopy of a nanostructured thick gold film. Our work paves the way to future fundamental studies and applications in quantum plasmonics that require an accurate positioning of single-plasmon sources and may open a new branch in plasmonics and nanophotonics, namely scanning quantum plasmonics.