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.

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.

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.

Electron Phase Shift at the Zero-Bias Anomaly of Quantum Point Contacts

The Kondo effect is the many-body screening of a local spin by a cloud of electrons at very low temperature. It has been proposed as an explanation of the zero-bias anomaly in quantum point contacts where interactions drive a spontaneous charge localization. However, the Kondo origin of this anomaly remains under debate, and additional experimental evidence is necessary. Here we report on the first phase-sensitive measurement of the zero-bias anomaly in quantum point contacts using a scanning gate microscope to create an electronic interferometer. We observe an abrupt shift of the interference fringes by half a period in the bias range of the zero-bias anomaly, a behavior which cannot be reproduced by single-particle models. We instead relate it to the phase shift experienced by electrons scattering off a Kondo system. Our experiment therefore provides new evidence of this many-body effect in quantum point contacts.

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.

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.

Plasmon scattering from holes: from single hole scattering to Young's experiment

In this paper, the scattering of surface plasmon polaritons (SPPs) into photons at holes is investigated. A local, electrically excited source of SPPs using a scanning tunneling microscope (STM) produces an outgoing circular plasmon wave on a thick (200 nm) gold film on glass containing holes of 250, 500 and 1000 nm diameter. Fourier plane images of the photons from hole-scattered plasmons show that the larger the hole diameter, the more directional the scattered radiation. These results are confirmed by a model where the hole is considered as a distribution of horizontal dipoles whose relative amplitudes, directions, and phases depend linearly on the local SPP electric field. An SPP-Young's experiment is also performed, where the STM-excited SPP wave is incident on a pair of 1 μm diameter holes in the thick gold film. The visibility of the resulting fringes in the Fourier plane is analyzed to show that the polarization of the electric field is maintained when SPPs scatter into photons. From this SPP-Young's experiment, an upper bound of ≈200 nm for the radius of this STM-excited source of surface plasmon polaritons is determined.

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.

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.

YAG:Ce nanoparticle lightsources

We investigate the luminescence properties of 10 nm yttrium aluminum garnet (YAG) nanoparticles doped with Ce ions at 0.2%, 4% and 13% that are designed as active probes for scanning near-field optical microscopy. They are produced by a physical method without any subsequent treatment, which is imposed by the desired application. The structural analysis reveals the amorphous nature of the particles, which we relate to some compositional defects as indicated by the elemental analysis. The optimum emission is obtained with a doping level of 4%. The emission of the YAG nanoparticles doped at 0.2% is strongly perturbed by the crystalline disorder whereas the 13% doped particles hardly exhibit any luminescence. In the latter case, the presence of Ce(4+) ions is confirmed, indicating that the Ce concentration is too high to be incorporated efficiently in YAG nanoparticles in the trivalent state. By a unique procedure combining cathodoluminescence and Rutherford backscattering spectrometry, we demonstrate that the enhancement of the particle luminescence yield is not proportional to the doping concentration, the emission enhancement being larger than the Ce concentration increase. Time-resolved photoluminescence reveals the presence of quenching centres likely related to the crystalline disorder as well as the presence of two distinct Ce ion populations. Eventually, nano-cathodoluminescence indicates that the emission and therefore the distribution of the doping Ce ions and of the defects are homogeneous.

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.

Transport inefficiency in branched-out mesoscopic networks: an analog of the Braess paradox

We present evidence for a counterintuitive behavior of semiconductor mesoscopic networks that is the analog of the Braess paradox encountered in classical networks. A numerical simulation of quantum transport in a two-branch mesoscopic network reveals that adding a third branch can paradoxically induce transport inefficiency that manifests itself in a sizable conductance drop of the network. A scanning-probe experiment using a biased tip to modulate the transmission of one branch in the network reveals the occurrence of this paradox by mapping the conductance variation as a function of the tip voltage and position.

Surface plasmon leakage radiation microscopy at the diffraction limit

This paper describes the image formation process in optical leakage radiation microscopy of surface plasmon-polaritons with diffraction limited spatial resolution. The comparison of experimentally recorded images with simulations of point-like surface plasmon-polariton emitters allows for an assignment of the observed fringe patterns. A simple formula for the prediction of the fringe periodicity is presented and practically relevant effects of abberations in the imaging system are discussed.

Large variation in the boundary-condition slippage for a rarefied gas flowing between two surfaces

We study the slippage of a gas along mobile rigid walls in the sphere-plane confined geometry and find that it varies considerably with pressure. The classical no-slip boundary condition valid at ambient pressure changes continuously to an almost perfect slip condition in a primary vacuum. Our study emphasizes the key role played by the mean free path of the gas molecules on the interaction between a confined fluid and solid surfaces and further demonstrates that the macroscopic hydrodynamics approach can be used with confidence even in a primary vacuum environment where it is intuitively expected to fail.

"Negative" backaction noise in interferometric detection of a microlever

Interferometric detection of mirror displacements is intrinsically limited by laser shot noise. In practice, however, it is often limited by thermal noise. Here we report on an experiment performed at the liquid helium temperature to overcome the thermal noise limitation and investigate the effect of classical laser noise on a microlever that forms a Fabry-Perot cavity with an optical fiber. The spectral noise densities show a region of "negative" contribution of the backaction noise close to the resonance frequency. We interpret this noise reduction as a coherent coupling of the microlever to the laser intensity noise. This optomechanical effect could be used to improve the detection sensitivity as discussed in proposals going beyond the standard quantum limit.

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.

A scheme for solving the plane-plane challenge in force measurements at the nanoscale

Non-contact interaction between two parallel flat surfaces is a central paradigm in sciences. This situation is the starting point for a wealth of different models: the capacitor description in electrostatics, hydrodynamic flow, thermal exchange, the Casimir force, direct contact study, third body confinement such as liquids or films of soft condensed matter. The control of parallelism is so demanding that no versatile single force machine in this geometry has been proposed so far. Using a combination of nanopositioning based on inertial motors, of microcrystal shaping with a focused-ion beam (FIB) and of accurate in situ and real-time control of surface parallelism with X-ray diffraction, we propose here a "gedanken" surface-force machine that should enable one to measure interactions between movable surfaces separated by gaps in the micrometer and nanometer ranges.

Giant slip lengths of a simple fluid at vibrating solid interfaces

It has been shown recently [A. Siria, A. Drezet, F. Marchi, F. Comin, S. Huant, and J. Chevrier, Phys. Rev. Lett. 102, 254503 (2009)] that in the plane-plane configuration, a mechanical resonator vibrating close to a rigid wall in a simple fluid can be overdamped to a frozen regime. Here, by solving analytically the Navier-Stokes equations with partial slip boundary conditions at the solid-fluid interface, we develop a theoretical approach justifying and extending these earlier findings. We show in particular that in the perfect-slip regime, the abovementioned results are, in the plane-plane configuration, very general and robust with respect to lever geometry considerations. We compare the results to those obtained previously for the sphere moving perpendicularly and close to a plane in a simple fluid and discuss in more details the differences concerning the dependence of the friction forces with the gap distance separating the moving object (i.e., plane or sphere) from the fixed plane. We show that the plane-plane geometry is more sensitive than the sphere-plane geometry for the measurement of slippage coefficients. Finally, we show that the submicron fluidic effect reported in the reference above, and discussed further in the present work, can have dramatic implications in the design of nanoelectromechanical systems.

Near-field optical microscopy with a nanodiamond-based single-photon tip

We introduce a point-like scanning single-photon source that operates at room temperature and offers an exceptional photostability (no blinking, no bleaching). This is obtained by grafting in a controlled way a diamond nanocrystal (size around 20 nm) with single nitrogen-vacancy color-center occupancy at the apex of an optical probe. As an application, we image metallic nanostructures in the near-field, thereby achieving a near-field scanning single-photon microscopy working at room temperature on the long term. Our work may be of importance to various emerging fields of nanoscience where an accurate positioning of a quantum emitter is required such as for example quantum plasmonics.

Scanning gate microscopy of quantum rings: effects of an external magnetic field and of charged defects

We study scanning gate microscopy (SGM) in open quantum rings obtained from buried semiconductor InGaAs/InAlAs heterostructures. By performing a theoretical analysis based on the Keldysh-Green function approach we interpret the radial fringes observed in experiments as the effect of randomly distributed charged defects. We associate SGM conductance images with the local density of states (LDOS) of the system. We show that such an association cannot be made with the current density distribution. By varying an external magnetic field we are able to reproduce recursive quasi-classical orbits in LDOS and conductance images, which bear the same periodicity as the Aharonov-Bohm effect.

Viscous cavity damping of a microlever in a simple fluid

We consider the problem of oscillation damping in air of a thermally actuated microlever as it gradually approaches an infinite wall in parallel geometry. As the gap is decreased from 20 microm down to 400 nm, we observe the increasing damping of the lever Brownian motion in the fluid laminar regime. This manifests itself as a linear decrease in the lever quality factor accompanied by a dramatic softening of its resonance, and eventually leads to the freezing of the CL oscillation. We are able to quantitatively explain this behavior by analytically solving the Navier-Stokes equation with perfect slip boundary conditions. Our findings may have implications for microfluidics and micro- and nanoelectromechanical applications.

Fluorescent oxide nanoparticles adapted to active tips for near-field optics

We present a new kind of fluorescent oxide nanoparticle (NP) with properties well suited to active-tip based near-field optics. These particles with an average diameter in the 5-10 nm range are produced by low energy cluster beam deposition (LECBD) from a YAG:Ce3+ target. They are studied by transmission electron microscopy (TEM), x-ray photoelectron spectroscopy (XPS), cathodoluminescence, near-field scanning optical microscopy (NSOM) and fluorescence in the photon-counting mode. Particles of extreme photo-stability as small as 10 nm in size are observed. These emitters are validated as building blocks of active NSOM tips by coating a standard optical tip with a 10 nm thick layer of YAG:Ce3+ particles directly in the LECBD reactor and by subsequently performing NSOM imaging of test surfaces.

Diamond nanocrystals hosting single nitrogen-vacancy color centers sorted by photon-correlation near-field microscopy

Diamond nanocrystals containing highly photoluminescent color centers are attractive, nonclassical, and near-field light sources. For near-field applications, the size of the nanocrystal is crucial, since it defines the optical resolution. Nitrogen-vacancy (NV) color centers are efficiently created by proton irradiation and annealing of a nanodiamond powder. Using near-field microscopy and photon statistics measurements, we show that nanodiamonds with sizes down to 25 nm can hold a single NV color center with bright and stable photoluminescence.

Imaging electron wave functions inside open quantum rings

Combining scanning gate microscopy (SGM) experiments and simulations, we demonstrate low temperature imaging of the electron probability density |Psi|(2)(x,y) in embedded mesoscopic quantum rings. The tip-induced conductance modulations share the same temperature dependence as the Aharonov-Bohm effect, indicating that they originate from electron wave function interferences. Simulations of both |Psi|(2)(x,y) and SGM conductance maps reproduce the main experimental observations and link fringes in SGM images to |Psi|(2)(x,y).

Surface plasmon mediated near-field imaging and optical addressing in nanoscience

We present an overview of recent progress in "plasmonics". We focus our study on the observation and excitation of surface plasmon polaritons (SPPs) with optical near-field microscopy. We discuss in particular recent applications of photon scanning tunnelling microscope (PSTM) for imaging of SPP propagating in metal and dielectric wave guides. We show how near-field scanning optical microscopy (NSOM) can be used to optically and actively address remote nano objects such as quantum dots. Additionally we compare results obtained with near-field microcopy to those obtained with other optical far-field methods of analysis such as leakage radiation microscopy (LRM).

Near-field optical imaging with a CdSe single nanocrystal-based active tip

We report near-field scanning optical imaging with an active tip made of a single fluorescent CdSe nanocrystal attached at the apex of an optical tip. Although the images are acquired only partially because of the random blinking of the semiconductor particle, our work validates the use of such tips in ultra-high spatial resolution optical microscopy.

Diffraction by a small aperture in conical geometry: application to metal-coated tips used in near-field scanning optical microscopy

Light diffraction through a subwavelength aperture located at the apex of a metallic screen with conical geometry is investigated theoretically. A method based on a multipole field expansion is developed to solve Maxwell's equations analytically using boundary conditions adapted both for the conical geometry and for the finite conductivity of a real metal. The topological properties of the diffracted field are discussed in detail and compared to those of the field diffracted through a small aperture in a flat screen, i.e., the Bethe problem. The model is applied to coated, conically tapered optical fiber tips that are used in near-field scanning optical microscopy. It is demonstrated that such tips behave over a large portion of space like a simple combination of two effective dipoles located in the apex plane (an electric dipole and a magnetic dipole parallel to the incident fields at the apex) whose exact expressions are determined. However, the large "backward" emission in the P plane--a salient experimental fact that has remained unexplained so far--is recovered in our analysis, which goes beyond the two-dipole approximation.

Far-field emission of a tapered optical fibre tip: a theoretical analysis

The far-field transmission pattern of a tapered optical tip with small aperture (radius approximately < 40 nm) is modelled by solving Maxwell's equations in the radiation zone with boundary conditions appropriate to the conical geometry. The model is able to reproduce the large differences between the S and P polarizations observed previously in the emission profile of such a tip [Obermüller and Karrai. Appl. Phys. Lett. (1995) 67, 3408].

Low-temperature near-field spectroscopy of CdTe quantum dots

A near-field optical microscope has been developed for operation at low temperature. This microscope is used to study the photoluminescence of CdTe-based quantum dots. Spectra collected upon approaching the optical tip into the near-field region of the sample reveal the evolution from a broad far-field luminescence band - that is typical for a large ensemble of dots - to a near-field structure made up of a few sharp peaks originating from individual dots. Experiments carried out in the excitation-collection mode through the optical tip allow study of the effect of an increase in excitation power on the near-field spectra. It is found that upon increasing the excitation by two orders of magnitude, a spatially resolved spectrum progressively transforms back into a broad 'far-field-like' spectrum. Photoluminescence images taken by scanning the sample under the tip are used to discriminate various contributions coming from individual dots.

Near-field optics on silicon-electrolyte junctions

A technique allowing near-field photocurrent (PC) mapping of silicon surfaces in contact with an electrolyte is presented. The illumination source is an optical fibre tip with a 100-nm aperture. A shear force detection system controls the tip-sample distance while scanning the tip across the silicon-electrolyte interface. Topographic and PC images on SiO2/Si mesas both show 300 nm resolution. It is shown that this PC contrast is induced by the tip-topography interaction and hence the PC resolution is limited by the resolution of the topography. Indeed, PC mapping on topography-less patterned porous-silicon/silicon samples shows that the lateral resolution is only limited by the aperture size which is of the order of 100 nm.