Justifying Born's Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie-Bohm Quantum Theory.

In this work, we derive Born's rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of "qubits" (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann's kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

Plasmonic fork-shaped hologram for vortex-beam generation and separation.

We introduce a multifunctional compact device that integrates a polarization beam splitter and an orbital angular momentum generator based on a plasmonic nano-aperture assisted detour phase meta-hologram. The proposed metasurface, which combines a phase singularity characterized fork hologram and polarization featured Λ-shaped antenna, achieves vortex generation and spin-based vortex splitting in transmission mode. Experimental demonstrations are launched under a linearly polarized incident beam, with polarization tomography as the analysis method. We expect this work to have applications in chip-level beam shaping and high-capacity communication.

Mechanical analog of quantum bradyons and tachyons.

We present a mechanical analog of a quantum wave-particle duality: a vibrating string threaded through a freely moving bead or "masslet." For small string amplitudes, the particle movement is governed by a set of nonlinear dynamical equations that couple the wave field to the masslet dynamics. Under specific conditions, the particle achieves a regime of transparency in which the field and the particle's dynamics appear decoupled. In that special case, the particle conserves its momentum and a guiding wave obeying a Klein-Gordon equation, with real or imaginary mass, emerges. Similar to the double-solution theory of de Broglie, this guiding wave is locked in phase with a modulating group wave comoving with the particle. Interestingly, both subsonic and supersonic particles can fall into a quantum regime as is the case with the slower-than-light bradyons and hypothetical, faster-than-light tachyons of particle physics.

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.

Spin-orbital angular momentum tomography of a chiral plasmonic lens using leakage radiation microscopy.

Based on the spin-dependent directional coupling of surface plasmons (SPs) by ∧-shaped antennas, ring-shaped structures built with such antennas have potential applications for optical tweezers and optical switch technology. In this Letter, we introduce an optical method for realizing a complete polarization tomography of coupled SP fields by such a chiral-planar structure. We use a far-field optical approach, namely leakage radiation microscopy (LRM), to map the SPs propagation and polarization. Here, we fully analyze the polarization state of the generated SPs inside the vortex lens structure. In addition, we provide a theoretical model which agrees well with the experimental results.

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.

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.

Imaging surface plasmons: from leaky waves to far-field radiation.

We show that, contrary to the common wisdom, surface plasmon poles are not involved in the imaging process in leakage radiation microscopy. Identifying the leakage radiation modes directly from a transverse magnetic potential leads us to reconsider the surface plasmon field and unfold the nonplasmonic contribution to the image formation. While both contributions interfere in the imaging process, our analysis reveals that the reassessed plasmonic field embodies a pole mathematically similar to the usual surface plasmon pole. This removes a long-standing ambiguity associated with plasmonic signals in leakage radiation microscopy.

Generating far-field orbital angular momenta from near-field optical chirality.

We demonstrate orbital angular momentum (OAM) transfer by chiral plasmonic nanostructures designed on both sides of a thin suspended metallic membrane. We show how far-field vortex beams with tunable OAM indices can be tailored through nanostructure designs. We reveal the crucial role played by the central aperture that connects the two sides of the membrane from which OAM selection rules are derived in perfect agreement with experimental data.

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.

"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.

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.

Miniature plasmonic wave plates.

Linear birefringence, as implemented in wave plates, is a natural way to control the state of polarization of light. We report on a general method for designing miniature planar wave plates using surface plasmons. The resonant optical device considered here is a single circular aperture surrounded by an elliptical antenna grating. The difference between the short and long axis of each ellipsis introduces a phase shift on the surface plasmons which enables the realization of a quarter wave plate. Furthermore, the experimental results and the theoretical analysis show that the general procedure used does not influence the optical coherence of the polarization state and allows us to explore completely the surface of the unit Poincaré sphere by changing only the shape of the elliptical grating.