Wavelength-scale errors in optical localization due to spin-orbit coupling of light

Nearfield observation of spin-orbit interactions at nanoscale using photoinduced force microscopy

Optical spin and orbital angular momenta are intrinsic characteristics of light determined by its polarization and spatial degrees of freedom, respectively. At the nanoscale, sharply focused structured light carries coupled spin-orbital angular momenta with complex 3D nearfield structures, crucial for manipulating multidimensional information of light in nanophotonics. However, characterizing these interactions faces challenges with conventional farfield-based methods, which typically lack the essential accuracy and resolution to interrogate the structured nearfield with high fidelity. To address this challenge, we experimentally observe spin-orbit interactions at the nanoscale using photoinduced force microscopy. Such interactions are enabled through sharply focused circularly polarized optical vortices, which are then mapped by nearfield optical forces in high resolution. Because the optical forces can reveal both longitudinal and transverse nearfield structures with high fidelity, the spin-orbit interactions are eventually evaluated quantitatively at the nearfield, as an important inspiration to use the coupled momenta in dense optical nano-device systems.

Tracking the extensive three-dimensional motion of single ions by an engineered point-spread function

Three-dimensional (3D) imaging of individual atoms is a critical tool for discovering new physical phenomena and developing new technologies in microscopic systems. However, the current single-atom-resolved 3D imaging methods are limited to static circumstances or a shallow detection range. Here, we demonstrate a generic dynamic 3D imaging method to track the extensive motion of single ions by exploiting the engineered point-spread function (PSF). We show that the image of a single ion can be engineered into a helical PSF, thus enabling single-snapshot acquisition of the position information of the ion in the trap. A preliminary application of this technique is demonstrated by recording the 3D motion trajectory of a single trapped ion and reconstructing the 3D dynamical configuration transition between the zig and zag structures of a 5-ion crystal. This work opens the path for studies on single-atom-resolved dynamics in both trapped-ion and neutral-atom systems.

Electrodynamic Interference and Induced Polarization in Nanoparticle-Based Optical Matter Arrays

Optical matter (OM) arrays are self-organizing, ordered arrangements of nanometer- to micrometer-size particles, where interparticle forces are mediated by incident and scattered coherent light. The structures that form and their dynamics depend on the properties (e.g., material, size) of the constituent particles, as well as the incident and scattered light. While significant progress has been made toward understanding how the OM arrays are affected by the phase, polarization, and intensity profile of the incident light, the polarization induced in the particles and the light scattered by OM arrays have received less attention. In this paper, we establish the roles of electrodynamic interference, many-body coupling, and induced-polarization concomitant with the coherent light scattered by OM arrays. Experiments and simulations together demonstrate that the spatial profile and directionality of coherent light scattered by OM arrays in the far field are primarily influenced by interference, while electrodynamic coupling (interactions) and the associated polarization induced in the nanoparticle constituents have a quantitative wavelength-dependent effect on the total amount of light scattered by the arrays. Furthermore, the electrodynamic coupling in silver nanoparticle OM arrays is significantly enhanced by constructive interference and increases superextensively with the number of particles in the array. Particle size, and hence polarizability, also has a significant effect on the strength of the coupling. Finally, we simulate larger hexagonal OM arrays of Ag nanoparticles to demonstrate that the electrodynamic coupling and scattering enhancement observed in small OM arrays develop into surface lattice resonances observed in the infinite array limit. Our work provides insights for designing OM arrays to tune many-body forces and the coherent light that they scatter.

Generation of pure transverse spin and nontrivial polarization structures of beams by dielectric metasurface

Transverse spin, a spin component with unique characteristics, provides a new dimension for plenty of applications, such as optical trapping, imaging, and communication. Here, we analyze the pure transverse spin in the Bessel beam, which is solely present in the azimuthal direction. Based on a single layer dielectric metasurface, we efficiently generate Bessel beams with pure transverse spin in a compact optical system. As designed, the transverse spin is flexibly tunable by converting the polarization of the incident light. Furthermore, in the scattered Bessel beam, the local electromagnetic field oscillates around the transverse axis, which is perpendicular to the beam propagation. At certain positions, the local polarization ellipse degenerates into a perfect circle, resulting in a ring-periodic distribution of circularly polarized points (C points) in the beam. This suggests that the local polarization demonstrates a nontrivial periodic structure. This work deepens our understanding of spin-related physics and opens a new avenue for the study and application of transverse spins in ultracompact, flat, multifunctional nanophotonic platforms.

Direct Observation of Spin-Orbit Interaction of Light via Chiroptical Responses

The spin-orbit interaction of light is a fundamental manifestation of controlling its angular momenta with numerous applications in photonic spin Hall effects and chiral quantum optics. However, observation of an optical spin Hall effect, which is normally very weak with subwavelength displacements, needs quantum weak measurements or sophisticated metasurfaces. Here, we theoretically and experimentally demonstrate the spin-orbit interaction of light in the form of strong chiroptical responses by breaking the in-plane inversion symmetry of a dielectric substrate. The chiroptical signal is observed at the boundary of a microdisk illuminated by circularly polarized vortex beams at normal incidence. The generated chiroptical spectra are tunable for different photonic orbital angular momenta and microdisk diameters. Our findings, correlating photonic spin-orbit interaction with chiroptical responses, may provide a route for exploiting optical information processing, enantioselective sensing, and chiral metrology.

Spiraling light: from donut modes to a Magnus effect analogy

The insight that optical vortex beams carry orbital angular momentum (OAM), which emerged in Leiden about 30 years ago, has since led to an ever expanding range of applications and follow-up studies. This paper starts with a short personal account of how these concepts arose. This is followed by a description of some recent ideas where the coupling of transverse orbital and spin angular momentum (SAM) in tightly focused laser beams produces interesting new effects. The deflection of a focused light beam by an atom in the focus is reminiscent of the Magnus effect known from aerodynamics. Momentum conservation dictates an accompanying light force on the atom, transverse to the optical axis. As a consequence, an atom held in an optical tweezer will be trapped at a small distance of up to λ/2π away from the optical axis, which depends on the spin state of the atom and the magnetic field direction. This opens up new avenues to control the state of motion of atoms in optical tweezers as well as potential applications in quantum gates and interferometry.

Spin-Orbit Mapping of Light

Spin-orbit photonics, involving the interaction between the spin angular momentum (SAM) and orbital angular momentum (OAM) of light, plays an important role in modern optics. Here, we present the spin-orbit mapping of light in a few-mode fiber that originates from the mode degeneracy lifting (TM_{01} and TE_{01}) property. We demonstrate two kinds of spin-orbit mapping phenomena, i.e., mapping from intrinsic SAM to OAM and mapping from polarization direction rotation to field pattern rotation. The demonstrated spin-orbit mapping shows high efficiency, large bandwidth, availability for short pulses, and scalability to high-order OAM states.

Optical Superresolution Sensing of a Trapped Ion's Wave Packet Size

We demonstrate superresolution optical sensing of the size of the wave packet of a single trapped ion. Our method extends the well-known ground state depletion (GSD) technique to the coherent regime. Here, we use a hollow beam to strongly saturate a coherently driven dipole-forbidden transition around a subdiffraction limited area at its center and observe state dependent fluorescence. By spatially scanning this laser beam over a single trapped ^{40}Ca^{+} ion, we are able to measure the wave packet sizes of cooled ions. Using a depletion beam waist of 4.2(1)  μm we reach a spatial resolution which allows us to determine a wave packet size of 39(9) nm for a near ground state cooled ion. This value matches an independently deduced value of 32(2) nm, calculated from resolved sideband spectroscopy measurements. Finally, we discuss the ultimate resolution limits of our adapted GSD imaging technique in view of applications to direct quantum wave packet imaging.

Tunable spin Hall shift of light from graphene-wrapped spheres

Graphene has taken impressive roles in light manipulation and optical engineering. The most attractive advantage of graphene is its tunable conductivity that could be dynamically modulated by various means. In this paper, we show that the spin Hall shift of light is dynamically tunable via changing the Fermi level of the graphene-wrapped spheres. Such tunability is prominent when different modes interfere with each other, such as at the interference of electric and magnetic dipolar modes or at the interference of electric dipolar and electric quadrupole modes. The circular polarization degree in the near field clearly demonstrates the strength of spin-orbit interaction, which is associated with spin Hall shift of light in the far-field. In addition, the spin Hall effect is shown in far-field detection plane and should be observed in experiment. Our results provide insights into how the spin Hall effect could be tuned and add new perspective in designing optical super-resolution imaging techniques.

Atomic scale displacements detected by optical image cross-correlation analysis and 3D printed marker arrays

For analyzing displacement-vector fields in mechanics, for example to characterize the properties of 3D printed mechanical metamaterials, routine high-precision position measurements are indispensable. For this purpose, nanometer-scale localization errors have been achieved by wide-field optical-image cross-correlation analysis. Here, we bring this approach to atomic-scale accuracy by combining it with well-defined 3D printed marker arrays. By using an air-lens with a numerical aperture of [Formula: see text] and a free working distance of [Formula: see text], and an [Formula: see text] array of markers with a diameter of [Formula: see text] and a period of [Formula: see text], we obtain 2D localization errors as small as [Formula: see text] in [Formula: see text] measurement time ([Formula: see text]). The underlying experimental setup is simple, reliable, and inexpensive, and the marker arrays can easily be integrated onto and into complex architectures during their 3D printing process.

Off-Axis Dipole Forces in Optical Tweezers by an Optical Analog of the Magnus Effect

It is shown that a circular dipole can deflect the focused laser beam that induces it and will experience a corresponding transverse force. Quantitative expressions are derived for Gaussian and angular top hat beams, while the effects vanish in the plane wave limit. The phenomena are analogous to the Magnus effect, pushing a spinning ball onto a curved trajectory. The optical case originates in the coupling of spin and orbital angular momentum of the dipole and the light. In optical tweezers the force causes off-axis displacement of the trapping position of an atom by a spin-dependent amount up to λ/2π, set by the direction of a magnetic field. This suggests direct methods to demonstrate and explore these effects, for instance, to induce spin-dependent motion.

The Panopticon device: An integrated Paul-trap-hemispherical mirror system for quantum optics

We present the design and construction of a new experimental apparatus for the trapping of single Ba⁺ ions in the center of curvature of an optical-quality hemispherical mirror. We describe the layout, fabrication, and integration of the full setup, consisting of a high-optical access monolithic "3D-printed" Paul trap, the hemispherical mirror, a diffraction-limited in-vacuum lens (NA = 0.7) for collection of atomic fluorescence, and a state-of-the art ultra-high vacuum vessel. This new apparatus enables the study of quantum electrodynamics effects such as strong inhibition and enhancement of spontaneous emission and achieves a collection efficiency of the emitted light in a single optical mode of 31%.

Ultrahigh-Speed Imaging of Rotational Diffusion on a Lipid Bilayer

We studied the rotational and translational diffusion of a single gold nanorod linked to a supported lipid bilayer with ultrahigh temporal resolution of two microseconds. By using a home-built polarization-sensitive dark-field microscope, we recorded particle trajectories with lateral precision of 3 nm and rotational precision of 4°. The large number of trajectory points in our measurements allows us to characterize the statistics of rotational diffusion with unprecedented detail. Our data show apparent signatures of anomalous diffusion such as sublinear scaling of the mean-squared angular displacement and negative values of angular correlation function at small lag times. However, a careful analysis reveals that these effects stem from the residual noise contributions and confirms normal diffusion. Our experimental approach and observations can be extended to investigate diffusive processes of anisotropic nanoparticles in other fundamental systems such as cellular membranes or other two-dimensional fluids.

Kerker Conditions upon Lossless, Absorption, and Optical Gain Regimes

The directionality and polarization of light show peculiar properties when the scattering by a dielectric sphere can be described exclusively by electric and magnetic dipolar modes. Particularly, when these modes oscillate in phase with equal amplitude, at the so-called first Kerker condition, the zero optical backscattering condition emerges for nondissipating spheres. However, the role of absorption and optical gain in the first Kerker condition remains unexplored. In this work, we demonstrate that either absorption or optical gain precludes the first Kerker condition and, hence, the absence of backscattered radiation light, regardless of the particle's size, incident wavelength, and incoming polarization. Finally, we derive the necessary prerequisites of the second Kerker condition of the zero forward light scattering, finding that optical gain is a compulsory requirement.

Topologically-tuned spin Hall shift around Fano resonance

The topological magnetoelectric effect is associated with the photonic spin-orbit interaction. However, due to the proportionate fine structure constant of the topological term, the topological magnetoelectric effect is usually weak. In this paper, we demonstrate that the axion term enables manipulation of the spin Hall shift of light around Fano resonance. And, the excited surface plasmon near the nanoparticle's interface could enhance the topological magnetoelectric effect for several orders. Numerical simulation of near field and far-field scattering confirms our theoretical results. Our work may pave the way to exploit the topological magnetoelectric effect in practical applications, such as optical sensing and nanoprobing.

High purity single photons entangled with an atomic qubit

Trapped atomic ions are an ideal candidate for quantum network nodes, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. The integrity of this photonic interface is generally reliant on the purity of single photons produced by the quantum memory. Here, we demonstrate a single-photon source for quantum networking based on a trapped ¹³⁸Ba⁺ ion with a single photon purity of g ⁽²⁾(0)=(8.1±2.3)×10^-5 without background subtraction. We further optimize the tradeoff between the photonic generation rate and the memory-photon entanglement fidelity for the case of polarization photonic qubits by tailoring the spatial mode of the collected light.

Photonic spin Hall effect on an ellipsoidal Rayleigh particle in scattering far-field

We present the photonic spin Hall effect on an ellipsoidal Rayleigh particle, which amounts to a polarization-dependent shift in scattering far-field. Based on the dipole model, we demonstrate that such shift is unavoidable when the light incidence is inclined with respect to the main axis of the ellipsoidal Rayleigh particle. The result has general validity and can be applied to metal and dielectric materials. In addition, the photonic spin Hall effect also manifests itself in the optical force and torque exerted on the particle, which is promising for precision metrology, spin-optics devices and optical driven micro-machines. Due to wide existence of the Rayleigh particles in nature, we believe that our findings might provide a useful toolset for investigating polarization-dependent scattering of particles.

Sectoral multipole focused beams

We discuss the properties of pure multipole beams with well-defined handedness or helicity, with the beam field a simultaneous eigenvector of the squared total angular momentum and its projection along the propagation axis. Under the condition of hemispherical illumination, we show that the only possible propagating multipole beams are "sectoral" multipoles. The sectoral dipole beam is shown to be equivalent to the non-singular time-reversed field of an electric and a magnetic point dipole Huygens' source located at the beam focus. Higher order multipolar beams are vortex beams vanishing on the propagation axis. The simple analytical expressions of the electric field of sectoral multipole beams, exact solutions of Maxwell's equations, and the peculiar behaviour of the Poynting vector and spin and orbital angular momenta in the focal volume could help to understand and model light-matter interactions under strongly focused beams.

Asymmetry and spin-orbit coupling of light scattered from subwavelength particles

Light scattering and spin-orbit angular momentum coupling phenomena from subwavelength objects, with electric and magnetic dipolar responses, are receiving an increasing interest. Under illumination by circularly polarized light, spin-orbit coupling effects have been shown to lead to significant shifts between the measured and actual position of particles. Here we show that the remarkable angular dependence of these "optical mirages" and those of the intensity, degree of circular polarization (DoCP), and spin and orbital angular momentum of scattered photons are all linked, and fully determined, by the dimensionless "asymmetry parameter" g, being independent of the specific optical properties of the scatterer. Interestingly, for g≠0, the maxima of the optical mirage and angular momentum exchange take place at different scattering angles. We further show that the g parameter is exactly half of the DoCP at a right-angle scattering, which opens the possibility to infer the whole angular properties of the scattered fields by a single far-field polarization measurement.

Enhanced broadband spin Hall effects by core-shell nanoparticles

Spin-orbit interaction of light is ubiquitous in any optical system. However, the relevant spin Hall effects are usually weak for the light scattering from nanoparticles, making it challengeable to detect directly in experiment. In this paper, we demonstrate enhanced broadband spin Hall effects by using core-shell nanoparticles. The electric and magnetic dipoles can be tuned by the core-shell nanostructure with great freedom, and are excited simultaneously in a broadband spectrum, resulting in robust enhanced spin Hall shifts. Moreover, the coupling of the electric dipole and electric quadrupole gives rise to enhanced spin Hall shifts at both forward and backward directions. Numerical results from far-field and near-field verify the strong spin-orbit interaction of light. Our work offers a new way to exploit spin Hall effects in superresolution imaging and spin-dependent displacement sensing.