Precisely measuring molecular orientation is key to understanding how molecules organize and interact in soft matter, but the maximum theoretical limit of measurement precision has yet to be quantified. We use quantum estimation theory and Fisher information (QFI) to derive a fundamental bound on the precision of estimating the orientations of rotationally fixed molecules. While direct imaging of the microscope pupil achieves the quantum bound, it is not compatible with widefield imaging, so we propose an interferometric imaging system that also achieves QFI-limited measurement precision. Extending our analysis to rotationally diffusing molecules, we derive conditions that enable a subset of second-order dipole orientation moments to be measured with quantum-limited precision. Interestingly, we find that no existing techniques can measure all second moments simultaneously with QFI-limited precision; there exists a fundamental trade-off between precisely measuring the mean orientation of a molecule versus its wobble. This theoretical analysis provides crucial insight for optimizing the design of orientation-sensitive imaging systems.
We study cooperative behavior of quantum dipole emitters coupled to a rectangular waveguide with dielectric core and silver cladding. We investigate cooperative emission and inter-emitter entanglement generation phenomena for emitters whose resonant frequencies are near the frequency cutoff of the waveguide, where the waveguide effectively behaves as zero-index metamaterial. We show that coupling emitters to a zero-index waveguide allows one to relax the constraint on precision positioning of emitters for observing inter-emitter entanglement generation and extend the spatial scale at which the…
We study the radiative decay rate and Purcell effect for a finite-size dipole emitter placed in a homogeneous uniaxial medium. We demonstrate that the radiative rate is strongly enhanced when the signs of the longitudinal and transverse dielectric constants of the medium are opposite, and the isofrequency contour has a hyperbolic shape. We reveal that the Purcell enhancement factor remains finite even in the absence of losses, and it depends on the emitter size.
We show that the surface plasmon polariton (SPP) radiation patterns of point-dipole emitters in the vicinity of a metal-dielectric interface are generally asymmetric with respect to the location of the emitter. In particular rotating dipoles, which emit elliptically polarized light, produce highly asymmetric SPP radiation fields that include unidirectional emission. Asymmetric SPP radiation patterns also result when a dipole oscillates tilted with respect to the plane of the interface and optical losses or gains are present in the materials. These effects can be used to directionally control S…
Single molecule localization microscopy has the potential to resolve structural details of biological samples at the nanometer length scale. However, to fully exploit the resolution it is crucial to account for the anisotropic emission characteristics of fluorescence dipole emitters. In case of slight residual defocus, localization estimates may well be biased by tens of nanometers. We show here that astigmatic imaging in combination with information about the dipole orientation allows to extract the position of the dipole emitters without localization bias and down to a precision of ~1nm, the…
We analytically study the spontaneous emission of a single optical dipole emitter in the vicinity of a plasmonic nanoshell, based on the Lorenz-Mie theory. We show that the fluorescence enhancement due to the coupling between optical emitter and sphere can be tuned by the aspect ratio of the core-shell nanosphere and by the distance between the quantum emitter and its surface. In particular, we demonstrate that both the enhancement and quenching of the fluorescence intensity are associated with plasmonic Fano resonances induced by near- and far-field interactions. These Fano resonances have as…
The efficiency of an organic light-emitting diode (OLED) depends on the microscopic orientation of transition dipole moments of the molecular emitters. The most effective materials used for light generation have threefold symmetry, which prohibit a priori determination of dipole orientation due to the degeneracy of the fundamental transition. Single-molecule spectroscopy reveals that the model triplet emitter tris(2-phenylisoquinoline)iridium(III) (Ir(piq)3) does not behave as a linear dipole, radiating with lower polarization anisotropy than expected. Spontaneous symmetry breaking occurs in t…
We introduce a generalized Dicke-like model to describe two-level systems coupled with a single bosonic mode. In addition, the two-level systems mutually interact via direct dipole-dipole interaction. We apply the model to an ensemble of dye molecules coupled to a plasmonic excitation in a metallic nanoparticle and study how the dipole-dipole interaction and configurational randomness introduced to the system affect the energy spectra. Comparing the system eigenenergies obtained by our model with the light spectra from a multiple-scattering simulation, we suggest a way to identify dark modes i…
We identify a solid-state quantum emitter whose room-temperature radiative decay is mediated by a nearly equal mixture of isotropic electric dipole (ED) and magnetic dipole (MD) transitions. Using energy-momentum spectroscopy, we experimentally show that the near-infrared $^3$T$_2{\rightarrow}^3$A$_2$ emission from divalent-nickel-doped magnesium oxide (Ni$^{2+}$:MgO) is composed of $\sim$50% MD and $\sim$50% ED transitions. We then demonstrate that the spontaneous emission rate of these ions near planar interfaces is determined by the combined electric and magnetic local density of optical st…
The interaction of magnetic dipole (MD) emitters and common photonic cavities is usually weak, which is partially due to the low magnetic near field enhancements of the cavities. Here, we show that whispering gallery modes (WGMs) of a subwavelength dielectric cavity can not only greatly boost the emission rate of a MD emitter but also bring efficient couplings between coherent MD emitters. In a WGM cavity, the maximal emission rate (γmax) of a single emitter occurs at an antinode of the field pattern. The emission of the MD emitter can also be greatly affected by another coherent one depending…
Control over transition rates between spin states of emitters is crucial in a wide variety of fields ranging from quantum information science to the nanochemistry of free radicals. We present an approach to drive a both electric and magnetic dipole-forbidden transition of a spin emitter by placing it in a nanomagnonic cavity, requiring a description of both the spin emitter beyond the point dipole approximation and the vacuum magnetic fields of the nanomagnonic cavity with a large spatial gradient over the volume of the spin emitter. We specifically study the SiV$^-$ defect in diamond, whose Z…
We provide a simple semi-classical formalism to describe the coupling between one or several quantum emitters and a structured environment. Describing the emitter by an electric polarizability, and the surrounding medium by a Green function, we show that an intuitive scattering picture allows one to derive a coupling equation from which the eigenfrequencies of the coupled system can be extracted. The model covers a variety of regimes observed in light-matter interaction, including weak and strong coupling, coherent collective interactions, and incoherent energy transfer. It provides a unified …
We investigate the impact of rotational diffusion on the electrodynamic coupling of fluorescent dye molecules (oscillating electric dipoles) to a tunable planar metallic nanocavity. Fast rotational diffusion of the molecules leads to a rapidly fluctuating mode density of the electromagnetic field along the molecules' dipole axis, which significantly changes their coupling to the field as compared to the opposite limit of fixed dipole orientation. We derive a theoretical treatment of the problem and present experimental results for rhodamine 6G molecules in cavities filled with low and high vis…
The collective spontaneous emission of two point-dipole emitters near a plasmonic core-shell nanosphere is theoretically investigated. Based on the expansion of mode functions in vector spherical harmonics, we derive closed analytical expressions for both the cooperative decay rate and the dipole-dipole interaction strength associated with two point dipoles close to a sphere. Considering a plasmonic nanoshell containing a linearly amplifying medium inside the core, the second-order correlation function for the two emitters shows that it is possible to tune the photon emission, selecting either…
Chiral emission can be achieved from a circularly polarized dipole emitter in a nanophotonic structure that possess special polarization properties such as a polarization singularity, namely with right or left circularly polarization (C-points). Recently, Chen et al. [Nature Physics 16, 571 (2020)] demonstrated the surprising result of chiral radiation from a linearly-polarized (LP) dipole emitter, and argued that this effect is caused by a decoupling with the underlying eigenmodes of a non-Hermitian system, working at an exceptional point (EP). Here we present a quasinormal mode (QNM) approac…
We theoretically investigate the emergence of lateral (recoil) forces acting on generic dipole-type emitters in the vicinity of a reciprocal translation-invariant substrate. Surprisingly, we find that for linearly-polarized electric dipoles the lateral force invariably vanishes, independent of the anisotropy (e.g., tilted optical axes) or chirality of the substrate. We identify a novel opportunity to have a recoil force relying on a superposition of two linearly-polarized and collinear electric and magnetic dipoles. Counterintuitively, it is shown that when such an emitter stands above a uniax…
Photon emission is the hallmark of light-matter interaction and the foundation of photonic quantum science, enabling advanced sources for quantum communication and computing. Although single-emitter radiation can be tailored by the photonic environment, the introduction of multiple emitters extends this picture. A fundamental challenge, however, is that the radiative dipole-dipole coupling rapidly decays with spatial separation, typically within a fraction of the optical wavelength. We realize distant dipole-dipole radiative coupling with pairs of solid-state optical quantum emitters embedded …
Presence of a metal nanoparticle near a quantum dipole emitter, when a localized surface plasmon mode is excited via the resonant coupling with an excited quantum dipole, changes dramatically the relaxation dynamics: it is no longer described by an exponential decay but exhibits step-like behavior. The main physical consequence of this relaxation process is that the emission, being largely determined by the metal nanoparticle, comes out with a substantial delay. A large number of system parameters in our analytical description opens new possibilities for controlling quantum emitter dynamics.
We investigate the propagation properties of the optical vortices emitted from a collectively polarized electric dipole array as a simple model of the several emitters. Using an analytical approach based on the Jacobi-Anger expansion, we derive a relationship between the topological charge of the optical vortices and the source conditions of the emitter, and clarify and report our new finding; there exists an intrinsic split of the singular points in the electric field due to the spin-orbit interaction of the dipole fields.
All-dielectric nanoantennas are a promising alternative to plasmonic optical antennas for engineering light emission because of their low-loss nature in the optical spectrum. Nevertheless, it is still challenging to manipulate directional light emission with subwavelength all-dielectric nanoantennas. Here, we propose and numerically demonstrate that a hollow silicon nanodisk can serve as a versatile antenna for directing and enhancing the emission from either an electric or magnetic dipole emitter. When primarily coupled to both electric and magnetic dipole modes of a nanoantenna, broadband ne…
Transverse Kerker effect is known by the directional scattering of an electromagnetic plane wave perpendicular to the propagation direction with nearly suppression of both forward and backward scattering. Compared with plane waves, localized electromagnetic emitters are more general sources in modern nanophotonics. As a typical example, manipulating the emission direction of a quantum dot is of virtue importance for the investigation of on-chip quantum optics and quantum information processing. Herein, we introduce the concept of transverse Kerker effect of localized electromagnetic sources ut…
Meta--surfaces are the bidimensional analogue of metamaterials. They are made on resonant elements periodically disposed on a surface. They have the ability of controlling the polarization of light and to generalized refraction laws as well. They have also been used to enhance the generation of the second harmonic. It seems however that their near-field properties have not been investigated. In this work, the coupling of an emitter with a meta-- surface made of a periodic set of resonant linear dipoles was studied. Bloch surface modes localized on the meta--surface exist due the resonance of t…
We study theoretically the rate of spontaneous emission of a two-level quantum emitter embedded in realistic systems: near a mirror, near a plasmonic sphere, or in a 3D photonic bandgap crystal. At constant frequency and position, we find striking (up to $10^{2}\times$) variations in emission rate by varying the orientation of the transition dipole moment. We present a general representation of rate versus orientation that only invokes symmetry of the Green function. The concomitant 3-dimensional geometric surfaces provide much insight in how preferred orientations for enhancement (or inhibiti…
Manipulating the spontaneous emission rate of optical emitters with all-dielectric nanoparticles benefits from their low-loss nature and thus provides relatively large extrinsic quantum yield. However, such Purcell effect greatly depends on the orientation of the dipole emitter. Here, we introduce the concept of isotropic magnetic Purcell effect with Purcell factors about 300 and large extrinsic quantum yield (more than 80%) for a magnetic dipole emitter of arbitrary orientation in an asymmetric silicon nanocavity. The extrinsic quantum yield can be even boosted up to nearly 100% by utilizing …
A detailed theory describing linear optics of vapors comprised of interacting multi-level quantum emitters is proposed. It is shown both by direct integration of Maxwell-Bloch equations and using a simple analytical model that at large densities narrow transparency windows appear in otherwise completely opaque spectra. The existence of such windows is attributed to overlapping resonances. This effect, first introduced for three-level systems in [R. Puthumpally-Joseph, M. Sukharev, O. Atabek and E. Charron, Phys. Rev. Lett. 113, 163603 (2014)], is due to strongly enhanced dipole-dipole interact…
On-demand, high repetition rate sources of indistinguishable, polarised single photons are the key component for future photonic quantum technologies. Colour centres in diamond offer a promising solution, and the narrow line-width of the recently identified nickel-based NE8 centre makes it particularly appealing for realising the transform-limited sources necessary for quantum interference. Here we report the characterisation of dipole orientation and coherence properties of a single NE8 colour centre in a diamond nanocrystal at room-temperature. We observe a single photon coherence time of 0.…
Spintronic emitters are a unique class of terahertz (THz) sources due to their quasi-two-dimensional geometry and thereby their capability to couple to resonator near fields. Global excitation of the emitters often obstructs the intricate details of the coupling mechanisms between local THz dipoles and the individual modes of resonator structures. Here, we demonstrate the spatial mapping of the coupling strength between a local terahertz source on a spintronic emitter and far-field light mediated by a structured metallic environment. For a bow-tie geometry, experimental results are reproduced …
Controlling photon emission by single quantum emitters with nanostructures is crucial for scalable on-chip quantum information processing. Nowadays nanoresonators can affect the lifetime of emitters and ultimately induce strong coupling between the emitters and the light field, while nanoantennas can control the directionality of the emission. Expanding this control to the manipulation of the emission of orbital angular momentum-changing transitions would enable coupling between long-lived solid-state qubits and flying qubits. As these transitions are associated with circular rather than linea…
In Nature Photonics 5, 166 (2011), we reported on a planar dielectric antenna that achieved 96% efficiency in collecting the photons emitted by a single molecule. In that work the transition dipole moment of the molecule was set perpendicular to the antenna plane. Here, we present an extension of that scheme that reaches collection efficiencies beyond 99% for emitters with arbitrarily oriented dipole moments. Our work opens important doors in a wide range of contexts including quantum optics, quantum metrology, nano-analytics, and biophysics. In particular, we provide antenna parameters to rea…
Quantum emitters in hexagonal boron nitride (hBN) are promising building blocks for the realization of integrated quantum photonic systems. However, their spectral inhomogeneity currently limits their potential applications. Here, we apply tensile strain to quantum emitters embedded in few-layer hBN films and realize both red and blue spectral shifts with tuning magnitudes up to 65 meV, a record for any two-dimensional quantum source. We demonstrate reversible tuning of the emission and related photophysical properties. We also observe rotation of the optical dipole in response to strain, sugg…
Considerable progress has been made in organic light-emitting diodes (OLEDs) to achieve high external quantum efficiency (EQE), among which the dipole orientation of OLED emitters has a remarkable effect. In most cases, EQE of the OLED emitter is theoretically predicted with only one orientation factor to match with corresponding experiments. Here, we develop a distribution theory with three independent parameters to fully describe the relationship between dipole orientations and power densities. Furthermore, we propose an optimal experiment configuration for measuring such distribution parame…
Based on the Lorenz-Mie theory, we derive analytical expressions of radiative and nonradiative transition rates for different orientations of a point dipole emitter in the vicinity of an infinitely long circular cylinder of arbitrary radius. Special attention is devoted to the spontaneous decay rate of a dipole emitter near a subwavelength-diameter nanowire coated with a graphene monolayer. We show that plasmonic Fano resonances associated with light scattering by graphene-coated nanowires appear in the Purcell factor as a function of transition wavelength. Furthermore, the Fano line shape of …
The spontaneous emission rate of dipole emitters close to plasmonic dimers are theoretically studied within a nonlocal hydrodynamic model. A nonlocal model has to be used since quantum emitters in the immediate environment of a metallic nanoparticle probe its electronic structure. Compared to local calculations, the emission rate is significantly reduced. The influence is mostly pronounced if the emitter is located close to sharp edges. We suggest to use quantum emitters to test nonlocal effects in experimentally feasible configurations.
The control and manipulation of quantum-entangled non-local states is a crucial step for the development of quantum information processing. A promising route to achieve such states on a wide scale is to couple solid-state quantum emitters through their coherent dipole-dipole interactions. Entanglement in itself is challenging, as it requires both nanometric distances between emitters and nearly degenerate electronic transitions. Implementing hyperspectral imaging to identify pairs of coupled organic molecules trapped in a low temperature matrix, we reach distinctive spectral signatures of maxi…
We determine the optical response of a thin and dense layer of interacting quantum emitters. We show that in such a dense system, the Lorentz redshift and the associated interaction broadening can be used to control the transmission and reflection spectra. In the presence of overlapping resonances, a Dipole-Induced Electromagnetic Transparency (DIET) regime, similar to Electromagnetically Induced Transparency (EIT), may be achieved. DIET relies on destructive interference between the electromagnetic waves emitted by quantum emitters. Carefully tuning material parameters allows to achieve narro…
The radiation of an emitter does not depend only on its intrinsic properties but also on the surrounding photonic environment, the notion of which is essential in the developments of lasers, quantum optics and other light-matter interaction related fields. However, in conventional wisdom, an emitter radiates into photonic eigenstates in the weak coupling regime and does not alter the property of the latter. Here, we report a counterintuitive phenomenon where the radiation field of a dipole in a parity-time symmetric ring resonator displays the opposite handedness to the eigenstates of the syst…
Tailoring of electromagnetic spontaneous emission predicted by E. M. Purcell more than 50 years ago has undoubtedly proven to be one of the most important effects in the rich areas of quantum optics and nanophotonics. Although during the past decades the research in this field has been focused on electric dipole emission, the recent progress in nanofabrication and study of magnetic quantum emitters, such as rare-earth ions, has stimulated the investigation of the magnetic side of spontaneous emission. Here, we review the state-of-the-art advances in the field of spontaneous emission enhancemen…
We investigate the impact of the dipole-active modes formed via the mode-mixing of the dipole mode with higher-order surface plasmon modes of a nanoegg on the radiative decay rate and quantum yield of an excited molecule near the nanoegg. The Purcell factor, rate of power dissipation by the emitter, antenna efficiency of the nanoegg, as well as quantum yield enhancement of the emitter, were studied using the quasistatic approximation and the semiclassical theory of radiation, following the Gersten-Nitzan and Ford-Weber approaches. Compared to the concentric nanoshell, we show that the dielectr…
We consider the generic problem of a two-level quantum emitter near a two-dimensional Chern insulator in the dipole approximation, and study how the frequency-dependent response and electronic density of states of the insulator modifies the transition rate of the emitter between the ground and excited levels. To this end, we obtain the full real-frequency behavior of the conductivity tensor by performing a tight-binding calculation based on the Qi-Wu-Zhang model and using a Kubo formula, and derive the full electromagnetic Green tensor of the system, which breaks Onsager reciprocity. This enab…
In this work, we propose an approach for the design of a waveguide structure that allows for efficient and highly asymmetric coupling of the quantum sources with circularly polarized transition dipole moments to the guided mode of the structure. The approach is based on the mixing of the two quasi-degenerate modes of a periodic waveguide with an auxiliary single-mode waveguide leading to the formation of the dispersion with a stationary inflection point and consequently to the high coupling efficiency of this mode with a dipole source. We show that the distribution of the field polarization in…
We demonstrate theoretically and experimentally that the three-dimensional orientation of a single fluorescent nano-emitter can be determined by polarization analysis of the emitted light (while excitation polarization analysis provides only the in-plane orientation). The determination of the emitter orientation by polarimetry requires a theoretical description including the objective numerical aperture, the 1D or 2D nature of the emitting dipole and the environment close to the dipole. We develop a model covering most experimentally relevant microscopy configurations and provide analytical re…
We theoretically characterize the collective radiative behaviour of N classical emitters near an interface between different dielectrics that supports the transfer of surface plasmon modes into the far-field of electromagnetic radiation. The phenomena of superradiance and surface plasmons can be combined to amplify the emitted radiation intensity S as S= A N^2 S_0 compared to a single emitter's intensity S_0 in free space. For a practical case study within the paper A=240, compared to A=1 in free space. We furthermore demonstrate that there are collective modes for which the intensity of the e…
In this paper we derive a general expression for the emission rate of an emitter which is placed at the center of a real cavity drilled in a generic random medium. We apply our formalism to the computation of the decay rate of a single atom which seats within a small molecule embedded in a continuous medium.
Generation of polarization-entangled photon pairs from two interacting quantum emitters
Centro de Física de Materiales (CMF-MPC), CSIC-UPV/EHU（材料物理中心（CMF-MPC），CSIC-巴斯克国立大学联盟）；Department of Electricity and Electronics, University of the Basque Country (UPV/EHU)（巴斯克国立大学（UPV/EHU）电力与电子工程系）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心（DIPC））；Ikerbasque, Basque Foundation for Science（伊克尔巴斯科，巴斯克科学基金会）
In this paper we develop a microscopic analysis of the light scattering on a periodic two-level atomic array coupled to an optical nanofiber. We extend the scattering matrix approach for two-level system interaction with nanofiber fundamental waveguiding mode HE_{11}, that allows us modeling the scattering spectra. We support these results considering the dispersion of the polaritonic states formed by the superposition of the fundamental mode of light HE_{11} and the atomic chain states. To illustrate our approach we start with considering a simple model of light scattering over atomic array i…
We investigate the emission of single photons from CdSe/CdS dot-in-rods which are optically trapped in the focus of a deep parabolic mirror. Thanks to this mirror, we are able to image almost the full 4$π$ emission pattern of nanometer-sized elementary dipoles and verify the alignment of the rods within the optical trap. From the motional dynamics of the emitters in the trap we infer that the single-photon emission occurs from clusters comprising several emitters. We demonstrate the optical trapping of rod-shaped quantum emitters in a configuration suitable for efficiently coupling an ensemble…
When arranged in a periodic geometry, arrays of metallic nanostructures are capable of supporting collective modes known as lattice resonances. These modes, which originate from the coherent multiple scattering between the elements of the array, give rise to very strong and spectrally narrow optical responses. Here, we show that, thanks to their collective nature, the lattice resonances of a periodic array of metallic nanoparticles can mediate an efficient long-range coupling between dipole emitters placed near the array. Specifically, using a coupled dipole approach, we calculate the Green te…
