One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements, since it requires a global reconstruction. Here we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.Shortly after the inception of the quantum state, Pauli questioned its measurability, and in particular, whether or not a wave function can be obtained from position and momentum measurements [1]. This question, now referred to as the Pauli problem, draws on concepts such as complementarity and measurement in an attempt to demystify the physical significance of the quantum state. Indeed, the task of determining a quantum state is a central issue in quantum physics due to both its foundational and practical implications. For instance, a method to verify the production of complicated states is desirable in quantum information and quantum metrology applications. Moreover, since a state fully characterizes a system, any possible measurement outcome can be predicted once the state is determined.A wave function describes a quantum system that can be isolated from its environment, meaning the two are non-interacting and the system is in a pure state. More generally, open quantum systems can interact with their environment and the two can become entangled. In such cases, or even in the presence of classical noise, the system is in a statistical mixture of states (i.e. mixed state), and one requires a density matrix to fully describe the quantum system. In fact, some regard the density matrix as more fundamental than the wave function because of its generality and its relationship to classical measurement theory [2].The standard way of measuring the density matrix is by using quantum state tomography (QST). In QST, one performs an often overcomplete set of measurements in incompatible bases on identically prepared copies of the state. Then, one fits a candidate state to the measurement results with the help of a reconstruction algorithm [3]. Many efforts have been made to optimize QST [4][5][6][7], but the scalability of the experimental apparatus and the complexity of the reconstruction algorithm renders the task increasingly difficult for large dimensional systems. In addition, since QST requires a global reconstruction, it ...

Interactions between a single emitter and cavity provide the archetypical system for fundamental quantum electrodynamics. Here we show that a single molecule of Atto647 aligned using DNA origami interacts coherently with a sub-wavelength plasmonic nanocavity, approaching the cooperative regime even at room temperature. Power-dependent pulsed excitation reveals Rabi oscillations, arising from the coupling of the oscillating electric field between the ground and excited states. The observed single-molecule fluorescent emission is split into two modes resulting from anti-crossing with the plasmonic mode, indicating the molecule is strongly coupled to the cavity. The second-order correlation function of the photon emission statistics is found to be pump wavelength dependent, varying from g (2) (0) = 0.4 to 1.45, highlighting the influence of vibrational relaxation on the Jaynes-Cummings ladder. Our results show that cavity quantum electrodynamic effects can be observed in molecular systems at ambient conditions, opening significant potential for device applications.

Metamaterials and metasurfaces provide a paradigm-changing approach for manipulating light. Their potential has been evinced by recent demonstrations of chiral responses much greater than those of natural materials. Here, we demonstrate theoretically and experimentally that the extrinsic chiral response of a metasurface can be dramatically enhanced by near-field diffraction effects. At the core of this phenomenon are lattice plasmon modes that respond selectively to the illumination’s polarization handedness. The metasurface exhibits sharp features in its circular dichroism spectra, which are tunable over a broad bandwidth by changing the illumination angle over a few degrees. Using this property, we demonstrate an ultra-thin circular-polarization sensitive spectral filter with a linewidth of ~10 nm, which can be dynamically tuned over a spectral range of 200 nm. Chiral diffractive metasurfaces, such as the one proposed here, open exciting possibilities for ultra-thin photonic devices with tunable, spin-controlled functionality.

In the past decade, advances in nanotechnology have led to the development of plasmonic nanocavities which facilitate light-matter strong coupling in ambient conditions. The most robust example is the nanoparticle-on-mirror (NPoM) structure whose geometry is controlled with subnanometer precision. The excited plasmons in such nanocavities are extremely sensitive to the exact morphology of the nanocavity, giving rise to unexpected optical behaviors. So far, most theoretical and experimental studies on such nanocavities have been based solely on their scattering and absorption properties. However, these methods do not provide a complete optical description of a NPoM. Here, the NPoM is treated as an open non-conservative system supporting a set of photonic quasinormal modes (QNMs). By investigating the morphology-dependent 1 arXiv:1910.02273v1 [physics.optics] 5 Oct 2019 optical properties of nanocavities, we propose a simple yet comprehensive nomenclature based on spherical harmonics and report spectrally overlapping bright and dark nanogap eigenmodes. The near-field and far-field optical properties of NPoMs are explored and reveal intricate multi-modal interactions. Introduction Metallic nanostructures have the ability to confine light below the diffraction limit via the collective excitation of conduction electrons, called localized surface plasmons. Through recent advances in nanofabrication techniques, gaps of just 1-2 nm between nanostructures have been achieved. 1,2 At such extreme nanogaps, the plasmonic modes of two nanostructures hybridize to allow an unprecedented light confinement, 3,4 making coupled nanostructures an ideal platform for field-enhanced spectroscopy, 5,6 photocatalysis 7 and nano-optoelectronics. 8One such nanostructure is the nanoparticle-on-mirror (NPoM) geometry where a nanoparticle is separated from an underlying metal film by a molecular mono-layer. 9,10 This geometry (which resembles the prototypical dimer but is more reliable and robust to fabricate) has attracted considerable interest since it enables light-matter strong-coupling of a single molecule at room temperature, 11 and it has many potential applications, including biosensing 12 and quantum information. 13,14 A wide range of theoretical and experimental studies have been conducted to investigate the optical properties of NPoM nanocavities. 12,15,16 Several studies examine resonances of NPoMs 17-21 and their influence on optical emission of single molecules in the nanogaps. [22][23][24] However, most studies on the nanocavities have so far described their optical response via a scattering method and infer their resonances from resulting far-field spectral peaks. Although

Plasmonics now delivers sensors capable of detecting single molecules. The emission enhancements and nanometer-scale optical confinement achieved by these metallic nanostructures vastly increase spectroscopic sensitivity, enabling real-time tracking. However, the interaction of light with such nanostructures typically loses all information about the spatial location of molecules within a plasmonic hot spot. Here, we show that ultrathin plasmonic nanogaps support complete mode sets which strongly influence the far-field emission patterns of embedded emitters and allow the reconstruction of dipole positions with 1-nm precision. Emitters in different locations radiate spots, rings, and askew halo images, arising from interference of 2 radiating antenna modes differently coupling light out of the nanogap, highlighting the imaging potential of these plasmonic “crystal balls.” Emitters at the center are now found to live indefinitely, because they radiate so rapidly.