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Polarization entanglement of the created hybrid entanglement bi-photon state. (A) Three different tests for polarization entanglement were performed: witness (dark red, Eqs. 2), steering (light red, Eqs. 3), Bell-CHSH (blue, Eqs. 4). For LG vector photons and Poincaré photons the Bell- CHSH inequality was tested with L, R, D and A polarization triggers instead of the usual H, V, D and A polarization settings. The different strengths of the criteria are directly visible in the size of the non-classical regions, i.e. regions where more than 100 photons contributed to every term of each criterion and the classical bound is exceeded by 3 stan- dard deviations (Poissonian count statistics assumed). (B) If the polarization setting in front of the ICCD camera is altered (rotation of the reference frame) to account for the varying polarizations within the vector photon’s polarization pattern an interesting entanglement pattern appears. Only where the modal overlap of the two components is big enough (and enough photons were detected) can entanglement in polarization be revealed (small insets: theory). (C) Similarly for custom-tailored Poincaré photons, the modal overlap is too small on the left and right parts of the beam irrespectively of the trigger polarization settings (left and right measurement and theory insets) thus regions of entanglement are rarely found there.
Source publication
We report the efficient creation and detection of hybrid entanglement between
one photon's polarization and another photon's complex transverse polarization
pattern. The polarization measurement of the first photon triggers a
polarization sensitive imaging of its partner photon, the vector photon, using
a single-photon sensitive camera. Thereby, we...
Contexts in source publication
Context 1
... α , α , β and β denote different measurement settings (orientations of the polarizer) and E is the nor- malized expectation value for photon pairs to be found with these settings. A violation of this Bell-CHSH-bound proves entanglement of the created state without relying on any quantum mechanical assumptions, thus it ex- cludes a larger class of states, i.e. every state described by local realism. In Fig. 4 A, regions are shown where the witness, the steering or the Bell-CHSH inequalities prove entanglement. The measured results depict visually, that the weaker the assumptions of the criterion the smaller are the regions of successful entanglement demonstration. Furthermore, a novel interesting feature of entangled vector photons can be demonstrated by testing locally for polarization entanglement (Fig. 4 B). To account for the spatially varying polarization, different “reference frames” i.e. polarizer angles can be used to measure entanglement at different regions of the transverse beam spread. Hereby, the substantial difference between the demonstrated vector photons becomes apparent: if they consist of two beams with the same spatial intensity pro- file (e.g. vector photons from circularly polarized LG modes of the same order), any transverse position shows polarization entanglement. In contrast, if vector photons are built by modes that have different transverse pro- files, entanglement in the polarization DOF can only be found in regions where the overlap is big enough. The- oretically only very small regions are separable, because a small overlap between the two modes already leads to (non-maximally) entangled photons. To experimentally demonstrate the effect we used the Bell-CHSH-criterion (Eqs. 4) where the regions of proven entanglement are the smallest for each reference frame. This interesting feature of being entangled and separable in the polarization DOF at the same time can be explained intuitively: at transverse positions where a polarization measurement can reveal the path of the photon inside the interferometer (with which we created the vector photon) no superposition and thus no entanglement is measurable. In summary, we have used hybrid entanglement between polarization and different types of vector ...
Context 2
... α , α , β and β denote different measurement settings (orientations of the polarizer) and E is the nor- malized expectation value for photon pairs to be found with these settings. A violation of this Bell-CHSH-bound proves entanglement of the created state without relying on any quantum mechanical assumptions, thus it ex- cludes a larger class of states, i.e. every state described by local realism. In Fig. 4 A, regions are shown where the witness, the steering or the Bell-CHSH inequalities prove entanglement. The measured results depict visually, that the weaker the assumptions of the criterion the smaller are the regions of successful entanglement demonstration. Furthermore, a novel interesting feature of entangled vector photons can be demonstrated by testing locally for polarization entanglement (Fig. 4 B). To account for the spatially varying polarization, different “reference frames” i.e. polarizer angles can be used to measure entanglement at different regions of the transverse beam spread. Hereby, the substantial difference between the demonstrated vector photons becomes apparent: if they consist of two beams with the same spatial intensity pro- file (e.g. vector photons from circularly polarized LG modes of the same order), any transverse position shows polarization entanglement. In contrast, if vector photons are built by modes that have different transverse pro- files, entanglement in the polarization DOF can only be found in regions where the overlap is big enough. The- oretically only very small regions are separable, because a small overlap between the two modes already leads to (non-maximally) entangled photons. To experimentally demonstrate the effect we used the Bell-CHSH-criterion (Eqs. 4) where the regions of proven entanglement are the smallest for each reference frame. This interesting feature of being entangled and separable in the polarization DOF at the same time can be explained intuitively: at transverse positions where a polarization measurement can reveal the path of the photon inside the interferometer (with which we created the vector photon) no superposition and thus no entanglement is measurable. In summary, we have used hybrid entanglement between polarization and different types of vector ...
Context 3
... a , b , and φ are real and a + b = 1; H and V denote the horizontal and vertical polarization of the unchanged photon; spM and its index represents the different spatial modes and their polarizations (H, V, R, L for horizontal, vertical, right and left hand circular respectively); the positions of the ket-vectors label the different photons. Due to the flexibility of the SLM, a huge variety of different vector beams including “cylindrical vector beams”, showing cylindrical symmetry in their polarization pattern [9], and “Poincaré beams”, containing all polarizations on the Poincaré sphere [13], can be realized [17, 23]. The crucial phase-stability of the interferometer was assured by a folded Sagnac-like structure [24]. The polarization pattern of the vector photon depends on the type and result of the polarization measurement of its partner photon. Therefore, we performed a coincidence imaging measurement [25] extending it with polarization analysis. The single-photon detector signal of a polarization measurement is used as a trigger for an intensified CCD camera (ICCD) (Andor iStar A-DH334T-18U-73, 5ns coincidence window, 20% quantum efficiency, effec- tive pixel size 13x13 μ m). From a polarization tomography of the vector photon, performed by a polarizing filter and the ICCD camera, the complex polarization pattern can be reconstructed with very high spatial resolution ( Fig. 2). Due to entanglement, different polarizations of the trigger photon result in different polarization patterns of its partner vector photon, thus the Bloch sphere for vector photons — the higher order Poincaré sphere — can be imaged [26][27]. The polarization patterns of cylindrical vector photons built by linearly polarized HG modes or circularly polarized LG modes can be distinctly recog- nized for different trigger polarizations (Fig. 3, first two rows). In addition, Poincaré photons are remotely generated which exhibit various polarization singularities, like C-points (orientation of the polarization ellipse is unde- fined) or L-lines (handedness of the polarization is unde- fined) [16, 17] (Fig. 3, third row). If the SLM surface is imaged on the ICCD camera chip and the diffraction efficiency of the displayed hologram is adjusted according to the desired intensity structure, the phase and the intensity of the photons can be modulated [28]. With this technique it is possible to create and entangle any custom-tailored polarization pattern for the vector photon. We demonstrate this remarkable flexibility by creating a square shaped vector beam consisting of two linearly polarized modes (Fig. 3, fourth row). For each mode the intensity changes linearly from left to right and the phase varies linearly from top to bottom. This results in a polarization pattern with a continuous change from V (left side) to H (right side) through all possible polarizations, as a function of the vertical position. So far, the high-contrast intensity images for different trigger polarizations and the subsequent changes of the polarization patterns have only suggested the successful generation of entanglement. However, to demonstrate the non-classicality of the state quantitatively, we evaluate locally “for every hybrid entangled photon pair” three different types of entanglement measures in the polarization DOF (Fig. 4). We register coincidence images for appropriate polarization combinations (trigger and image polarization) and evaluate the average photon number within regions of 10x10 pixels. From these local measurements we calculate the value for each entanglement criterion. Note, that this is only feasible with our real-time coincidence imaging technique [25]. Relying on counting single-photon events in sparse images or scan- ning single-pixel detectors across the beam would have been extremely challenging and time consuming. The first measure of entanglement is an entanglement ...
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A single photon is well known to have spin S = hbar, which would correspond
to circular polarization, and all quantum transitions with photon absorption or
emission correspond to DeltaS = +/-hbar. However, it is also widely believed
that a single photon may be linearly polarized, which would correspond to a
state with S = 0. Indeed, linearly polari...
Citations
... However, other kinds of vortex beams came up along with the development of sophisticated optical approaches for generating, manipulating, and analyzing light fields [2][3][4][5][6][7][8] . In fact, it was found that it was possible to construct stable optical modes for which the polarization varies across the plane transverse to the propagation direction [9][10][11][12] . To this kind of light beams was given the name Vector Vortex Beams (VVB) 13 . ...
We experimentally demonstrate resonance of first-order vector vortex beams (VVB) with a triangular optical cavity. We also show that, due to their symmetry properties, the VVBs commonly known as radial and azimuthal beams do not resonate at the same cavity length, which could be explored to use the triangular resonator as a mode sorter. In addition, an intracavity Pancharatnam phase shifter (PPS) is implemented in order to compensate for any birefringent phase that the cavity mirrors may introduce.
... While VV beams have been generated both actively [27,28]-i.e., via laser intracavity devices-and passively-through extra-cavity devices [29]-entangled photons in VV modes have so far been generated in a two-step sequence. Thus, single photons are first generated in standard modes, which are subsequently transformed into structured modes using dedicated optical components [22,24,[30][31][32]. However, generating structured single photons directly at the source could prove to be more convenient for compactness, flexibility, and/or scalability in the implementation of quantum information protocols. ...
We demonstrate an experimental protocol for the preparation and control of heralded single photons in inhomogeneously polarized states, such as vector vortex and full Poincaré beam states. A laser beam is shaped by a voltage-controlled spin-to-orbital angular momentum converter q-plate device, which eliminates the need for an interferometer for the robust preparation of high-quality inhomogeneously polarized beams. Such a beam is then used as a pump in a spontaneous parametric down-conversion (SPDC) photon-pair source. We demonstrate the full pump to heralded single-photon transfer of the intensity and phase distributions, as well as of the vector polarization structure. Additionally, we show that by controlling the polarization to which the heralding idler photon is projected before detection, we can toggle between the direct and basis-switched pump-single-photon transfer. We show that this nonlocal control of the heralded single photon pertains also to the topological class of the resulting heralded single photon. We believe that our work will lead to opportunities in photon-based quantum information processing science.
... By using a triggerable intensified CCD (ICCD) camera, where a single-pixel detector triggers the ICCD, a total of ðN × NÞ × 16 data acquisition runs will be required where in each run a polarization measurement is taken simultaneously between each pixel of the camera and the single-pixel detector. This is partially demonstrated in the case of a homogeneously polarized mode entangled to a VM [27,31]. ...
... To showcase the versatility of our technique, we perform the characterization for various polarization topological patterns, including vector-vortex, lemon, star, and spiral polarization patterns, all exhibiting exceptional agreement with the anticipated entanglement pattern derived from theory. Compared to past demonstrations [27][28][29]31], this is the first time the fourdimensional spatially dependent polarization entanglement structure of EVMs is fully characterized without requiring prior knowledge of the involved VMs. The ability to perform this type of measurement within a reasonable time will have a profound impact on the fundamental studies of structured light entanglement as well as their potential applications in fields such as quantum communications and quantum sensing. ...
... This is the first experiment in which the four-dimensional entanglement structure of EVMs is fully characterized and has revealed previously unseen entanglement structures. Past experiments could only perform the characterization in either two or three dimensions [27][28][29]31]. The demonstrated method can be invaluable for quickly characterizing spatially varying entanglement in EVMs, which are gaining interest in various high-dimensional quantum systems such as quantum communication and quantum imaging. ...
Vector modes are fully polarized modes of light with spatially varying polarization distributions, and they have found widespread use in numerous applications such as microscopy, metrology, optical trapping, nanophotonics, and communications. The entanglement of such modes has attracted significant interest, and it has been shown to have tremendous potential in expanding existing applications and enabling new ones. However, due to the complex spatially varying polarization structure of entangled vector modes (EVMs), a complete entanglement characterization of these modes remains challenging and time consuming. Here, we have used a time-tagging event camera to demonstrate the ability to completely characterize the entanglement of EVMs. Leveraging the camera’s capacity to provide independent measurements for each pixel, we simultaneously characterize the entanglement of approximately 2.6×106 modes between a bipartite EVM through measuring only 16 observables in polarization. We reveal that EVMs can naturally generate various polarization-entangled Bell states. This achievement is an important milestone in high-dimensional entanglement characterization of structured light, and it could significantly impact the implementation of related quantum technologies. The potential applications of this technique are extensive, and it could pave the way for advancements in quantum communication, quantum imaging, and other areas where structured entangled photons play a crucial role.
... This fact makes vector beam an excellent paradigm of quantum-classical connection, enabling the simulation of diverse quantum processes using classical light [40][41][42]. Moreover, quantum entanglement has also been realized for the vector beam as carriers with both the spatial and polarization information [43][44][45], which may have some interesting applications in alignment-free quantum key distribution [46][47][48]. ...
Based on the electromagnetically induced transparency (EIT) model and the higher-order Poincaré sphere (HOPS) framework, we establish a general paradigm to investigate the paraxial evolution of a vector beam in a tripod EIT system. By quantum-optical analogy, we introduce a formalism with a generalized Pauli-like equation under rotational invariance, in which the pseudo-spin-orbit coupling (PSOC) and the spin-orbit nonseparability of light can coexist. More importantly, we find that both the PSOC-based real and imaginary potentials play a key role in controlling and modulating the nonseparable state of the vector beam to traverse the entire HOPS, where the orientation and ellipticity of the transmitted polarization can be modified by varying the PSOC coefficients. Therefore, an all-optical scheme can be proposed to improve the flexibility for tailoring the space-variant polarization of light in coherent media, where the tunable spatial-polarization multiplexing may be useful in conventional and quantum information processing.
... Employing single-pixel detectors, such as avalanche photodiodes, necessitates (N ×N ) 2 ×16 measurements, with N × N representing the number of spatial locations on each beam to be probed, and 16 denoting the required polarization measurement combinations [30]. By using a triggerable intensified CCD (ICCD) camera, where a single-pixel detector triggers the ICCD, the number of measurements can be reduced to (N × N ) × 16, as partially demonstrated in the case of a homogeneously polarized beam entangled to a VB [27,31]. ...
Vector beams (VBs) are fully polarized beams with spatially varying polarization distributions, and they have found widespread use in numerous applications such as microscopy, metrology, optical trapping, nano-photonics, and communications. The entanglement of such beams has attracted significant interest, and it has been shown to have tremendous potential in expanding existing applications and enabling new ones. However, due to the complex spatially varying polarization structure of entangled VBs (EVBs), a complete entanglement characterization of these beams remains challenging and time-consuming. Here, we have used a time-tagging event camera to demonstrate the ability to simultaneously characterize approximately $2.6\times10^6$ modes between a bi-partite EVB using only 16 measurements. This achievement is an important milestone in high-dimensional entanglement characterization of structured light, and it could significantly impact the implementation of related quantum technologies. The potential applications of this technique are extensive, and it could pave the way for advancements in quantum communication, quantum imaging, and other areas where structured entangled photons play a crucial role.
... To efficiently implement spatial modes in QKD schemes, appropriate techniques for "preparation" and "measurement" of MUB states are required; in this context, future commercialization demands, in particular, stable, compact, and robust tools. So far, mainly bulky, complex techniques for encoding or decoding spatial modes have been realized, using spatial light modulators, digital mirror devices, combinations of q-and waveplates, or mode sorters [15,17,[21][22][23][24][25][26][27]. In contrast, integrated quantum photonics [1,28] holds the potential of miniaturizing and stabilizing encoding and decoding systems at low cost, scalability, and industrial compatibility. ...
Spatial modes of light have become highly attractive to increase the dimension and, thereby, security and information capacity in quantum key distribution (QKD). So far, only transverse electric field components have been considered, while longitudinal polarization components have remained neglected. Here, we present an approach to include all three spatial dimensions of electric field oscillation in QKD by implementing our tunable, on-a-chip vector beam decoder (VBD). This inversely designed device pioneers the "preparation" and "measurement" of three-dimensionally polarized mutually unbiased basis states for high-dimensional (HD) QKD and paves the way for the integration of HD QKD with spatial modes in multifunctional on-a-chip photonics platforms.
... Vector beams (VBs) with spatially nonuniform polarization and phase distribution have attracted much interest for their potential applications in optical manipulation, [1,2] optical trapping, [3,4] and quantum communication. [5][6][7] The VBs, maintaining two orthogonal circular polarizations with opposite orbital angular momentum (OAM), are usually selected as the good candidate for coding hybrid quantum states in quantum information protocols. [8,9] Essentially, the VBs carry a form of entanglement in their two degrees of freedom, which can represent classically entangled light, and are widely used in quantum communication. ...
Vector beams with spiral phase and spatially varying polarization profiles have many applications from optical micromanipulation to materials processing. Here, we propose and demonstrate an atomic spatial mode extracting scheme for the vector beam based on polarization-dependent absorption in the atom vapor. By employing the linear polarization pump beam which induces polarization sensitive absorption in the atomic ensemble, a counter-propagated weak probe vector beam is extracted by spatial absorption, and extracted part still maintains the original polarization and the vortex phase. The topological charges of the extracted mode are verified by interfering with the Gaussian beam, and it can be found that the orbital angular momentum is conserved in the extracting process. Our work will have potential applications in non-destructive spatial mode identification, and is also useful for studying higher-dimensional quantum information based on atomic ensembles.
... Такие пучки можно, например, формировать с помощью двух повернутых относительно друг друга полуволновых пластин [1], многосекторного поляризатора [3], метаповерхности [4], четвертьволновых пластинок [5] и модулятора света [6]. Цилиндрические векторные пучки применяются в микроманипулировании частицами [7], микроскопии [8], квантовой информатике [9,10]. ...
In this work, the sharp focusing of a laser beam whose initial polarization pattern is formed by superposition of a cylindrical mth-order vector beam and a homogeneous linearly polarized beam is considered theoretically and numerically. Although in the source plane of such a beam both the angular spin momentum and the third Stokes parameter are equal to zero, we reveal that given odd m, subwavelength local regions are formed in the focal plane, where transverse vortex energy flows occur and the third Stokes parameter (the on-axis component of the angular spin momentum) is non-zero. Thus, at odd m, at the focus of such a beam there are – sub-regions with elliptical polarization of light with alternating handedness in the adjacent sub-regions (clockwise and counterclockwise). This phenomenon can be interpreted as a variant of an optical Hall effect. We note that at even m, the field at the focus is linearly polarized at every point and no transverse energy flow is observed.
... Such beams can, for example, be formed using two half-wave plates rotated relative to each other [1], multisection polarizers [3], metasurfaces [4], quarter-wave plates and a light modulator [5]. Cylindrical vector beams (CVB) are used in particle micromanipulation [6], microscopy [7] and quantum informatics [8,9]. ...
... A feature of the intensity distribution in Figures 3-5 is that the longitudinal component is absent for the case of a = 1. This unique case takes place only when m = 2 and a = 1 and is described by the formula (8). Figures 3d-5d confirm the formula (7), according to which the longitudinal intensity I z at a = 1 has two local intensity maxima on the horizontal axis at ϕ = 0 and ϕ = π. ...
... A feature of the intensity distribution in Figures 3-5 is that the longitudinal component is absent for the case of a = 1. This unique case takes place only when m = 2 and a = 1 and is described by the formula (8). Figures 3d-5d confirm the formula (7), according to which the longitudinal intensity Iz at a ≠ 1 has two local intensity maxima on the horizontal axis at φ = 0 and φ = π. ...
In this paper, spin-orbital conversion in the tight focus of an axial superposition of a high-order (order m) cylindrical vector beam and a beam with linear polarization is theoretically and numerically considered. Although such a beam does not have a spin angular momentum in the initial plane and the third projection of its Stokes vector is equal to zero, subwavelength local regions with a transverse vortex energy flow and with the non-zero third Stokes projection (the longitudinal component of the spin angular momentum) are formed in the focal plane for an odd number m. This means that such a beam with an odd m has regions of elliptical or circular polarization with alternating directions of rotation (clockwise and counterclockwise) in the focus. For an even m, the field is linearly polarized at every point of the focal plane, and the transverse energy flux is absent. These beams can be used to create a micromachine in which two microparticles in the form of gears are captured in the focus of the beam into neighboring local areas in which the energy flow rotates in different directions, and therefore, these gears will also rotate in different directions.
... While laser beams typically have homogeneous polarization profiles, recent years have seen an increasing interest in light designed with spatially varying polarization structures, including vector vortex beams [1][2][3][4][5], Poincaré beams [6][7][8] and even skyrmionic beams [9,10]. These vector beams are characterized by non-separable correlations between their polarization and spatial degree of freedom [11,12], with intriguing applications for quantum [13][14][15][16] and quantum inspired protocols [17][18][19][20][21][22][23]. ...
... We confirm that the unitary transformations expressed in Eqs. (11) are identical to the desired unitary transformation matrix U shown in Fig. 2 and given in the Supplementary Documentation Eq. (S2). ...
Vector vortex beams, featuring independent spatial modes in orthogonal polarization components, offer an increase in information density for emerging applications in both classical and quantum communication technology. Recent advances in optical instrumentation have led to the ability of generating and manipulating such beams. Their tomography is generally accomplished by projection measurements to identify polarization as well as spatial modes. In this paper we demonstrate spatially resolved generalized measurements of arbitrary vector vortex beams. We perform positive operator valued measurements (POVMs) in an interferometric setup that characterizes the vector light mode in a single-shot. This offers superior data acquisition speed compared to conventional Stokes tomography techniques, with potential benefits for communication protocols as well as dynamic polarization microscopy of materials.
