Fig. 5: Measurements of the XPDC cone extended.<\/b> All scattering images from Fig.\u00a02d<\/a> [main text] arranged in 2D51<\/a>. Scattering angles (2\u03b8, \u03c7) are fixed to the same range for all frames; individual sample angle \u2206\u03a9 is indicated above each plot.<\/p>\n Angle calibration<\/p>\n We calibrate the 2-dimensional detector images from pixels to scattering angles [deg] by means of the sample\u2019s (111) Bragg-reflection. This locates the (nominal) scattering angle 2\u03b8\u2009=\u20092\u03b8B, corresponding to pixel 117 vertically, and also defines the scattering plane around \u03c7\u2009=\u20090, corresponding to pixel 79 horizontally. The scale relative to this reference is obtained by moving the detection-arm (i.e., the assembly including analyzer and detector) along 2\u03b8 by \u00b12\u00b0. We convert the pixel positions that the Bragg reflex traverses on the detector during this movement into the calibration: 1 pixel \u225c 0.0205\u00b0.<\/p>\n This holds for both the \u03c7 – and the 2\u03b8-axes, as the pixels are quadratic.<\/p>\n $$2\\theta \\left[{{{\\rm{deg}}}} \\right]=\\left(2\\theta \\left[{{{\\rm{pixel}}}}\\right]-117\\, {{{\\rm{pixel}}}}\\right)\\times 0.0205\\, {{{\\rm{deg}}}} \/{{{\\rm{pixel}}}}$$<\/p>\n \n (4)\n <\/p>\n $$\\chi \\left[{{{\\rm{deg}}}} \\right]=\\left(\\chi \\left[{{{\\rm{pixel}}}}\\right]-79\\,{{{\\rm{pixel}}}}\\right)\\times 0.0205\\,{{{\\rm{deg}}}} \/{{{\\rm{pixel}}}}.$$<\/p>\n \n (5)\n <\/p>\n Mapping to momentum transfer<\/p>\n Mapping from scattering angles (2\u03b8, \u03c7) to momentum transfer \u210fq<\/b>\u2009=\u2009\u210f(k<\/b>p\u2013k<\/b>s) proceeds in a system of spherical coordinates. The pump beam defines the polar axis along k<\/b>p\u2009=\u2009\u03c9p\/ce<\/b>z, where c is the speed of light in vacuo and e<\/b>z the unit vector along z. The signal photon\u2019s k<\/b>s is fully determined by its magnitude |k<\/b>s\u2009|\u2009= \u03c9s\/c as well as the scattering angles 2\u03b8\u2009=\u2009\u03b8s for its azimuth and<\/p>\n $$\\chi \\to \\phi s=\\left(\\chi -{{{\\pi }}}\/2\\right)\\left(\\sin 2\\theta \\right)-1+{{{\\pi }}}\/2$$<\/p>\n \n (6)\n <\/p>\n for its polar angle. Following Eq. (3<\/a>) [main text], q<\/b>\u00a0relates to the photonic level of the TLS via<\/p>\n $${{{{{\\bf{k}}}}}^{{{{\\rm{eff}}}}}}_{{{{\\gamma }}}}={{{\\bf{q}}}}+{{{\\bf{G}}}}={{{{\\bf{k}}}}}_{{{{\\bf{p}}}}}-{{{{\\bf{k}}}}}_{{{{\\bf{s}}}}}+{{{\\bf{G}}}}$$<\/p>\n \n (7)\n <\/p>\n analogous to the phase-matching condition. Writing the reciprocal lattice vector in the same coordinate system<\/p>\n $${{{\\bf{G}}}}={\\omega }_{p}{c}^{-1}\\sin {\\theta }_{B}\\left(\\begin{array}{c}0\\\\ \\cos \\theta B+\\Delta \\Omega \\\\ \\sin \\theta B+\\Delta \\Omega \\end{array}\\right),$$<\/p>\n \n (8)\n <\/p>\n we can compute \\({{{{\\bf{k}}}}}_{{{\\gamma }}}^{{{{\\rm{eff}}}}}\\) for all scattering angles and evaluate the pertaining dispersion relations \u03c9\u03b3(q<\/b>) or E\u00b1(\u03c9\u03b3) numerically. The prefactor in Eq. (8<\/a>) reflects Bragg\u2019s law.<\/p>\n Background subtraction<\/p>\n The nonlinear conversion signal is imprinted on top of a stronger background, approximately within a ratio of 1\/10. This background consists predominantly of (diffuse) Compton-scattering, which is further modulated by aberrations due to the crystal optics. To expose the XPDC signal, we subtract a scaled back-ground image from each recorded frame individually:<\/p>\n $${{{Frame}}_{{corrected}}}^{\\left(i\\right)}{={Frame}}^{\\left(i\\right)}-\\left({{Frame}}^{\\left({offPM}\\right)} * \\frac{\\sum {{Frame}}^{\\left(i\\right)}}{\\sum {{Frame}}^{\\left({offPM}\\right)}}\\right)$$<\/p>\n \n (9)\n <\/p>\n For that purpose we acquire a scattering image off the phase-matching condition, viz., Frame(off PM), that contains no XPDC, but still features the background with imprints of the analyzer. Scaling is based on the total (background) counts per frame, i.e., Frame(i), and varies slowly across the phase-matching range.<\/p>\n Polarization-imprint on coupling V<\/p>\n We have postulated previously that parametric conversion from X-ray to optical photons will exhibit circumferential modulations of its scattering cones that relate to the polarization of the idler photons24<\/a>. Confirming the same pattern experimentally in the EUV-case, we seek to incorporate this characteristic into our TLS-model as well. The transversality constraint from ref. 23<\/a> translates into our simplified coupling scheme as:<\/p>\n $$V\\to V\\times \\left(1-{\\left|{\\hat{{{{\\bf{k}}}}}}_{{{{\\rm{\\gamma }}}}}^{{{{\\rm{eff}}}}}\\cdot \\hat{{{{\\bf{G}}}}}\\right|}^{2}\\right).$$<\/p>\n \n (10)\n <\/p>\n Angular variations derive from the orientation of the idler photon\u2019s wavevector \\({{{{\\bf{k}}}}}_{{{\\gamma }}}^{{{{\\rm{eff}}}}}\\) relative to the reciprocal lattice vector G<\/b>, represented through their respective unit vectors.<\/p>\n Using the modulation (10) in our simulations, we find excellent agreement with measured data in Fig.\u00a04<\/a> [main text] (cf. minima around \u03c7\u2009=\u20090), thus establishing first evidence for a non-trivial polarization dependence also in the case of polaritonic XPDC. In the extended data below (Fig.\u00a06<\/a>), we illustrate how the polarization imprint can also be simulated for the other cases of Fig.\u00a02a\u2013c<\/a> [main text]. While the first column reproduces the earlier experimental images (for sample detunings of \u2206\u03a9a\u2009=\u20090.47\u00b0, \u2206\u03a9b\u2009=\u20091.07\u00b0 and \u2206\u03a9c\u2009=\u20091.87\u00b0, respectively), the second column juxtaposes the TLS simulations with coupling according to Eq. (10<\/a>). For comparison, we also include a simplified version of constant, isotropic coupling in the third column of extended data Fig.\u00a06<\/a>. Finally, its fourth column visualizes the phase-matching condition for each case. This influences the signal via Eq. (10<\/a>), rendering it predominantly sensitive to EUV-quanta that are polarized in the same direction as the reciprocal lattice vector G<\/b>. As such, all side-lobes of the XPDC cones (i.e., for phasematching \\({{{{\\bf{k}}}}}_{{{\\gamma }}}^{{{{\\rm{eff}}}}}\\) out of plane) show pronounced signal strength, because there is a component of its polarization along G<\/b> to be imaged. In contrast, the polariton\u2019s propagation direction (\\({{{{\\bf{k}}}}}_{{{{\\boldsymbol{\\gamma }}}}}^{{{{\\bf{eff}}}}}\\)) at the upper or lower point of the cone may align with G<\/b>, rendering its polarization largely orthogonal. This results in signal suppression, which is most visible in Fig.\u00a02b<\/a> around \u03c7\u2009=\u20090. Similarly, for the conditions shown in Fig.\u00a02a or c<\/a>, \\({{{{\\bf{k}}}}}_{{{{\\boldsymbol{\\gamma }}}}}^{{{{\\bf{eff}}}}}\\) aligns with G<\/b> at the lower- or uppermost phase-matching point, respectively. Again, this leads to signal suppression – while on each opposite side of the cone, the EUV-idler\u2019s polarization is allowed to be parallel to G<\/b>, giving rise to strong signal and an overall horseshoe-shape.<\/p>\n Fig. 6: Polarization imprint on the\u00a0XPDC cone.<\/b> Juxtaposition of measured XPDC signal cones at different rocking angles (left column; a<\/b>\u2013c<\/b>) with respective simulations that include (center-left; d<\/b>\u2013f<\/b>) or disregard (center-right; g<\/b>\u2013i<\/b>) polarization effects of the EUV-idler. The associated phase-matching conditions are sketched in the right-most column (j<\/b>\u2013l<\/b>).<\/p>\n The effect merits future investigation, concerning its interplay with more complex dielectric structures.<\/p>\n Theoretical motivation of the TLS-model<\/p>\n To trace the imprint of polaritonic effects on XPDC, we base our description on the dynamic structure factor for inelastic X-ray scattering (IXS)37<\/a>, which we express in atomic units below:<\/p>\n $$S({{{\\bf{q}}}},\\omega )=\\frac{1}{2\\pi }{\\int }_{-\\infty }^{\\infty }{dt}{e}^{{{{\\rm{i}}}}\\omega t}\\int {d}^{3}x\\int {d}^{3}{x}^{{\\prime} }{e}^{-{{{\\rm{i}}}}{{{\\bf{q}}}}\\cdot ({{{\\bf{x}}}}-{{{{\\bf{x}}}}}^{{\\prime} })}\\left\\langle \\hat{n}({{{\\bf{x}}}},t)\\, \\hat{n}({{{{\\bf{x}}}}}^{{\\prime} },0)\\right\\rangle .$$<\/p>\n \n (11)\n <\/p>\n Focusing on the density-density correlator and expanding its intermediate states, we write<\/p>\n $$\\left\\langle \\hat{n}({{{\\bf{x}}}},t)\\, \\hat{n}({{{{\\bf{x}}}}}^{{\\prime} },0)\\right\\rangle \\approx \t {\\sum }_{{n}_{i}}^{{{{\\rm{VB}}}}}{\\sum }_{{{{{\\bf{k}}}}}_{i}}^{1.{{{\\rm{BZ}}}}} |0 > ,$$<\/p>\n \n (12)\n <\/p>\n where we have expressed electronic states as Bloch-waves and\u2014unconventionally for S(q,<\/b>\u03c9)\u2014included additional photonic degrees of freedom in terms of initially unoccupied Fock states |0>. Assuming phase-matching conditions and the dipole-approximation for the EUV-light-matter interaction48<\/a> all terms remain approximately diagonal in their respective k<\/b>-space coordinates, which is reflected in the single summation over k<\/b>i. The central matrix element \\( {|}0 > \\) consists of highly excited electronic states, which would conventionally be considered only for their role as Compton-electrons\u2014evolving quasi-free at ~100\u2009eV. Within the band structure, however, such an electron also has a finite chance of returning to its initial valence-band state (now a hole at \\({\\varphi }_{{n}_{i},{{{{\\bf{k}}}}}_{i}}\\)) by emission of a 100\u2009eV photon. This photonic coupling of states gives rise to the EUV-polariton. Notwithstanding the large number of overall bands nm, there will typically be only very few (if any) states that match the photonic resonance at \\(100\\,{{{\\rm{eV}}}}={\\epsilon }_{{n}_{m},{{{{\\bf{k}}}}}_{i}}-{\\epsilon }_{{n}_{i},{{{{\\bf{k}}}}}_{i}}\\). For our modeling, we will focus on those pairs of states \\({\\varphi }_{{n}_{m},{{{{\\bf{k}}}}}_{i}}\\); \\({\\varphi }_{{n}_{i},{{{{\\bf{k}}}}}_{i}}\\), that are closest to the transition at each k<\/b>-point. This effectively establishes a set of near-resonant two-level systems (TLS) with Hamiltonians deriving from<\/p>\n $$\\hat{H}={\\hat{H}}_{{{{\\rm{Bloch}}}}}+{\\hat{H}}_{{{{\\rm{phot}}}}}+{\\hat{H}}_{{{{\\rm{interaction}}}}}$$<\/p>\n \n (13)\n <\/p>\n $$\\Rightarrow \\left(\\begin{array}{cc}{\\epsilon }_{{n}_{i},{{{{\\bf{k}}}}}_{i}} & 0\\\\ 0 & {\\epsilon }_{{n}_{m},{{{{\\bf{k}}}}}_{i}}\\end{array}\\right)+\\left(\\begin{array}{cc}{\\omega }_{{{{{\\bf{k}}}}}_{\\gamma }} & 0\\\\ 0 & 0\\end{array}\\right)+\\left(\\begin{array}{cc}0 & V({n}_{i},{{{{\\bf{k}}}}}_{i})\\\\ {V}^{{{\\dagger}} }({n}_{i},{{{{\\bf{k}}}}}_{i}) & 0\\end{array}\\right),$$<\/p>\n \n (14)\n <\/p>\n including coupling elements \\(V({n}_{i},{{{{\\bf{k}}}}}_{i})={\\sum}_{{{{{\\bf{k}}}}}_{\\gamma }}^{{PM}}{\\sum }_{\\lambda }\\sqrt{\\frac{2\\pi }{V{\\omega }_{{{{{\\bf{k}}}}}_{\\gamma }}}} \\) based on the interaction terms of ref. 48<\/a>, with the range of photon momenta being constraint by phase-matching (PM). Equivalent reductions to resonant few-level emitters are at the core of many polaritonic descriptions\u2014typically leading to Tavis-Cummings or Dicke-type models (see, e.g., ref. 14<\/a>). We choose to diagonalize each k<\/b>-point and frequency individually, leading to the well-known eigenenergies<\/p>\n $${E}_{\\pm }({n}_{i},{{{{\\bf{k}}}}}_{i})=\t \\frac{({\\epsilon }_{{n}_{m},{{{{\\bf{k}}}}}_{i}}-{\\epsilon }_{{n}_{i},{{{{\\bf{k}}}}}_{i}})+{\\omega }_{{{{{\\bf{k}}}}}_{\\gamma }}}{2} \\\\ \t \\pm \\sqrt{\\frac{1}{4}({({\\epsilon }_{{n}_{m},{{{{\\bf{k}}}}}_{i}}-{\\epsilon }_{{n}_{i},{{{{\\bf{k}}}}}_{i}})-{\\omega }_{{{{{\\bf{k}}}}}_{\\gamma }}})^{2}+{\\left|V({n}_{i},{{{{\\bf{k}}}}}_{i})\\right|}^{2}}.$$<\/p>\n \n (15)\n <\/p>\n The corresponding eigenstates are obtained by the transformation<\/p>\n $$\\begin{array}{c}\\hat{T}\\left({n}_{i},{{{{\\bf{k}}}}}_{i}\\right)\\left|{\\varphi }_{{n}_{m},{{{{\\bf{k}}}}}_{i}}\\right. > \\left|0\\right. > ={\\sum }_{\\pm }{c}_{e\\pm }({n}_{i},{{{{\\bf{k}}}}}_{i})\\left|{\\phi }_{\\pm }^{{{{\\rm{pol}}}}}({n}_{i},{{{{\\bf{k}}}}}_{i}) > \\right.\\\\ {{{\\rm{with}}}}\\,{c}_{e\\pm }\\left({n}_{i},{{{{\\bf{k}}}}}_{i}\\right)={\\left(1+\\frac{{\\left|V\\left({n}_{i},{{{{\\bf{k}}}}}_{i}\\right)\\right|}^{2}}{({E}_{\\pm }{({n}_{i},{{{{\\bf{k}}}}}_{i})-{\\omega }_{{{{{\\bf{k}}}}}_{\\gamma }}})^{2}}\\right)}^{-\\frac{1}{2}},\\end{array}$$<\/p>\n \n (16)\n <\/p>\n which also transforms the original matrix element into<\/p>\n $$ \\, |0 \\, > ={\\sum}_{\\pm }{\\left|{c}_{e\\pm }\\left({n}_{i},{{{{\\bf{k}}}}}_{i}\\right)\\right|}^{2}{e}^{-i{E}_{\\pm }\\left({n}_{i},{{{{\\bf{k}}}}}_{i}\\right)t}$$<\/p>\n \n (17)\n <\/p>\n Combining Eqs. (1<\/a>), (2<\/a>) and (7<\/a>), the dynamic structure factor near phase-matching (PM) becomes<\/p>\n $${S}^{{{{\\rm{pol}}}}}({{{\\bf{q}}}},\\omega )=\t \\frac{1}{{V}_{\\diamond }}{\\sum}_{{n}_{i}}^{{{{\\rm{VB}}}}}{\\sum}_{{{{{\\bf{k}}}}}_{i}}^{1.{{{\\rm{BZ}}}}}\\left({\\left|\\int {d}^{3}x{e}^{-{{{\\rm{i}}}}{{{\\bf{qx}}}}} \\right|}^{2}\\right. \\\\ \t \\left.{\\sum}_{{{{{\\bf{k}}}}}_{\\gamma }}{\\sum}_{\\pm }{\\left|{c}_{e\\pm }\\left({n}_{i},{{{{\\bf{k}}}}}_{i}\\right)\\right|}^{2}\\delta \\left({E}_{\\pm }\\left({n}_{i},{{{{\\bf{k}}}}}_{i}\\right)-\\omega \\right)\\right)$$<\/p>\n \n (18)\n <\/p>\n This represents the sum of partial scattering factors from all initial electronic states \\({\\varphi }_{{n}_{i},{{{{\\bf{k}}}}}_{i}}\\) \u2013 each dressed by a TLS, subject to energy conservation. Interpreting the summation as an average, we approximate the result as a single, effective TLS that dresses the overall dynamic structure factor with its Hopfield coefficients \\({c}_{e\\pm }\\):<\/p>\n $${S}^{{{{\\rm{pol}}}}}({{{\\bf{q}}}},\\omega )\\approx {S}^{{{{\\rm{IXS}}}}}({{{\\bf{q}}}},\\omega )\\cdot {\\sum}_{\\pm }{\\left|{c}_{e\\pm }\\right|}^{2}{e}^{-{({E}_{\\pm }-\\omega )}^{2}\/{2\\Gamma }_{{{{\\rm{in}}}}}^{2}}$$<\/p>\n \n (19)\n <\/p>\n The single, effective two-level system marks the starting point for our main discussion. It is governed by the Hamiltonian of Eq. (M8), where \u03c9e is the average transition energy and \u03c9\u03b3 the average frequency of coupled photonic modes. Any relative variation within a sector is taken to be small and accounted for by an intrinsic broadening factor \u0393in, while the overall coupling of electronic and photonic sectors is now mediated by the collective coupling strength V.<\/p>\n Scattering yield from TLS-model<\/p>\n In order to connect our effective model to the observable scattering yield, we first relate \\({S}^{{{{\\rm{pol}}}}}({{{\\bf{q}}}},\\omega )\\) to the double-differential scattering cross section of regular inelastic X-ray scattering (IXS)40<\/a> as follows<\/p>\n $$\\frac{d{\\sigma }^{{{{\\rm{pol}}}}}}{d{\\Omega }_{s}d{\\omega }_{s}}={\\left(\\frac{d\\sigma }{d{\\Omega }_{s}}\\right)}_{{Th}}\\frac{{\\omega }_{s}}{{\\omega }_{p}}{S}^{{{{\\rm{pol}}}}}\\left({{{\\bf{q}}}},{\\omega }_{p}-{\\omega }_{s}\\right),$$<\/p>\n \n (20)\n <\/p>\n with the Thomson cross section (\u2026)Th governing the proportionality40<\/a>. After convoluting Eq. (20<\/a>) with the incident fluence as well as the (Gaussian-modeled) transmission function of the analyzer-setup, we integrate for the scattering yield per pixel (i.e., covering (20.5\u2009mdeg)2):<\/p>\n $${Y}_{{pix}}=p\\cdot {\\sum}_{\\pm }{\\left|{c}_{e \\pm }\\right|}^{2}{e}^{-{\\left({{\\hslash }}\\Delta {\\omega }_{{an}}-{E}_{\\pm }\\right)}^{2}\/2({{\\hslash }}{\\Gamma })^{2}}.$$<\/p>\n \n (21)\n <\/p>\n Both E\u00b1 and ce\u00b1 are implicit functions of the scattering angles 2\u03b8 and \u03c7 at each point of evaluation. The overall bandwidth \u0393 as well as the energy-loss determined by the analyzer \u2206\u03c9an\u2009~\u2009\u03c9\u03b3 are left as fitting parameters for simplicity, while the overall prefactor p is obtained from intrinsic background scattering (see below). Note that we have re-instated \u210f starting from Eq. (21<\/a>).<\/p>\n Fitting procedure<\/p>\n We, consistently, resort to background-subtracted data for fitting, using Yfit=Ypix\u2212Ybg. The pertinent background consists of inelastic (Compton) scattering and is captured by our Eq. (8<\/a>) in the limit Spol(q<\/b>, \u03c9) \u2192SIXS(q,<\/b> \u03c9). For regions of q<\/b>-space away from polaritonic phase-matching. This translates onto Eq. (21<\/a>) as<\/p>\n $${{{\\mathrm{lim}}}}_{n\\to \\infty }{Y}_{{pix}}\\left({{{{\\rm{\\omega }}}}}_{{{{\\rm{\\gamma }}}}}\\right)={Y}_{{BG}}=p{e}^{-{\\left(-\\Delta {\\omega }_{{an}}-{\\omega }_{e}\\right)}^{2}\/2{\\Gamma }^{2}}.$$<\/p>\n \n (22)\n <\/p>\n and automatically determines the prefactor p.<\/p>\n Binning the 2D data in a line-out along \u03c7 of width 7 pixel [see main text], we fit Yfit using the curve fit-routine from the freely-available python-package scipy.optimize. The result is shown in Fig.\u00a04<\/a> [main text], with the underlying parameters determined to be: \u210f\u03c9e\u2009=\u200998.36\u2009\u00b1\u20090.39\u2009eV, V\u2009=\u20090.82\u2009\u00b1\u20090.08\u2009eV, \u210f\u0393 = 1.64\u2009\u00b1\u20090.22\u2009eV and for the setup \u210f\u0394\u03c9an\u2009=\u200999.90\u2009\u00b1\u20090.22\u2009eV. The latter refines our knowledge of the difference \u210f(\u03c9p\u2009\u2212\u2009\u03c9s)\u2009\u2248\u2009100\u2009eV. We assess the quality of the fitting by estimating the uncertainty by its reduced \u03a72\u2009\u2248\u20092.1, which is based on the counting error and indicates good agreement.<\/p>\n We note that the line shape could also be fitted by the Fano-formula49<\/a> on a phenomenological basis. This was done by Tamasaku et al. under similar conditions, suggesting an interference between Compton scattering and XPDC35<\/a>. However, these processes should not interfere quantum mechanically (see also Tamasaku et al.50<\/a>), which renders a Fano-model inapplicable. In contrast, our polaritonic interpretation reconciles both processes and yields Eq. (15<\/a>) to describe the full, hybridized phenomenon.<\/p>\n","protected":false},"excerpt":{"rendered":"Experimental setup We performed the experiment at the large solid-angle spectrometer of beamline ID20 at ESRF26. The setup\u2019s…\n","protected":false},"author":3,"featured_media":16254,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25],"tags":[10046,10047,16163,492,16164,836,159,67,132,68,16165],"class_list":{"0":"post-16253","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-humanities-and-social-sciences","9":"tag-multidisciplinary","10":"tag-nonlinear-optics","11":"tag-physics","12":"tag-polaritons","13":"tag-quantum-physics","14":"tag-science","15":"tag-united-states","16":"tag-unitedstates","17":"tag-us","18":"tag-x-rays"},"share_on_mastodon":{"url":"https:\/\/pubeurope.com\/@us\/114749634544838297","error":""},"_links":{"self":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts\/16253","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/comments?post=16253"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/posts\/16253\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/media\/16254"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/media?parent=16253"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/categories?post=16253"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/us\/wp-json\/wp\/v2\/tags?post=16253"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"figure](\"https:\/\/www.europesays.com\/us\/wp-content\/uploads\/2025\/06\/41467_2025_60845_Fig5_HTML.png\")
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