An efficient neural optimizer for resonant nanostructures: demonstration of highly-saturated red silicon structural color

Freeform nanostructures have the potential to support complex resonances and their interactions, which are crucial for achieving desired spectral responses. However, the design optimization of such structures is nontrivial and computationally intensive. Furthermore, the current "black box" design approaches for freeform nanostructures often neglect the underlying physics. Here, we present a hybrid data-efficient neural optimizer for resonant nanostructures by combining a reinforcement learning algorithm and Powell's local optimization technique. As a case study, we design and experimentally demonstrate silicon nanostructures with a highly-saturated red color. Specifically, we achieved CIE color coordinates of (0.677, 0.304)-close to the ideal Schrodinger's red, with polarization independence, high reflectance (>85%), and a large viewing angle (i.e., up to ~ 25deg). The remarkable performance is attributed to underlying generalized multipolar interferences within each nanostructure rather than the collective array effects. Based on that, we were able to demonstrate pixel size down to ~400 nm, corresponding to a printing resolution of 65,000 pixels per inch. Moreover, the proposed design model requires only ~300 iterations to effectively search a 13-dimensional design space - an order of magnitude more efficient than the previously reported approaches. Our work significantly extends the free-form optical design toolbox for high-performance flat-optical components and metadevices

From fidelity to entanglement of entropy of the one-dimensional transverse-field quantum compass model

We study fidelity and fidelity susceptibility by addition of entanglement of entropy in the one-dimensional quantum compass model in a transverse magnetic field numerically. The whole four recognized gapped regions in the ground state phase diagram are in the range of our investigation. Power-law divergence at criticality accompanied by finite size scaling indicates the field induced quantum phase transitions are of second order as well as from the scaling behavior of the extremum of fidelity susceptibility is shown the quantum critical exponents are different in the various regions of phase diagram. We further calculate a recently proposed quantum information theoretic measure, von-Neumann entropy, and show that this measure provide appropriate signatures of the quantum phase transitions (QPT)s occurring at the critical fields. Von-Neumann entropy indicates a measure of entanglement between some-particle block and the rest of the system. We show the value of entanglement between a two-particle block with the rest of the system is more dependent on the power of exchange couplings connecting the block with the rest of the system than the power of exchange coupling between two particles in the block

Kinematic Effects in Radiative Quarkonia Decays

Non-relativistic QCD (NRQCD) predicts colour octet contributions to be significant not only in many production processes of heavy quarkonia but also in their radiative decays. We investigate the photon energy distributions in these processes in the endpoint region. There the velocity expansion of NRQCD breaks down which requires a resummation of an infinite class of colour octet operators to so-called shape functions. We model these non-perturbative functions by the emission of a soft gluon cluster in the initial state. We found that the spectrum in the endpoint region is poorly understood if the values for the colour octet matrix elements are taken as large as indicated from NRQCD scaling rules. Therefore the endpoint region should not be taken into account for a fit of the strong coupling constant at the scale of the heavy quark mass.Comment: LaTeX, 17 pages, 5 figures. The complete paper is also available via the www at http://www-ttp.physik.uni-karlsruhe.de/Preprints

Colour-Octet Effects in Radiative Υ\Upsilon Decays

We investigate the effects of colour-octet contributions to the radiative $\Upsilon$ decay within the Bodwin, Braaten and Lepage NRQCD factorization framework. Photons coming both from the coupling to hard processes (`direct') and by collinear emission from light quarks (`fragmentation') are consistently included at next-to-leading order (NLO) in $\alpha_s$. An estimate for the non-perturbative matrix elements which enter in the final result is then obtained. By comparing the NRQCD prediction at NLO for total decay rates with the experimental data, it is found that the non-perturbative parameters must be smaller than expected from the na\"\i ve scaling rules of NRQCD. Nevertheless, colour-octet contributions to the shape of the photon spectrum turn out to be significant.Comment: 25 pages, Latex, 8 figure

Updated Analysis of a_1 and a_2 in Hadronic Two-body Decays of B Mesons

Using the recent experimental data of $B\to D^{(*)}(\pi,\rho)$, $B\to D^{(*)} D_s^{(*)}$, $B\to J/\psi K^{(*)}$ and various model calculations on form factors, we re-analyze the effective coefficients a_1 and a_2 and their ratio. QCD and electroweak penguin corrections to a_1 from $B\to D^{(*)}D_s^{(*)}$ and a_2 from $B\to J/\psi K^{(*)}$ are estimated. In addition to the model-dependent determination, the effective coefficient a_1 is also extracted in a model-independent way as the decay modes $B\to D^{(*)}h$ are related by factorization to the measured semileptonic distribution of $B\to D^{(*)}\ell \bar\nu$ at $q^2=m_h^2$. Moreover, this enables us to extract model-independent heavy-to-heavy form factors, for example, $F_0^{BD}(m_\pi^2)=0.66\pm0.06\pm0.05$ and $A_0^{BD^*}(m_\pi^2)=0.56\pm0.03\pm0.04$. The determination of the magnitude of a_2 from $B\to J/\psi K^{(*)}$ depends on the form factors $F_1^{BK}$, $A_{1,2}^{BK^*}$ and $V^{BK^*}$ at $q^2=m^2_{J/\psi}$. By requiring that a_2 be process insensitive (i.e., the value of a_2 extracted from $J/\psi K$ and $J/\psi K^*$ states should be similar), as implied by the factorization hypothesis, we find that $B\to K^{(*)}$ form factors are severely constrained; they respect the relation $F_1^{BK}(m^2_{J/\psi})\approx 1.9 A_1^{BK^*}(m^2_{J/\psi})$. Form factors $A_2^{BK^*}$ and $V^{BK^*}$ at $q^2=m^2_{J/\psi}$ inferred from the measurements of the longitudinal polarization fraction and the P-wave component in $B\to J/\psi K^*$ are obtained. A stringent upper limit on a_2 is derived from the current bound on \ov B^0\to D^0\pi^0 and it is sensitive to final-state interactions.Comment: 33 pages, 2 figures. Typos in Tables I and IX are corrected. To appear in Phys. Rev.

Knots: Attractive Places with High Path Tortuosity in Mouse Open Field Exploration

When introduced into a novel environment, mammals establish in it a preferred place marked by the highest number of visits and highest cumulative time spent in it. Examination of exploratory behavior in reference to this “home base” highlights important features of its organization. It might therefore be fruitful to search for other types of marked places in mouse exploratory behavior and examine their influence on overall behavior

Power counting and effective field theory for charmonium

We hypothesize that the correct power counting for charmonia is in the parameter Lambda_QCD/m_c, but is not based purely on dimensional analysis (as is HQET). This power counting leads to predictions which differ from those resulting from the usual velocity power counting rules of NRQCD. In particular, we show that while Lambda_QCD/m_c power counting preserves the empirically verified predictions of spin symmetry in decays, it also leads to new predictions which include: A hierarchy between spin singlet and triplet octet matrix elements in the J/psi system. A quenching of the net polarization in production at large transverse momentum. No end point enhancement in radiative decays. We discuss explicit tests which can differentiate between the traditional and new theories of NRQCD.Comment: 18 pages, 1 figure Replaced plot of the psi polarization parameter alpha as a function of transverse momentum. Alpha is now closer to zero for large transverse moment

Leading power SCET analysis of e+e−→J/ψgge^+ e^- \to J/\psi g g

Recently, Belle and BaBar Collaborations observed surprising suppression in the endpoint $J/\psi$ spectrum, which stimulates us to examine the endpoint behaviors of the $e^+ e^- \to J/\psi gg$ production. We calculate the $J/\psi$ momentum and angular distributions for this process within the framework of the soft-collinear effective theory (SCET). The decreasing spectrum in the endpoint region is obtained by summing the Sudakov logarithms. We also find a large discrepancy between the NRQCD and SCET spectrum in the endpoint region even before the large logarithms are summed, which is probably due to the fact that only the scalar structure of the two-gluon system is picked out in the leading power expansion. A comparison with the process $\Upsilon \to \gamma gg$ is made.Comment: 12 pages, 3 figures, one reference added and some minor changes, version to appear in Phys. Lett.

Soft, collinear and non-relativistic modes in radiative decays of very heavy quarkonium

We analyze the end-point region of the photon spectrum in semi-inclusive radiative decays of very heavy quarkonium (m alpha_s^2 >> Lambda_QCD). We discuss the interplay of the scales arising in the Soft-Collinear Effective Theory, m, m(1-z)^{1/2} and m(1-z) for z close to 1, with the scales of heavy quarkonium systems in the weak coupling regime, m, m alpha_s and m alpha_s^2. For 1-z \sim alpha_s^2 only collinear and (ultra)soft modes are seen to be relevant, but the recently discovered soft-collinear modes show up for 1-z << alpha_s^2. The S- and P-wave octet shape functions are calculated. When they are included in the analysis of the photon spectrum of the Upsilon (1S) system, the agreement with data in the end-point region becomes excellent. The NRQCD matrix elements and are also obtained.Comment: Revtex, 11 pages, 6 figures. Minor improvements and references added. Journal versio