Final Spin Research Articles

Highly Spin-Polarized Molecules via Collisional Microwave Pumping.

We propose a general technique to produce cold spin-polarized molecules in the electronic states of Σ symmetry, in which rotationally excited levels are first populated by coherent microwave excitation, and then allowed to spin flip and relax via collisional quenching, which populates a single final spin state. The steady-state spin polarization is maximized in the regime, where collisional slip-flipping transitions in the ground rotational manifold (N=0) are suppressed by a factor of ≥10 compared to those in the first rotationally excited manifold (N=1), as generally expected for Σ-state molecules at temperatures below the rotational spacing between the N=0 and N=1 manifolds. We theoretically demonstrate the high selectivity of the technique for ^{13}C^{16}O molecules immersed in a cold buffer gas of helium atoms, achieving a high degree (≥95%) of nuclear spin polarization at 1K.

Bell inequality is violated in charmonium decays

The experimental data on the helicity amplitudes of charmonium decays allow us to measure entanglement in final state spin correlations and test possible violations of the Bell inequality. We find that the Bell inequality is violated with a significance of 5σ or more in the decays ηc,χc0,J/ψ→Λ+Λ¯, J/ψ→Ξ−+Ξ¯+,Ξ0+Ξ¯0,Σ−+Σ¯+,Σ0+Σ¯0, ψ(3686)→Ξ−+Ξ¯+,Σ−+Σ¯+,Σ0+Σ¯0, χc0,χc1→ϕ+ϕ. The decays ψ(3686)→Λ+Λ¯ and Ξ0+Ξ¯0 show the same violation but with less significance. The decay ψ(3686)→Ω−+Ω¯+ displays entanglement. These results firmly establish the presence of entanglement and quantum nonseparability at high energies, in a setting with particles of different spins and interacting through electroweak and strong interactions. In addition, the relatively long lifetime of some of the strange baryons produced in the decays provides a natural probe to test whether quantum spin correlations remain after the particles have interacted with the beam pipe and the first few layers of the detector. Published by the American Physical Society 2024

Direct Observation and Analysis of Low-Energy Magnons with Raman Spectroscopy in Atomically Thin NiPS3.

van der Waals (vdW) magnets have rapidly emerged as a fertile playground for fundamental physics and exciting applications. Despite the impressive developments over the past few years, technical limitations pose a severe challenge to many other potential breakthroughs. High on the list is the lack of suitable experimental tools for studying spin dynamics on atomically thin samples. Here, Raman scattering techniques are employed to directly observe the low-lying magnon (∼1 meV) even in bilayer NiPS3. The advantage is that it offers excellent energy resolutions far better on low-energy sides than most inelastic neutron spectrometers can offer. More importantly, with appropriate theoretical analysis, the polarization dependence of the Raman scattering by those low-lying magnons also provides otherwise hidden information on the dominant spin-exchange scattering paths for different magnons. By comparing with high-resolution inelastic neutron scattering data, these low-energy Raman modes are confirmed to be indeed of magnon origin. Because of the different scattering mechanisms involved in inelastic neutron and Raman scattering, this information is fundamental in pinning down the final spin Hamiltonian. This work demonstrates the capability of Raman spectroscopy to probe the genuine two-dimensional spin dynamics in atomically thin vdW magnets, which can provide insights that are obscured in bulk spin dynamics.

Emergent chiral spin textures in centrosymmetric iron garnet with spin alignment constraints

Chiral spin textures have emerged as a captivating class of topological matter. These intriguing structures harbor localized and topologically protected magnetic textures, rendering them promising candidates for novel spintronic applications. Here, the emergent chiral spin textures in an iron garnet with nanodisk configuration have been micromagnatically simulated based on the Landau-Lifshitz-Gilbert equation (LLG) of COMSOL Multiphysics. The modification of magnetic spin texture in the considered iron garnet has been controlled by introducing the interfacial Dzyaloshinskii-Moriya interaction (I-DMI) and spin alignment constraints as locally pinned spins and curvilinear defects at edges. These boundary conditions induced interesting chiral textures not commonly observed in such iron garnet due to its centrosymmetric crystal structure. The simulation results showed the presence of two distinct regions of spin texture: inside and outside the pinning boundary. By systematically varying the DMI strength (D) with the size of the pinning boundary (Rpin) and the number of defects (Ndef), the emerging chiral spin textures have been explored and reported, including the existence of ramified helical stripes, skyrmions, and skyrmions-like textures such as elongated skyrmions, chiral horseshoe domains, biskyrmions and target skyrmions (TSk) (2π-TSk and 3π-TSk). Also, it has been reported that various collapses occur in the final spin texture states, leading to the transition from one state to another when varying the values of Rpin and Ndef with D.

Analysis of final state lepton polarization-dependent observables in H → ℓ+ℓ−γ in the SM at loop level

Recently, the CMS and ATLAS collaborations have announced the results for H → Z[→ ℓ+ℓ−]γ with ℓ = e or μ [1, 2], where H → Zγ is a sub-process of H → ℓ+ℓ−γ. This semi-leptonic Higgs decay gets both resonant and non-resonant contributions from the loop-induced H → Z[→ ℓ+ℓ−]γ. To probe further features coming from these contributions to H → ℓ+ℓ−γ, we argue that the polarization of the final state leptons is also an important parameter. We show that the interference of resonant and non-resonant contributions, which is negligible in the case of unpolarized leptons, plays a significant role when considering the polarization of the final state lepton. For this purpose, we have calculated the polarized decay rates and the longitudinal (PL), normal (PN), and transverse (PT) polarization asymmetries. We find that these asymmetries purely come from the loop contributions and are helpful to further investigate the resonant and non-resonant nature of H → Z[→ ℓ+ℓ−]γ decay. We observe that for ℓ = e, μ, the longitudinal decay rate is highly suppressed around mℓℓ ≈ 60 GeV when the final lepton spin is −12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ -\\frac{1}{2} $$\\end{document}, dramatically increasing the corresponding lepton polarization asymmetries. Furthermore, we analyze another observable, the ratio of decay rates Ri±ll′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {R}_{i\\pm}^{{\\mathcal{ll}}^{\\prime }} $$\\end{document}, where ℓ and ℓ′ refer to different final state lepton generations. Precise measurements of these observables at the HL-LHC and the planned e+e− collider can provide fertile ground to test not only the SM but also to examine the signatures of possible NP beyond the SM.

Merger estimates for a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories* *Supported by the National Key Research and Development Program of China (2020YFC2201400), and the National Natural Science Foundation of China (12275079, 12035005, 12275078)

We investigate the main features of a disformal Kerr black hole merger in quadratic degenerate higher-order scalar-tensor theories. In the ringdown stage of the black hole merger, for the prograde orbit, the real part of the quasinormal modes decreases with an increase in the disformal parameter, and the imaginary part also decreases, except in the Kerr case for a large spin parameter. However, for the retrograde orbit, the real part increases with an increase in the disformal parameter, and the imaginary part always decreases with it. For the approximate final spin, regardless of an equal spin, unequal spin, or generic spin configuration merger, the final black hole spin always increases with an increase in the disformal parameter. Our results show that the disformal parameter in the disformal Kerr solution and the MOG parameter in the Kerr-MOG case have obviously different effects on the black hole merger, which suggests the differences between these two spacetime structures.

Collapsar Gamma-Ray Bursts Grind Their Black Hole Spins to a Halt

The spin of a newly formed black hole (BH) at the center of a massive star evolves from its natal value due to two competing processes: accretion of gas angular momentum that increases the spin and extraction of BH angular momentum by outflows that decreases the spin. Ultimately, the final, equilibrium spin is set by a balance between both processes. In order for the BH to launch relativistic jets and power a γ-ray burst (GRB), the BH magnetic field needs to be dynamically important. Thus, we consider the case of a magnetically arrested disk (MAD) driving the spin evolution of the BH. By applying the semianalytic MAD BH spin evolution model of Lowell et al. to collapsars, we show that if the BH accretes ∼20% of its initial mass, its dimensionless spin inevitably reaches small values, a ≲ 0.2. For such spins, and for mass accretion rates inferred from collapsar simulations, we show that our semianalytic model reproduces the energetics of typical GRB jets, L jet ∼ 1050 erg s−1. We show that our semianalytic model reproduces the nearly constant power of typical GRB jets. If the MAD onset is delayed, this allows powerful jets at the high end of the GRB luminosity distribution, L jet ∼ 1052 erg s−1, but the final spin remains low, a ≲ 0.3. These results are consistent with the low spins inferred from gravitational wave detections of binary BH mergers. In a companion paper by Gottlieb et al., we use GRB observations to constrain the natal BH spin to be a ≃ 0.2.

Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout

We show that the lowest quantum Cramér-Rao bound achievable in interferometry with a one-axis twisted spin coherent state is saturated by the asymptotic method of moments error of a protocol that uses one call to the one-axis twisting, one call to time-reversed one-axis twisting, and a final total spin measurement (i.e., a twist-untwist protocol). The result is derived by first showing that the metrological phase diagram for one-axis twisting is asymptotically characterized by a single quantum Fisher information value N(N + 1)/2 for all times, then constructing a twist-untwist protocol having a method of moments error that saturates this value. The case of finite-range one-axis twisting is similarly analyzed, and a simple functional form for the metrological phase diagram is found in both the short-range and long-range interaction regimes. Numerical evidence suggests that the finite-range analogues of twist-untwist protocols can exhibit a method of moments error that asymptotically saturates the lowest quantum Cramér-Rao bound achievable in interferometry with finite-range one-axis twisted spin coherent states for all interaction times.

Spinning primordial black holes formed during a matter-dominated era

We study the formation of spinning primordial black holes during an early matter-dominated era. Using non-linear 3+1D general relativistic simulations, we compute the efficiency of mass and angular momentum transfer in the process, which we find to be 𝒪(10%) and 𝒪(5%), respectively. We show that subsequent evolution is important due to the seed PBH accreting non-rotating matter from the background, which decreases the dimensionless spin. Unless the matter era is short, we argue that the final dimensionless spin will be negligible.

Self-gravitating collapsing star and black hole spin-up in long gamma ray bursts

Context. Long gamma ray bursts (GRBs) originate from the collapse of massive, rotating stars. Some of the GRBs exhibit much stronger variability patterns in the prompt GRB emission than the usual stochastic variations. We discuss the mechanisms able to account for this effect. Aims We aim to model the process of stellar collapse in the scenario of a self-gravitating collapsing star. We account for the changes in Kerr metric induced by the growth of the black hole; accretion of angular momentum; and the self-gravity effect due to a large mass of the collapsing stellar core falling onto black hole in a very short time. We also investigate the existence of accretion shocks in the collapsar, and the role of magnetic field in their propagation. Methods. We compute the time-dependent axially symmetric general relativistic magnetohydrodynamic model of a collapsing stellar core in the dynamical Kerr metric. We explore the influence of self-gravity in such a star, where the newly formed black hole is increasing the mass and changing its spin. The Kerr metric evolves according to the mass and angular momentum changes during the collapse. We parameterize the rotation inside the star, and account for the presence of large-scale poloidal magnetic field. For the set of the global parameters, such as the initial black hole spin and the initial content of specific angular momentum in the stellar envelope, we determine the evolution of black hole parameters (mass and spin) and quantify the strength of the gravitational instability. We then estimate the variability timescales and amplitudes. Results. We find that the role of the gravitational instability measured by the value of the Toomre parameter is relatively important in the innermost regions of the collapsing star. The character of accretion rate variability strongly depends on the assumption of self-gravity in the model, and is also affected by the magnetic field. Additional factors are initial spin and rotation of the stellar core. We find that for subcritical rotation of the precollapsed star, a centrifugally supported mini-disc is present at the equatorial plane, and it may be subject to fragmentation due to self-gravitating instability. We also find that self-gravity may play a role in the angular momentum transport and that it generally lowers the final mass and spin of the black hole, while the accretion-rate variability amplitude is much larger in self-gravitating objects. The effect of magnetic field is rather weak, while it seems to decrease the strength of accretion shocks. The magnetisation affects the global properties of the flow in a non-linear way, and is manifested mostly in models with moderate initial black hole spins but supercritical rotation of the collapsing star. Conclusions. Our computations confirm that gravitational instability can account for flaring activity in GRBs and the variations in their prompt emission. Rapid variability detected in the brightest GRBs (most likely powered by rapidly spinning black holes) is consistent with the self-gravitating collapsar model, where the transonic shocks are formed. The effect should be weakened by magnetic field.

Enhancing the alignment of the optically brightGaiareference frame with respect to the International Celestial Reference System

Context.The link of theGaiaframe in terms of non-rotation with respect to the International Celestial Reference System (ICRS), which is realized via very long baseline interferometry (VLBI) at radio wavelengths, has to be conducted for the wide range of optical magnitudes in which the spacecraft observes. There is a sufficient number of suitable counterparts between the two measurement systems for optically faint objects. However, the number of common optically bright (G≤ 13 mag) objects is sparse as most are faint at radio frequencies, and only a few objects suitable for astrometry have been observed by VLBI in the past. As a result, rotation parameters for the optically brightGaiareference frame are not yet determined with sufficient accuracy.Aims.The verification of theGaiabright frame of DR2 and EDR3 is enhanced by the reevaluation of existing VLBI observations and the addition of newly acquired data for a sample of optically bright radio stars.Methods.Historical data from the literature were reevaluated, ensuring that the calibrator positions and uncertainties (used for the determination of the absolute star positions in the phase-referencing analysis) were updated and homogeneously referred to the ICRF3, the third realization of the International Celestial Reference Frame. We selected 46 suitable optically bright radio stars from the literature for new radio observations, out of which 32 were detected with the VLBA in continuum mode in the X or C band, along with radio-bright calibrators in the ICRF3. ImprovedGaia-VLBI rotation parameters were obtained by adding new observations and utilizing more realistic estimates of the absolute position uncertainties for all phase-referenced radio observations.Results.The homogenization greatly improved the steadiness of the results when the most discrepant stars were rejected one after another through a dedicated iterative process. ForGaiaDR2, this homogenization reduced the magnitude of the orientation parameters to less than 0.5 mas but increased that of the spin parameters, with the largest component being the rotation around the Y axis. An adjustment of the position uncertainties improved the reliability of the orientation parameters and the goodness of fit for the iterative solutions. Introducing the new single-epoch positions to the analysis reduced the correlations between the rotation parameters. The final spin forGaiaDR2 as determined by VLBI observations of radio stars is (−0.056, −0.113, +0.033) ± (0.046, 0.058, 0.053) mas yr−1. A comparison of the new results with external, independently derived spin parameters forGaiaDR2 reveals smaller differences than when using the historical data from the literature. Applying the VLBI data toGaiaEDR3, which was already corrected for spin duringGaiaprocessing, the derived residual spin is (+0.022, +0.065, −0.016) ± (0.024, 0.026, 0.024)mas yr−1, showing that the component in Y is significant at the 2.4σlevel.Conclusions.Even though our analysis provides a more accurate frame tie, more VLBI data are needed to refine the results and reduce the scatter between iterative solutions.

Comparative Study on Accuracy of Intra-Operative Computed Tomography-Navigation Based Pedicle Screw Placement With Skin vs Bone Fixed Dynamic Reference Frame in Minimally Invasive Transforaminal Lumbar Interbody Fusion.

Retrospective comparative study. To compare the accuracy of intra-operative navigation-assisted percutaneous pedicle screw insertion between bone fixed and skin fixed dynamic reference frame (DRF) in Minimally invasive transforaminal lumbar interbody fusion (MIS-TLIF). Between October 2018 and September 2022, patients who underwent MIS-TLIF were included in this study with DRF fixed either on bone (group B) or skin (group S). Pedicle screws were inserted under the guidance of intra-operative Cone bean Computed tomography (cbCT) based navigation. Accuracy of pedicle screw placement was immediately checked by a final intra-operative cbCT Spin. Among 170 patients, group B included 91 patients and group S included 79 patients. Out of total 680 screws, 364 screws (group B) and 316 screws (group S) were placed. Patient's demographic data and distribution of screws showed no statistically significant difference. The accuracy showed no significant difference between both the groups (94.5% in group B and 94.3% in group S). Skin fixed DRF can serve as an alternate way for placement and avoids extra incision with similar accuracy in pedicle screw insertions with bone fixed DRF using intra-operative CT guided navigation in MIS TLIF.

Spin-dependent reactivity and spin-flipping dynamics in oxygen atom scattering from graphite

The formation of two-electron chemical bonds requires the alignment of spins. Hence, it is well established for gas-phase reactions that changing a molecule’s electronic spin state can dramatically alter its reactivity. For reactions occurring at surfaces, which are of great interest during, among other processes, heterogeneous catalysis, there is an absence of definitive state-to-state experiments capable of observing spin conservation and therefore the role of electronic spin in surface chemistry remains controversial. Here we use an incoming/outgoing correlation ion imaging technique to perform scattering experiments for O(3P) and O(1D) atoms colliding with a graphite surface, in which the initial spin-state distribution is controlled and the final spin states determined. We demonstrate that O(1D) is more reactive with graphite than O(3P). We also identify electronically nonadiabatic pathways whereby incident O(1D) is quenched to O(3P), which departs from the surface. With the help of molecular dynamics simulations carried out on high-dimensional machine-learning-assisted first-principles potential energy surfaces, we obtain a mechanistic understanding for this system: spin-forbidden transitions do occur, but with low probabilities.

Evolution from two- to one-dimensional magnetic interactions in Cu2F5−x through electron doping by fluoride nonstoichiometry

The copper fluoride ${\mathrm{Cu}}_{2}{\mathrm{F}}_{5}$ is a compound with two-dimensional (2D) magnetic exchange interactions between the Cu ions in the $S=1$ and $S=\frac{1}{2}$ spin states. Using ab initio calculations, we predict that the existence of 5% vacancies in the fluoride sublattice of ${\mathrm{Cu}}_{2}{\mathrm{F}}_{5}$ results in a drastic transformation of the spin state of all copper ions and the final spin states are $S=\frac{1}{2}$ and $S=0$. Consequently, the anisotropy of the magnetic interactions increases, and 1D linear chains of Cu ${d}^{9}, S=\frac{1}{2}$ ions appear. We also propose a microscopic mechanism of such a transformation of the exchange interaction via ${\mathrm{CuO}}_{6}$ octahedra elongation.

Diagnosis of ultrafast ultraintense laser pulse characteristics by machine-learning-assisted electron spin

The rapid development of ultrafast ultraintense laser technology continues to create opportunities for studying strong-field physics under extreme conditions. However, accurate determination of the spatial and temporal characteristics of a laser pulse is still a great challenge, especially when laser powers higher than hundreds of terawatts are involved. In this paper, by utilizing the radiative spin-flip effect, we find that the spin depolarization of an electron beam can be employed to diagnose characteristics of ultrafast ultraintense lasers with peak intensities around 1020–1022 W/cm2. With three shots, our machine-learning-assisted model can predict, simultaneously, the pulse duration, peak intensity, and focal radius of a focused Gaussian ultrafast ultraintense laser (in principle, the profile can be arbitrary) with relative errors of 0.1%–10%. The underlying physics and an alternative diagnosis method (without the assistance of machine learning) are revealed by the asymptotic approximation of the final spin degree of polarization. Our proposed scheme exhibits robustness and detection accuracy with respect to fluctuations in the electron beam parameters. Accurate measurements of ultrafast ultraintense laser parameters will lead to much higher precision in, for example, laser nuclear physics investigations and laboratory astrophysics studies. Robust machine learning techniques may also find applications in more general strong-field physics scenarios.

Inelastic Collision Influencing the Rotational Dynamics of a Non-Rigid Asteroid (of Rubble Pile Type)

We have considered here a novel particular model for dynamics of a non-rigid asteroid rotation, assuming the added mass model instead of the concept of Viscoelastic Oblate Rotators to describe the physically reasonable response of a ‘rubble pile’ volumetric material of asteroid with respect to the action of a projectile impacting its surface. In such a model, the response is approximated as an inelastic collision in which the projectile pushes the ‘rubble pile’ parts of the asteroid together to form a mostly solidified plug in the crater during the sudden impact on the asteroid’s surface. Afterwards, the aforementioned ‘solidified plug’ (having no sufficient adhesion inside the after-impact crater) will be pushed outside the asteroid’s surface by centrifugal forces, forming a secondary rotating companion around the asteroid. Thus, according to the fundamental law of angular momentum conservation, the regime of the asteroid’s rotation should be changed properly. Namely, changes in rotational dynamics stem from decreasing the asteroid’s mass (due to the fundamental law of angular momentum conservation). As the main finding, we have presented a new solving procedure for a semi-analytical estimation of the total mass of the aforementioned ‘solidified plug’, considering the final spin state of rotation for the asteroid with minimal kinetic energy reduced during a long time period by the inelastic (mainly, tidal) dissipation. The asteroid is assumed to be rotating mainly along the maximal inertia axis with a proper spin state corresponding to minimal energy with a fixed angular momentum.

Black-hole ringdown as a probe of higher-curvature gravity theories

Detecting gravitational waves from coalescing compact binaries allows us to explore the dynamical, nonlinear regime of general relativity and constrain modifications to it. Some of the gravitational-wave events observed by the LIGO-Virgo Collaboration have sufficiently high signal-to-noise ratio in the merger, allowing us to probe the relaxation of the remnant black hole to its final, stationary state---the so-called black-hole ringdown, which is characterized by a set of quasinormal modes. Can we use the ringdown to constrain deviations from general relativity, as predicted by several of its contenders? Here, we address this question by using an inspiral-merger-ringdown waveform model in the effective-one-body formalism, augmented with a parametrization of the ringdown based on an expansion in the final black hole's spin. We give a prescription on how to include in this waveform model, the quasinormal mode frequencies calculated on a theory-by-theory basis. In particular, we focus on theories that modify general relativity by higher-order curvature corrections, namely, Einstein-dilaton-Gauss-Bonnet, dynamical Chern-Simons theories, and cubic- and quartic-order effective-field-theories of general relativity. We use this parametrized waveform model to measure the ringdown properties of the two loudest ringdown signals observed so far, GW150914 and GW200129. We find that while the Einstein-dilaton-Gauss-Bonnet theory cannot be constrained with these events, we can place upper bounds on the fundamental lengthscale of cubic- (${\ensuremath{\ell}}_{\text{cEFT}}\ensuremath{\le}38.2\text{ }\text{ }\mathrm{km}$) and quartic-order (${\ensuremath{\ell}}_{\text{qEFT}}\ensuremath{\le}51.3\text{ }\text{ }\mathrm{km}$) effective-field-theories of general relativity, and of dynamical Chern-Simons gravity (${\ensuremath{\ell}}_{\text{dCS}}\ensuremath{\le}38.7\text{ }\text{ }\mathrm{km}$). The latter result is a concrete example of a theory presently unconstrained by inspiral-only analyses which, however, can be constrained by merger-ringdown studies with current gravitational-wave data.

Systematic bias on the inspiral-merger-ringdown consistency test due to neglect of orbital eccentricity

The inspiral-merger-ringdown (IMR) consistency test checks the consistency of the final mass and final spin of a binary black hole merger remnant, independently inferred via the inspiral and merger-ringdown parts of the waveform. As binaries are expected to be nearly circularized when entering the frequency band of ground-based detectors, tests of general relativity (GR) currently employ quasicircular waveforms. We quantify the effect of residual orbital eccentricity on the IMR consistency test. We find that eccentricity causes a significant systematic bias in the inferred final mass and spin of the remnant black hole at an orbital eccentricity (defined at $10$ Hz) of $e_0 \gtrsim 0.1$ in the LIGO band (for a total binary mass in the range $65$-$200 \,M_{\odot}$). For binary black holes observed by Cosmic Explorer (CE), the systematic bias becomes significant for $e_0 \gtrsim 0.015$ (for $200$-$600 \,M_{\odot}$ systems). This eccentricity-induced bias on the final mass and spin leads to an apparent inconsistency in the IMR consistency test, manifesting as a false violation of GR. Hence, eccentric corrections to waveform models are important for constructing a robust test of GR, especially for third-generation detectors. We also estimate the eccentric corrections to the relationship between the inspiral parameters and the final mass and final spin; they are shown to be quite small.

Optimization with photonic wave-based annealers.

Many NP-hard combinatorial optimization (CO) problems can be cast as a quadratic unconstrained binary optimization model, which maps naturally to an Ising model. The final spin configuration in the Ising model can adiabatically arrive at a solution to a Hamiltonian, given a known set of interactions between spins. We enhance two photonic Ising machines (PIMs) and compare their performance against classical (Gurobi) and quantum (D-Wave) solvers. The temporal multiplexed coherent Ising machine (TMCIM) uses the bistable response of an electro-optic modulator to mimic the spin up and down states. We compare TMCIM performance on Max-cut problems. A spatial photonic Ising machine (SPIM) convolves the wavefront of a coherent laser beam with the pixel distribution of a spatial light modulator to adiabatically achieve a minimum energy configuration, and solve a number partitioning problem (NPP). Our computational results on Max-cut indicate that classical solvers are still a better choice, while our NPP results show that SPIM is better as the problem size increases. In both cases, connectivity in Ising hardware is crucial for performance. Our results also highlight the importance of better understanding which CO problems are most likely to benefit from which type of PIM. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

Transverse Single Spin Asymmetries of Heavy Flavor Electrons and Charged Pions in 200 GeV $p+p^{\uparrow}$ Collisions at Midrapidity

Transverse single spin asymmetries of particles produced in p+p^{\uparrow}p+p↑ collisions provide insight on the partonic spin and momentum structure of hadrons; heavy flavor electrons provide access to initial state spin-momentum correlations of gluons in the proton, while charged pions provide access to initial and final state transverse spin effects. Charged particles are measured at midrapidity at PHENIX using the silicon vertex detector and central arm spectrometer, made of an electromagnetic calorimeter, a ring-imaging Cherenkov detector, and drift and pad chambers. Recent results for both electron and charged pion measurements from the 2015 running period will be presented.