Spin Manifolds Research Articles

Spin Mixing in Intramolecular Singlet Fission: A First-Principles-Based Quantum Dynamical Study.

We investigate the dynamical interplay between the different triplet-pair spin states that are formed in the intramolecular singlet fission process in a series of pentacene-based dimers covalently bonded to a phenylene linker in ortho, meta, and para positions. Using first-principles calculations and a density matrix quantum dynamical approach we show that the spin dipole-dipole interaction leads to significant population of the quintet spin manifold in these regioisomers when the singlet, triplet and quintet triplet-pair states are quasidegenerate. Furthermore, we also show that the relative arrangement of the pentacene-like moieties has a profound impact on the dynamics of the spin-mixing process, affecting both the relative population of the different spin-states involved in the dynamics and the time scale of the process.

Optical manipulation of spin states in ultracold magnetic atoms via an inner-shell hz transition

Lanthanides, like erbium and dysprosium, have emerged as powerful platforms for quantum-gas research due to their diverse properties, including a significant large spin manifold in their absolute ground state. However, effectively exploiting the spin richness necessitates precise manipulation of spin populations, a challenge yet to be fully addressed in this class of atomic species. In this work, we present an all-optical method for deterministically controlling the spin composition of a dipolar bosonic erbium gas, based on a clocklike transition in the telecom window at 1299nm. The atoms can be prepared in just a few tens of microseconds in any spin-state composition using a sequence of Rabi-pulse pairs, selectively coupling Zeeman sublevels of the ground state with those of the long-lived clocklike state. Finally, we demonstrate that this transition can also be used to create spin-selective light shifts, thus fully suppressing spin-exchange collisions. These experimental results unlock exciting possibilities for implementing advanced spin models in isolated, clean, and fully controllable lattice systems. Published by the American Physical Society 2024

A Microlocal Investigation of Stochastic Partial Differential Equations for Spinors with an Application to the Thirring Model

On a d-dimensional Riemannian, spin manifold (M, g) we consider non-linear, stochastic partial differential equations for spinor fields, driven by a Dirac operator and coupled to an additive Gaussian, vector-valued white noise. We extend to the case in hand a procedure, introduced in Dappiaggi et al (Commun Contemp Math 27(07):2150075, 2022), for the scalar counterpart, which allows to compute at a perturbative level the expectation value of the solutions as well as the associated correlation functions accounting intrinsically for the underlying renormalization freedoms. This framework relies strongly on tools proper of microlocal analysis and it is inspired by the algebraic approach to quantum field theory. As a concrete example we apply it to a stochastic version of the Thirring model proving in particular that it lies in the subcritical regime if d≤2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\le 2$$\\end{document}.

Intersystem Crossing Control of the Nb+ + CO2 → NbO+ + CO Reaction.

The transfer of an oxygen atom from carbon dioxide (CO2) to a transition metal cation in the gas phase offers atomic level insights into single-atom catalysis for CO2 activation. Given that these reactions often involve open-shell transition metals, they may proceed through intersystem crossing between different spin manifolds. However, a definitive understanding of such spin-forbidden reaction requires dynamical calculations on multiple global potential energy surfaces (PESs) coupled by spin-orbit couplings. In this work, we report global PESs and spin-orbit couplings for three low-lying spin (quintet, triplet, and singlet) states for the reaction between the niobium cation (Nb+) and CO2, which are used to investigate the nonadiabatic reaction dynamics and kinetics. Comparison with experimental data of kinetics and collision dynamics shows satisfactory agreement. This reaction is found to be very similar to that between Ta+ + CO2. Specifically, our theoretical findings suggest that the rate-limiting step in this reaction is intersystem crossing, rather than potential barriers.

Understanding Spin-Triplet Excited States in Carbene-Metal-Amides.

Carbene-metal-amides (CMAs) are emerging delayed fluorescence materials for organic light-emitting diode (OLED) applications. CMAs possess fast, efficient emission owing to rapid forward and reverse intersystem crossing (ISC) rates. The resulting dynamic equilibrium between singlet and triplet spin manifolds distinguishes CMAs from most purely organic thermally activated delayed fluorescence emitters. However, direct experimental triplet characterization in CMAs is underutilized, limiting our detailed understanding of the ISC mechanism. In this work, we combine time-resolved spectroscopy with tuning of state energies through environmental polarity and metal substitution, focusing on the interplay between charge-transfer (3CT) and local exciton (3LE) triplets. Unlike previous photophysical work, we investigate evaporated host : guest films of CMAs and small-molecule hosts for increased device relevance. Transient absorption reveals an evolution in the triplet excited-state absorption (ESA) consistent with a change in orbital character between hosts with differing dielectric constants. Using quantum chemical calculations, we simulate ESAs of the lowest triplet states, highlighting the contribution of only 3CT and donor-moiety 3LE states to spectral features, with no strong evidence for a low-lying acceptor-centered 3LE. Thus, our work provides a blueprint for understanding the role of triplet excited states in CMAs which will enable further intelligent optimization of this promising class of materials.

Connes fusion of spinors on loop space

The loop space of a string manifold supports an infinite-dimensional Fock space bundle, which is an analog of the spinor bundle on a spin manifold. This spinor bundle on loop space appears in the description of two-dimensional sigma models as the bundle of states over the configuration space of the superstring. We construct a product on this bundle that covers the fusion of loops, i.e. the merging of two loops along a common segment. For this purpose, we exhibit it as a bundle of bimodules over a certain von Neumann algebra bundle, and realize our product fibrewise using the Connes fusion of von Neumann bimodules. Our main technique is to establish novel relations between string structures, loop fusion, and the Connes fusion of Fock spaces. The fusion product on the spinor bundle on loop space was proposed by Stolz and Teichner as part of a programme to explore the relation between generalized cohomology theories, functorial field theories, and index theory. It is related to the pair of pants worldsheet of the superstring, to the extension of the corresponding smooth functorial field theory down to the point, and to a higher-categorical bundle on the underlying string manifold, the stringor bundle.

Killing spinors and hypersurfaces

We consider spin manifolds with an Einstein metric, either Riemannian or indefinite, for which there exists a Killing spinor. We describe the intrinsic geometry of nondegenerate hypersurfaces in terms of a PDE satisfied by a pair of induced spinors, akin to the generalized Killing spinor equation. Conversely, we prove an embedding result for real analytic pseudo-Riemannian manifolds carrying a pair of spinors satisfying this condition.

Spectral metric and Einstein functionals for the Hodge–Dirac operator

We examine the metric and Einstein bilinear functionals of differential forms introduced by Dąbrowski et al. (2023), for the Hodge–Dirac operator d+\delta on an oriented, closed, even-dimensional Riemannian manifold. We show that they are equal (up to a numerical factor) to these functionals for the canonical Dirac operator on a spin manifold. Furthermore, we demonstrate that the spectral triple for the Hodge–Dirac operator is spectrally closed, which implies that it is torsion-free.

Understanding Spin‐Triplet Excited States in Carbene‐Metal‐Amides

Carbene‐metal‐amides (CMAs) are emerging delayed fluorescence materials for organic light‐emitting diode (OLED) applications. CMAs possess fast, efficient emission owing to rapid forward and reverse intersystem crossing (ISC) rates. The resulting dynamic equilibrium between singlet and triplet spin manifolds distinguishes CMAs from most purely organic thermally activated delayed fluorescence emitters. However, direct experimental triplet characterization in CMAs is underutilized, limiting our detailed understanding of the ISC mechanism. In this work, we combine time‐resolved spectroscopy with tuning of state energies through environmental polarity and metal substitution, focusing on the interplay between charge‐transfer (3CT) and local exciton (3LE) triplets. Unlike previous photophysical work, we investigate evaporated host:guest films of CMAs and small‐molecule hosts for increased device relevance. Transient absorption reveals an evolution in the triplet excited‐state absorption (ESA) consistent with a change in orbital character between hosts with differing dielectric constants. Using quantum chemical calculations, we simulate ESAs of the lowest triplet states, highlighting the contribution of only 3CT and donor‐moiety 3LE states to spectral features, with no strong evidence for a low‐lying acceptor‐centered 3LE. Thus, our work provides a blueprint for understanding the role of triplet excited states in CMAs which will enable further intelligent optimization of this promising class of materials.

Spectral Torsion

We introduce a trilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue. We demonstrate that for a canonical spectral triple over a closed spin manifold it recovers the torsion of the linear connection. We examine several spectral triples, including Hodge-de Rham, Einstein-Yang-Mills, almost-commutative two-sheeted space, conformally rescaled noncommutative tori, and quantum SU(2) group, showing that the third one has a nonvanishing torsion if nontrivially coupled.

Non-compactness results for the spinorial Yamabe-type problems with non-smooth geometric data

Let (M,g,σ) be an m-dimensional closed spin manifold, with a fixed Riemannian metric g and a fixed spin structure σ; let S(M) be the spinor bundle over M. The spinorial Yamabe-type problems address the solvability of the following equationDgψ=f(x)|ψ|g2m−1ψ,ψ:M→S(M),x∈M where Dg is the associated Dirac operator and f:M→R is a given function. The study of such nonlinear equation is motivated by its important applications in Spin Geometry: when m=2, a solution corresponds to a conformal isometric immersion of the universal covering M˜ into R3 with prescribed mean curvature f; meanwhile, for general dimensions and f≡constant≠0, a solution provides an upper bound estimate for the Bär-Hijazi-Lott invariant.The aim of this paper is to establish non-compactness results related to the spinorial Yamabe-type problems. Precisely, concrete analysis is made for two specific models on the manifold (Sm,g) where the solution set of the spinorial Yamabe-type problem is not compact: 1). the geometric potential f is constant (say f≡1) with the background metric g being a Ck perturbation of the canonical round metric gSm, which is not conformally flat somewhere on Sm; 2). f is a perturbation from constant and is of class C2, while the background metric g≡gSm.

Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory

In this paper, we study Lagrangian correspondences between Hilbert spaces. A main focus is the question when the composition of two Lagrangian correspondences is again Lagrangian. Our answer leads in particular to a well-defined composition law in a category of Lagrangian correspondences respecting given polarizations of the Hilbert spaces involved. As an application, we construct a functorial field theory on geometric spin manifolds with values in this category of Lagrangian correspondences, which can be viewed as a formal Wick rotation of the theory associated to a free fermionic particle in a curved spacetime.

Sensing at the Nanoscale Using Nitrogen-Vacancy Centers in Diamond: A Model for a Quantum Pressure Sensor.

The sensing of stress under harsh environmental conditions with high resolution has critical importance for a range of applications including earth's subsurface scanning, geological CO2 storage monitoring, and mineral and resource recovery. Using a first-principles density functional theory (DFT) approach combined with the theoretical modelling of the low-energy Hamiltonian, here, we investigate a novel approach to detect unprecedented levels of pressure by taking advantage of the solid-state electronic spin of nitrogen-vacancy (NV) centers in diamond. We computationally explore the effect of strain on the defect band edges and band gaps by varying the lattice parameters of a diamond supercell hosting a single NV center. A low-energy Hamiltonian is developed that includes the effect of stress on the energy level of a ±1 spin manifold at the ground state. By quantifying the energy level shift and split, we predict pressure sensing of up to 0.3 MPa/Hz using the experimentally measured spin dephasing time. We show the superiority of the quantum sensing approach over traditional optical sensing techniques by discussing our results from DFT and theoretical modelling for the frequency shift per unit pressure. Importantly, we propose a quantum manometer that could be useful to measure earth's subsurface vibrations as well as for pressure detection and monitoring in high-temperature superconductivity studies and in material sciences. Our results open avenues for the development of a sensing technology with high sensitivity and resolution under extreme pressure limits that potentially has a wider applicability than the existing pressure sensing technologies.

Multiexcitonic and optically bright states in subunits of pentacene crystals: A hybrid DFT/MRCI and molecular mechanics study.

A hybrid quantum mechanics/molecular mechanics setup was used to model electronically excited pentacene in the crystal phase. Particularly interesting in the context of singlet fission (SF) is the energetic location of the antiferromagnetically coupled multiexcitonic singlet state, 1(TT), and the ferromagnetically coupled analog in relation to the optically bright singlet state. To provide photophysical properties of the accessible spin manifold, combined density functional theory and multi-reference configuration interaction calculations were performed on pentacene dimers and a trimer, electrostatically embedded in the crystal. The likelihood of a quintet intermediate in the SF process was estimated by computing singlet-quintet electron spin-spin couplings employing the Breit-Pauli Hamiltonian. The performance of the applied methods was assessed on the pentacene monomer. The character of the optically bright state and the energetic location of the 1(TT) state depend strongly on the relative orientation of the pentacene units. In the V-shaped dimers and in the trimer, the optically bright state is dominated by local and charge transfer (CT) excitations, with admixtures of doubly excited configurations. The CT excitations gain weight upon geometry relaxation, thus supporting a CT-mediated SF mechanism as the primary step of the SF process. For the slip-stacked dimer, the energetic order of the bright and the 1(TT) states swaps upon geometry relaxation, indicating strong nonadiabatic coupling close to the Franck-Condon region-a prerequisite for a coherent SF process. The multiexcitonic singlet, triplet, and quintet states are energetically too far apart and their spin-spin couplings are too small to bring about a noteworthy multiplicity mixing.

Nonlinear Dirac Equation on Compact Spin Manifold with Chirality Boundary Condition

Nonlinear Dirac Equation on Compact Spin Manifold with Chirality Boundary Condition

Non-symmetric Pauli spin blockade in a silicon double quantum dot

Spin qubits in gate-defined silicon quantum dots are receiving increased attention thanks to their potential for large-scale quantum computing. Readout of such spin qubits is done most accurately and scalably via Pauli spin blockade (PSB), however, various mechanisms may lift PSB and complicate readout. In this work, we present an experimental study of PSB in a multi-electron low-symmetry double quantum dot (DQD) in silicon nanowires. We report on the observation of non-symmetric PSB, manifesting as blockaded tunneling when the spin is projected to one QD of the pair but as allowed tunneling when the projection is done into the other. By analyzing the interaction of the DQD with a readout resonator, we find that PSB lifting is caused by a large coupling between the different electron spin manifolds of 7.90 μeV and that tunneling is incoherent. Further, magnetospectroscopy of the DQD in 16 charge configurations, enables reconstructing the energy spectrum of the DQD and reveals the lifting mechanism is energy-level selective. Our results indicate enhanced spin-orbit coupling which may enable all-electrical qubit control of electron spins in silicon nanowires.

Extending the Range of Distances Accessible by 19F Electron-Nuclear Double Resonance in Proteins Using High-Spin Gd(III) Labels.

Fluorine electron-nuclear double resonance (19F ENDOR) has recently emerged as a valuable tool in structural biology for distance determination between F atoms and a paramagnetic center, either intrinsic or conjugated to a biomolecule via spin labeling. Such measurements allow access to distances too short to be measured by double electron-electron resonance (DEER). To further extend the accessible distance range, we exploit the high-spin properties of Gd(III) and focus on transitions other than the central transition (|-1/2⟩ ↔ |+1/2⟩), that become more populated at high magnetic fields and low temperatures. This increases the spectral resolution up to ca. 7 times, thus raising the long-distance limit of 19F ENDOR almost 2-fold. We first demonstrate this on a model fluorine-containing Gd(III) complex with a well-resolved 19F spectrum in conventional central transition measurements and show quantitative agreement between the experimental spectra and theoretical predictions. We then validate our approach on two proteins labeled with 19F and Gd(III), in which the Gd-F distance is too long to produce a well-resolved 19F ENDOR doublet when measured at the central transition. By focusing on the |-5/2⟩ ↔ |-3/2⟩ and |-7/2⟩ ↔ |-5/2⟩ EPR transitions, a resolution enhancement of 4.5- and 7-fold was obtained, respectively. We also present data analysis strategies to handle contributions of different electron spin manifolds to the ENDOR spectrum. Our new extended 19F ENDOR approach may be applicable to Gd-F distances as large as 20 Å, widening the current ENDOR distance window.

A uniqueness result for the Calderón problem for $U(N)$-connections coupled to spinors

In this paper we define a Dirichlet-to-Neumann map for a twisted Dirac Laplacian acting on bundle-valued spinors over a spin manifold. We show that this map is a pseudodifferential operator of order 1 whose symbol determines the Taylor series of the metric and connection at the boundary. We go on to show that if two real-analytic connections couple to a spinor via the Yang–Mills–Dirac equations with appropriate boundary conditions, and have equal Dirichlet-to-Neumann maps, then the two connections are globally gauge equivalent in the smooth category. In the abelian case, the global gauge equivalence is in the real-analytic category.

Structural and vibrational properties of lanthanide Lindqvist polyoxometalate complexes.

Molecular spin qubits have demonstrated immense potential in quantum information science research due to the addressability of electron spins using microwave frequencies, and the scalability and tunability of molecular systems. Exemplary in this regard is the holmium polyoxometalate, [Na9Ho(W5O18)2]·35H2O (HoW10), which features an accessible atomic clock transition at 9.4 GHz; however, the coherence time of this molecule is limited by spin-phonon coupling driven decoherence processes. To limit these decoherence pathways, materials need to be designed to reduce energy overlap between spin and phonon states, and this necessitates developing a better understanding on how structural modifications impact the vibrational landscape for classes of complexes. Herein we conducted a full investigation into the fundamental structural and vibrational properties of the lanthanide Lindqvist polyoxometalate series, [Na9Ln(W5O18)2]·xH2O (Ln = La(III)-Lu(III), except Pm(III)) (LnW10), to assess how structural changes effect vibrational characteristics and to elucidate pathways to improve the coherence properties of HoW10. Single crystal X-ray diffraction results revealed four distinct structural polymorphs in complexes 1-14 wherein first coordination spheres were identical, and differences manifested as changes in lattice packing. Interestingly, the subtle changes in packing exhibited by the four polymorphs were found to impact distortions away from ideal D4d symmetry for each of the LnW10 complexes. Raman and far-infrared (FIR) spectra of complexes 1-14 were collected to identify vibrational modes present in low energy regions and peak fitting assignments were made according to literature precedents. Qualitative and Partial least squares (PLS) analysis show correlations between complex structural parameters with the low energy Raman and FIR vibrational modes of interest. Overall, this investigation shows that the second coordination sphere plays an integral role in modulation of the structural and vibrational characteristics of LnW10 complexes, which makes it a viable route for tuning spin and vibrational manifolds of species within this series.

Multiple solutions to the nonlinear Dirac systems on compact spin manifolds with boundary

Multiple solutions to the nonlinear Dirac systems on compact spin manifolds with boundary