Orbital Rotations Research Articles

Acoustic spin-controlled orbital rotations in double spiral acoustic beams

Similar to optical spin-orbit interactions (SOIs), acoustic SOIs are anticipated to offer fresh perspectives and capabilities for acoustic manipulation beyond conventional scalar degrees of freedom. However, the acoustic extrinsic SOIs caused by particular properties of the medium were seldom explored. Here, the acoustic extrinsic SOI is observed in a double spiral acoustic beam (DSAB), as evidenced by the rotation of the spatial intensity pattern along the propagation axis. The interaction of the acoustic plane wave with the well-designed artificial flat structure generates two non-paraxial focused acoustic vortices (NFAVs) with different spin angular momentums. The coaxial coupling between them leads to acoustic spin-controlled orbital rotation (SOR). Theoretical formulations, supported by numerical simulations and experimental results, are provided to demonstrate the validity of acoustic SOR. Our work provides new perspectives and capabilities for understanding sound processing, and may open an avenue for the development of spin-orbit acoustics.

Quantum Information Orbitals (QIO): Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality.

The simultaneous treatment of static and dynamic correlations in strongly correlated electron systems is a critical challenge. In particular, finding a universal scheme for identifying a single-particle orbital basis that minimizes the representational complexity of the many-body wave function is a formidable and longstanding problem. As a contribution toward its solution, we show that the total orbital correlation actually reveals and quantifies the intrinsic complexity of the wave function, once it is minimized via orbital rotations. To demonstrate the power of this concept in practice, an iterative scheme is proposed to optimize the orbitals by minimizing the total orbital correlation calculated by the tailored coupled cluster singles and doubles (TCCSD) ansatz. The optimized orbitals enable the limited TCCSD ansatz to capture more nontrivial information on the many-body wave function, indicated by the improved wave function and energy. An initial application of this scheme shows great improvement of TCCSD in predicting the singlet ground state potential energy curves of the strongly correlated C2 and Cr2 molecule.

The regenerative solar system. Unified theory of physics

The Euler’s holomorphic regenerative universe is a quantum-gravitational theory of Earth development recognizing that oxygen, hydrogen, nitrogen and carbon dioxide in the Earth’s hydrosphere engender biological processes along with living organisms able to reshape the planet as surely as any physical force, but with delayed effects, the so-called torsional/gravitational buckling lag. Herein, the environmental sciences as a Vernadsky’s hypothesis precursor to these, become vital for preserving biological recurrent cycles, their nature being artificially changed by a vicious human intervention. The present paper describes the thermal gravitational mechanism of a solar system associated with the regenerative processes of molecular structures (in biology called metabolism or growth) at the quantum-gravitational scale, too slow to be perceived. The term “morph” (or the concept of “morphing” in aeronautics, in mathematics called topological holomorphism) originates from ancient Greeks and refers to the shape, figure, or other related aspects of an evolving entity. Therefore, morphing/morphism pertains to the process of modifying the original form or appearance of a particular object or system. The planets of solar system like “cosmic organisms” can manipulate the curvature and twist of their surfaces to maintain precise control over their recurrent cyclical complex motions (double, orbital and sideral rotations) by the thermal gravitational waves. The out of order function of the thermal gravitational mechanism can lead to the global warming effects associated with both reshaping (earthquakes, fires, floods) surfaces and morphing (as a whole energy metabolism) mutations, crucial for perpetuity of human beings. At the same time, the concept of quantum-gravity light with a topological dual isomorphic structure solves the fundamental problem of a unified theory of physical forces, as kinematic fast dynamo electromagnetic forces for splitting quanta bonded into atomic structures, and persistent (long time) gravitational forces for non-splitting quanta bonded into thermomolecular morphing structures. The only problem remains to gauge such multiple cooperative physical phenomena induced by light, which is solved by diverse reciprocity/equivalence theorems and corresponding conversion factors.

Toward Reliable Dipole Moments without Single Excitations: The Role of Orbital Rotations and Dynamical Correlation.

The dipole moment is a crucial molecular property linked to a molecular system's bond polarity and overall electronic structure. To that end, the electronic dipole moment, which results from the electron density of a system, is often used to assess the accuracy and reliability of new electronic structure methods. This work analyses electronic dipole moments computed with the pair coupled cluster doubles (pCCD) ansätze and its linearized coupled cluster (pCCD-LCC) corrections using the canonical Hartree-Fock and pCCD-optimized (localized) orbital bases. The accuracy of pCCD-based dipole moments is assessed against experimental and CCSD(T) reference values using relaxed and unrelaxed density matrices and different basis set sizes. Our test set comprises molecules of various bonding patterns and electronic structures, exposing pCCD-based methods to a wide range of electron correlation effects. Additionally, we investigate the performance of pCCD-in-DFT dipole moments of some model complexes. Finally, our work indicates the importance of orbital relaxation in the pCCD model and shows the limitations of the linearized couple cluster corrections in predicting electronic dipole moments of multiple-bonded systems. Most importantly, pCCD with a linearized CCD correction can reproduce the dipole moment surfaces in singly bonded molecules, which are comparable to the multireference ones.

Exponential amplification of the magnetic field in the primordial star-forming cloud

In the study of the initial mass function associated with the first generation of stars, known as Population III (Pop III) stars, a fundamental yet unresolved question pertains to the ultimate destiny of the secondary protostars emerging within the accretion disk – specifically, their likelihood of either merging or persisting as distinct entities. Our research concentrates on the magnetic influences affecting the genesis of these first stars under the conditions set by the cosmological initial magnetic field strength. We employ ideal magnetohydrodynamic simulations, utilizing a stiff equation-of-state (EOS) model, to accurately depict the magnetic field structure interconnecting these protostars. We observe that the magnetic field experiences rapid intensification due to the gas near the protostar completing multiple tens of orbital rotations in the initial decade following the formation of the protostar. Concurrently, as mass accretion continues, the region influenced by the significant magnetic field expands outward. This process of magnetic braking effectively curtails the disk fragmentation that would typically occur without a magnetic field. The resulting exponential augmentation of the magnetic field is posited to facilitate the formation of supermassive first stars.

Generalized perturbative singles corrections to the random phase approximation method: Impact on noncovalent interaction energies of closed- and open-shell dimers.

The post-Kohn-Sham (KS) random phase approximation (RPA) method may provide a poor description of interaction energies of weakly bonded molecules due to inherent density errors in approximate KS functionals. To overcome these errors, we develop a generalized formalism to incorporate perturbative singles (pS) corrections to the RPA method using orbital rotations as a perturbation parameter. The pS schemes differ in the choice of orbital-rotation gradient and Hessian. We propose a pS scheme termed RPA singles (RPAS)[Hartree-Fock (HF)] that uses the RPA orbital-rotation gradient and time-dependent HF Hessian. This correction reduces the errors in noncovalent interaction energies of closed- and open-shell dimers. For the open-shell dimers, the RPAS(HF) method leads to a consistent error reduction by 50% or more compared to the RPA method for the cases of hydrogen-bonding, metal-solvent, carbene-solvent, and dispersion interactions. We also find that the pS corrections are more important in error reduction compared to higher-order exchange corrections to the RPA method. Overall, for open shells, the RPAS(HF)-corrected RPA method provides chemical accuracy for noncovalent interactions and is more reliable than other perturbative schemes and dispersion-corrected density functional approximations, highlighting its importance as a reliable beyond-RPA correction.

Topological atom optics and beyond with knotted quantum wavefunctions

Atom optics demonstrates optical phenomena with coherent matter waves, providing a foundational connection between light and matter. Significant advances in optics have followed the realization of structured light fields hosting complex singularities and topologically non-trivial characteristics. However, analogous studies are still in their infancy in the field of atom optics. Here, we investigate and experimentally create knotted quantum wavefunctions in spinor Bose–Einstein condensates which display non-trivial topologies. In our work we construct coordinated orbital and spin rotations of the atomic wavefunction, engineering a variety of discrete symmetries in the combined spin and orbital degrees of freedom. The structured wavefunctions that we create map to the surface of a torus to form torus knots, Möbius strips, and a twice-linked Solomon’s knot. In this paper we demonstrate close connections between the symmetries and underlying topologies of multicomponent atomic systems and of vector optical fields—a realization of topological atom-optics.

Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations.

In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.

Motor generated torque drives coupled yawing and orbital rotations of kinesin coated gold nanorods

Kinesin motor domains generate impulses of force and movement that have both translational and rotational (torque) components. Here, we ask how the torque component influences function in cargo-attached teams of weakly processive kinesins. Using an assay in which kinesin-coated gold nanorods (kinesin-GNRs) translocate on suspended microtubules, we show that for both single-headed KIF1A and dimeric ZEN-4, the intensities of polarized light scattered by the kinesin-GNRs in two orthogonal directions periodically oscillate as the GNRs crawl towards microtubule plus ends, indicating that translocating kinesin-GNRs unidirectionally rotate about their short (yaw) axes whilst following an overall left-handed helical orbit around the microtubule axis. For orientations of the GNR that generate a signal, the period of this short axis rotation corresponds to two periods of the overall helical trajectory. Torque force thus drives both rolling and yawing of near-spherical cargoes carrying rigidly-attached weakly processive kinesins, with possible relevance to intracellular transport.

Generalization of ETS-NOCV and ALMO-COVP Energy Decomposition Analysis to Connect Any Two Electronic States and Comparative Assessment.

Energy decomposition analysis (EDA) is a useful tool for obtaining chemically meaningful insights into molecular interactions. The extended transition-state method with natural orbitals for chemical valence (ETS-NOCV) and the absolutely localized molecular orbital-based method with complementary occupied-virtual pairs (ALMO-COVP) are two successful EDA schemes. Working within ground-state generalized Kohn-Sham density functional theory (DFT), we extend these methods to perform EDA between any two electronic states that can be connected by a unitary transformation of density matrices. A direct proof that the NOCV eigenvalues are symmetric pairs is given, and we also prove that the charge and energy difference defined by ALMO are invariant under certain orbital rotations, allowing us to define COVPs. We point out that ETS is actually a 1-point quadrature to obtain the effective Fock matrix, and though it is reasonably accurate, it can be systematically further improved by adding more quadrature points. We explain why the calculated amount of transferred charge measured by ALMO-COVP is typically much smaller than that of ETS-NOCV and explain why the ALMO-COVP values should be preferred. While the two schemes are independent, ETS-NOCV and ALMO-COVP in fact give a very similar chemical picture for a variety of chemical interactions, including H-H+, the transition structure for the Diels-Alder reaction between ethene and butadiene, and two hydrogen-bonded complexes, H2O···F- and H2O···HF.

Exponentially Amplified Magnetic Field Eliminates Disk Fragmentation around Population III Protostars

One critical remaining issue that is unclear in the initial mass function of the first (Population III) stars is the final fate of secondary protostars that formed in the accretion disk—specifically, whether they merge or survive. We focus on the magnetic effects on the formation of the first star under a cosmological magnetic field. We perform a suite of ideal magnetohydrodynamic simulations for 1000 yr after the first protostar formation. Instead of the sink particle technique, we employ a stiff equation of state approach to represent the magnetic field structure connecting protostars. Ten years after the first protostar formation in the cloud initialized with B 0 = 10−20 G at n 0 = 104 cm−3, the magnetic field strength around the protostars has amplified from pico- to kilo-Gauss, which is the same strength as the present-day star. The magnetic field rapidly winds up since the gas in the vicinity of the protostar (≤10 au) has undergone several tens of orbital rotations in the first decade after protostar formation. As the mass accretion progresses, the vital magnetic field region extends outward, and magnetic braking eliminates the fragmentation of the disk that would happen in an unmagnetized model. On the other hand, assuming a gas cloud with a small angular momentum, this amplification might not work because the rotation would be slower. However, disk fragmentation would not occur in that case. We conclude that the exponential amplification of the cosmological magnetic field strength, about 10−18 G, eliminates disk fragmentation around Population III protostars.

A combined first- and second-order optimization method for improving convergence of Hartree–Fock and Kohn–Sham calculations

In this work, we investigate the optimization of Hartree-Fock (HF) orbitals with our recently proposed combined first- and second-order (SO-SCI) method, which was originally developed for multi-configuration self-consistent field (MCSCF) and complete active space SCF (CASSCF) calculations. In MCSCF/CASSCF, it unites a second-order optimization of the active orbitals with a Fock-based first-order treatment of the remaining closed-virtual orbital rotations. In the case of the single-determinant wavefunctions, the active space is replaced by a preselected "second-order domain," and all rotations involving orbitals in this subspace are treated at second-order. The method has been implemented for spin-restricted and spin-unrestricted Hartree-Fock (RHF, UHF), configuration-averaged Hartree-Fock (CAHF), as well as Kohn-Sham (KS) density functional theory (RKS, UKS). For each of these cases, various choices of the second-order domain have been tested, and appropriate defaults are proposed. The performance of the method is demonstrated for several transition metal complexes. It is shown that the SO-SCI optimization provides faster and more robust convergence than the standard SCF procedure but requires, in many cases, even less computation time. In difficult cases, the SO-SCI method not only speeds up convergence but also avoids convergence to saddle-points. Furthermore, it helps to find spin-symmetry broken solutions in the cases of UHF or UKS. In the case of CAHF, convergence can also be significantly improved as compared to a previous SCF implementation. This is particularly important for multi-center cases with two or more equal heavy atoms. The performance is demonstrated for various two-center complexes with different lanthanide atoms.

Wave Function Adapted Hamiltonians for Quantum Computing.

The use of the variational quantum eigensolver (VQE) for quantum chemistry is one of the most promising applications for noisy intermediate-scale quantum (NISQ) devices. A major limitation is represented by the need to build compact and shallow circuit ansatzes having the variational flexibility to catch the complexity of the electronic structure problem. To alleviate this drawback, we introduce a modified VQE scheme in which the form of the molecular Hamiltonian is adapted to the circuit ansatz through an optimization procedure. Exploiting the invariance of the Hamiltonian by molecular orbital rotations, we can optimize it using gradients that can be calculated without significant computational overload. The proposed method, named Wavefunction Adapted Hamiltonian Through Orbital Rotation (WAHTOR), has been applied to small molecules in numerical state vector simulations. The results demonstrate that, at variance with standard VQE, the method is less dependent on circuit topology and less prone to be trapped into high-energy local minima. It is able to recover a significant amount of electron correlation even with only empirical ansatzes with shallow circuit depth. Noisy calculations demonstrate the robustness and feasibility of the proposed methodology and indicate the hardware requirements to effectively apply the procedure using forthcoming NISQ devices.

Spinning rigid bodies driven by orbital forcing: the role of dry friction

A "circular orbital forcing" makes a chosen point on a rigid body follow a circular motion while the body spins freely around that point. We investigate this problem for the planar motion of a body subject to dry friction. We focus on the effect called reverse rotation (RR), where spinning and orbital rotations are antiparallel. Similar reverse dynamics include the rotations of Venus and Uranus, journal machinery bearings, tissue production reactors, and chiral active particles. Due to dissipation, RRs are possible only as a transient. Here the transient or flip time $t_\textrm{f}$ depends on the circular driving frequency $\omega$, unlike the viscous case previously studied. We find $t_\textrm{f}\sim\omega^{\gamma-1}\mu^{-\gamma/2}$, where $\mu$ is the friction coefficient and $\gamma=0$ ($\gamma=2$) for low (high) $\omega$. Whether RRs really occur depends on the initial conditions as well as on $\mu$ and $H$, a geometrical parameter. The critical $H_\textrm{c}(\mu)$ where RRs become possible follows a $q$-exponential with $q\simeq1.9$, a more restrictive RR scenario than in the wet case. We use animations to visualize the different dynamical regimes that emerge from the highly nonlinear dissipation mechanism of dry friction. Our results are valid across multiple investigated rigid body shapes.

ICISCF: An Iterative Configuration Interaction-Based Multiconfigurational Self-Consistent Field Theory for Large Active Spaces.

An iterative configuration interaction (iCI)-based multiconfigurational self-consistent field (SCF) theory, iCISCF, is proposed to handle systems that require large active spaces. The success of iCISCF stems from three ingredients: (1) efficient selection of individual configuration state functions spanning the active space while maintaining full spin symmetry; (2) the use of Jacobi rotation for optimization of the active orbitals in conjunction with a quasi-Newton algorithm for the core/active-virtual and core-active orbital rotations; (3) a second-order perturbative treatment of the residual space left over by the selection procedure (i.e., iCISCF(2)). Several examples that go beyond the capability of CASSCF are taken as showcases to reveal the efficacy of iCISCF and iCISCF(2), facilitated by iCAS for imposed automatic selection and localization of active orbitals.

Local, expressive, quantum-number-preserving VQE ansätze for fermionic systems

We propose VQE circuit fabrics with advantageous properties for the simulation of strongly correlated ground and excited states of molecules and materials under the Jordan–Wigner mapping that can be implemented linearly locally and preserve all relevant quantum numbers: the number of spin up (α) and down (β) electrons and the total spin squared. We demonstrate that our entangler circuits are expressive already at low depth and parameter count, appear to become universal, and may be trainable without having to cross regions of vanishing gradient, when the number of parameters becomes sufficiently large and when these parameters are suitably initialized. One particularly appealing construction achieves this with just orbital rotations and pair exchange gates. We derive optimal four-term parameter shift rules for and provide explicit decompositions of our quantum number preserving gates and perform numerical demonstrations on highly correlated molecules on up to 20 qubits.

Doped spin–orbital Mott insulators: Orbital dilution versus spin–orbital polarons

Here we compare two kinds of doping in transition metal oxides by considering defects due to the substitution of the transition metal or rare earth element. The focus is on insulating t2g orbital systems and we present various mechanisms that lead to reorganization of spin–orbital order. Substitutional doping of d4-transition metal by d3 ions generally results in removal of the local orbital degrees of freedom and the exchange on hybrid d4−d3 bonds modifying locally (or globally) spin–orbital order. Different routes of rearrangement of spin–orbital patterns are also found when considering doping by d2 ions. Here we demonstrate that in the regime of strong impurity-host coupling ferro-orbital type ordering is favored. This analysis can find application to ruthenate oxides with Mn or Cr replacing the Ru atoms. In contrast, charged (Sr,Ca) defect replacing R ion in the R1−x(Ca,Sr)xVO3 (R=La,Y) perovskites generates a spin–orbital polaron in the defect cube. We show that t2g orbital rotations are then induced near the charged defect and a doped hole disturbs orbital order. As a result, the collapse of G-type orbital order occurs but C-AF spin order stays robust under increasing doping.

Evidence for an atomic chiral superfluid with topological excitations

Topological superfluidity is an important concept in electronic materials as well as ultracold atomic gases1. However, although progress has been made by hybridizing superconductors with topological substrates, the search for a material—natural or artificial—that intrinsically exhibits topological superfluidity has been ongoing since the discovery of the superfluid 3He-A phase2. Here we report evidence for a globally chiral atomic superfluid, induced by interaction-driven time-reversal symmetry breaking in the second Bloch band of an optical lattice with hexagonal boron nitride geometry. This realizes a long-lived Bose–Einstein condensate of 87Rb atoms beyond present limits to orbitally featureless scenarios in the lowest Bloch band. Time-of-flight and band mapping measurements reveal that the local phases and orbital rotations of atoms are spontaneously ordered into a vortex array, showing evidence of the emergence of global angular momentum across the entire lattice. A phenomenological effective model is used to capture the dynamics of Bogoliubov quasi-particle excitations above the ground state, which are shown to exhibit a topological band structure. The observed bosonic phase is expected to exhibit phenomena that are conceptually distinct from, but related to, the quantum anomalous Hall effect3–7 in electronic condensed matter.

Experimental Realization of Topological On-Chip Acoustic Tweezers

Acoustic tweezers are gaining increasing attention due to their excellent biological compatibility. Recently, the concept of topology has been expanded from condensed-matter physics into acoustics, giving rise to robust wave manipulation against various defects. So far, topological acoustics have not been experimentally realized at an on-chip level to act as tweezers for microparticle manipulations. Here, we achieve topological on-chip acoustic tweezers based on the topologically protected phononic mode. These tweezers consist of one-dimensional arrays of Helmholtz resonant air cavities. Strong microfluidic oscillations induced by acoustic waves are experimentally observed at water-air surfaces of Helmholtz resonant air cavities at the topological interface. Acoustic radiation forces and streaming induced by these microfluidic oscillations capture microparticles, the sizes of which are up to 20 \textmu{}m, and make them undergo orbital rotations. Our topological on-chip acoustic tweezers realize noncontact label-free microparticle manipulations in microfluidics and exhibit enormous application potential in the biomedical field.

Non-equilibrium properties of an active nanoparticle in a harmonic potential

Active particles break out of thermodynamic equilibrium thanks to their directed motion, which leads to complex and interesting behaviors in the presence of confining potentials. When dealing with active nanoparticles, however, the overwhelming presence of rotational diffusion hinders directed motion, leading to an increase of their effective temperature, but otherwise masking the effects of self-propulsion. Here, we demonstrate an experimental system where an active nanoparticle immersed in a critical solution and held in an optical harmonic potential features far-from-equilibrium behavior beyond an increase of its effective temperature. When increasing the laser power, we observe a cross-over from a Boltzmann distribution to a non-equilibrium state, where the particle performs fast orbital rotations about the beam axis. These findings are rationalized by solving the Fokker-Planck equation for the particle’s position and orientation in terms of a moment expansion. The proposed self-propulsion mechanism results from the particle’s non-sphericity and the lower critical point of the solution.