Symmetry Of States Research Articles

Asymptotic phase-locking and synchronization in two-qubit systems

The paper concerns spontaneous asymptotic phase-locking and synchronization in two-qubit systems undergoing continuous Markovian evolution described by Lindbladian dynamics with normal Lindblad operators. Using analytic methods, all phase-locking-enforcing mechanisms within the given framework are obtained and classified. Detailed structures of their respective attractor spaces are provided and used to explore their properties from various perspectives. Amid phase-locking processes those additionally enforcing identical stationary parts of both qubits are identified, including as a special case the strictest form of synchronization conceivable. A prominent basis is presented which reveals that from a physical point of view two main types of phase-locking mechanisms exist. The ability to preserve information about the initial state is explored and an upper bound on the amplitude of oscillations of the resulting phase-locked dynamics is established. Permutation symmetry of both asymptotic states and phase-locking mechanisms is discussed. Lastly, the possibility of entanglement production playing the role of a phase-locking witness is rebutted by three analytically treatable examples.

Mixed symmetry states in 96Mo and 98Ru isotones in the framework of interacting boson model

The software package IBM code for interacting boson model-1 and Neutron Proton Boson NPBOS code for interacting boson model-2 have been used to calculate energy levels for, for by estimating a set of parameters which are used to predict the behavior of even-even isotones within the current scope of work there is clear competition between the two parameters (ε and a2) in isotones, as an inverse relationship. This means that vibrational qualities are continuous mixed with the rotational properties. In interacting boson model-2 parameters(ε, κ, χπ and χν) have been shown similarity with interacting boson model-1 expected. The Majorana parameter effect (ζ2) on the calculated excitation energy level for isotones has been accomplished by vary the ζ2 around the optimum-matches to practical data. The effect of increasing ζ2 on mixing symmetry states is the same in all isotones but different from state to another, we find the state J+ = 23+ was the lowest mixing symmetry states still approximately constant in the all. In that time,isotones have 1+, 3+1, 5+1 mixed symmetry states, rapidly increasing with increasing ζ2. The results of the calculated energy levels were in acceptable agreement with the experimental data. There is no pure vibrational property of these isotones

Spin and orbital metallic magnetism in rhombohedral trilayer graphene

We provide a complete theoretical interpretation of the metallic broken spin/valley symmetry states recently discovered in ABC trilayer graphene (ABC) perturbed by a large transverse displacement field. Our conclusions combine insights from ABC trilayer graphene electronic structure models and mean field theory, and are guided by precise magneto-oscillation Fermi-surface-area measurements. We conclude that the physics of ABC trilayer graphene is shaped by the principle of momentum-space condensation, which favors Fermi surface reconstructions enabled by broken spin/valley flavor symmetries when the single-particle bands imply thin annular Fermi seas. We find one large outer Fermi surface enclosed majority-flavor states and one or more small inner hole-like Fermi surfaces enclosed minority-flavor states that are primarily responsible for nematic order. The smaller surfaces can rotate along a ring of van-Hove singularities or reconstruct into multiple Fermi surfaces with little cost in energy. We propose that the latter property is responsible for the quantum oscillation frequency fractionalization seen experimentally in some regions of the carrier-density/displacement-field phase diagram.

Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits.

Although near-term quantum computing devices are still limited by the quantity and quality of qubits in the so-called NISQ era, quantum computational advantage has been experimentally demonstrated. Moreover, hybrid architectures of quantum and classical computing have become the main paradigm for exhibiting NISQ applications, where low-depth quantum circuits are repeatedly applied. In order to further scale up the problem size solvable by the NISQ devices, it is also possible to reduce the number of physical qubits by "cutting" the quantum circuit into different pieces. In this work, we experimentally demonstrated a circuit-cutting method for simulating quantum circuits involving many logical qubits, using only a few physical superconducting qubits. By exploiting the symmetry of linear-cluster states, we can estimate the effectiveness of circuit-cutting for simulating up to 33-qubit linear-cluster states, using at most 4 physical qubits for each subcircuit. Specifically, for the 12-qubit linear-cluster state, we found that the experimental fidelity bound can reach as much as 0.734, which is about 19% higher than a direct implementation on the same 12-qubit superconducting processor. Our results indicate that circuit-cutting represents a feasible approach of simulating quantum circuits using much fewer qubits, while achieving a much higher circuit fidelity.

Photodissociation of water molecule at short photon wavelengths: Dynamical studies

In our last study [J. Phys. B At. Mol. Opt. Phys. 54, 125,102 (2021).], we reported the ab initio calculation of the full-dimensional potential energy surfaces of water molecule including 9 A’ and 9 A” states in Cs symmetry. In this study, we performed additional non-adiabatic semi-classical studies based on the potential energy surfaces. Our simulation successfully repeated the near picosecond lifetime of the F∼1A′ state measured by time resolved photo-electron spectra experiment [Chinese J. Chem. Phys. 32, 53 (2019)]. We also determined the dissociation branching ratio including H + OH(X, A), H + H + O and H2+O channels. In addition, the reaction path corresponding to H2+O (1S) channel is clearly marked out, which is found in recent free-electron laser experiment [Nat. Commun. 12, 6,303 (2021)].

Spectroscopic study of the F[formula omitted] outer well state in H2, HD and D2

Two-photon UV-photolysis of hydrogen sulfide molecules is applied to produce hydrogen molecules in highly excited vibrational levels in the X1Σg+ electronic ground state, up to the dissociation energy and into the quasibound region. Photolysis precursors H2S, HDS and D2S are used to produce vibrationally hot H2, HD and D2. The wave function density at large internuclear separation is excited via two-photon transitions in the F1Σg+ - X1Σg+ system to probe ro-vibrational levels in the first F1Σg+ outer well state of gerade symmetry. Combining with accurate knowledge of the X1Σg+ (v,J) levels from advanced ab initio calculations, energies of rovibrational levels in the F1Σg+ state are determined. For the H2 isotopologue a three-laser scheme is employed yielding level energies at accuracies of 4×10−3 cm−1 for F(v=0,J) up to J=21 and for some low J values of F(v=1). A two-laser scheme was applied to determine level energies in H2 for F(v=0−4) levels as well as for various F levels in HD and D2, also up to large rotational quantum numbers. The latter measurements in the two-laser scheme are performed at lower resolution and the accuracy is strongly limited to 0.5 cm−1 by ac-Stark effects. For H2 a new quasibound resonance X1Σg+ (v=6, J=23) is detected through the Q(23) and O(23) transitions in the F0-X6 band. Also a quasi-bound resonance in D2 is assigned, for the first time in this species: X1Σg+ (v=17 , J=15). The experimental results on F(v,J) level energies are compared with previously reported theoretical results from multi-channel quantum-defect calculations as well as with results from newly performed non-adiabatic quantum calculations.

Theory of Projectors and Its Application to Molecular Symmetry

Projector theory can serve as a powerful tool to perform the symmetric computation of molecular systems. The work of William Harter has long demonstrated the effectiveness of this theory in molecular spectroscopy; however, it seems its usefulness has not been realized by many in the field. We have described this methodology and have considered the D3 symmetry system and the tetrahedral symmetry of methane molecules as concrete examples where the computed rotation tensors and vibrational wavefunction were derived for some symmetry states.

Phase Dependent Parity Time Symmetry in a quantum dot nanostructure

We present a diamond configuration quantum dots nanostructure trapped in two-dimensional (2D) optical lattices for the investigation of parity time (PT) symmetry. We trap quantum dots in a Gaussian density distribution to examine the PT, non-PT, and anti-PT symmetry in periodic 2D optical lattices. The variation in the relative phase of the optical beams in the quantum dots spectrum indicates either PT, anti-PT, or non-PT symmetry, resulting in an intriguing modulation of imaginary and real refractive index (RI) components. Controlling the appropriate modulation of the RI leads in PT symmetry being controlled by a single parameter, the relative phase of the optical fields. Using detuning and the coupling field of Rabi frequencies, we may determine the state of PT symmetry as well as the direction of field propagation. Coherent control of PT symmetry in 2D quantum dot nanostructure trapped in optical lattices may also have applications in 2D optical devices such as diodes, modulators and photonic transistors.

Chiral broken symmetry descendants of the kagome lattice chiral spin liquid

The breaking of chiral and time-reversal symmetries provides a pathway to exotic quantum phenomena and topological phases. Recent work has extensively explored the resulting emergence of chiral charge orders and chiral spin liquids (CSLs) on the kagome lattice. Such CSLs are closely tied to bosonic fractional quantum Hall states with anyonic quasiparticles; however, their connection to nearby ordered states has remained a mystery. Here, we use spin-wave theory, parton Gutzwiller wave functions, and exact diagonalization to show that two distinct magnetic orders with uniform scalar chirality---the XYZ umbrella state and the octahedral spin crystal--emerge as competing orders in close proximity to the CSL. In this letter, we highlight the intimate link between a topologically ordered liquid and broken symmetry states with nontrivial real-space topology.

Pseudospin symmetry in resonant states in deformed nuclei

Pseudospin symmetry (PSS) plays critical roles in the formation of many physical phenomena, and has been studied extensively from spherical nuclei to deformed nuclei. However, there remains an open question about the PSS in resonant states in deformed systems. For the first time, we investigate the PSS in resonant states in deformed nuclei by solving the Dirac equation in the complex-momentum representation for a potential with quadrupole deformation at the first order obtained from relativistic mean-field (RMF) calculations. Taking 170Yb as an example, we explore the PSS in the single-particle resonant states by examining the energies, widths and the density distribution. Compared with the bound states, the pseudospin splittings between the resonant pseudospin doublets are found to be small, and the radial density distributions of pseudospin doublets look very similar, which indicates that the PSS of resonant states is well reserved in deformed nuclei. Moreover, we have comprehensively studied the dependencies of the PSS on nuclear deformations and the shape of potential, which are helpful to recognize the evolution of resonant pseudospin doublets in weakly-bound deformed nuclei and understand their exotic properties.

Design of highly nonlinear confusion component based on entangled points of quantum spin states

Cryptosystems are commonly deployed to secure data transmission over an insecure line of communication. To provide confusion in the data over insecure networks, substitution boxes are the solitary components for delivering a nonlinear mapping between inputs and outputs. A confusion component of a block cipher with high nonlinearity and low differential and linear approximation probabilities is considered secure against cryptanalysis. This study aims to design a highly nonlinear substitution-permutation network using the blotch symmetry of quantum spin states on the Galois field GF (28). To observe the efficiency of the proposed methodology, some common and advanced measures were evaluated for performance, randomness, and cryptanalytics. The outcomes of these analyses validate that the generated nonlinear confusion components are effective for block ciphers and attain better cryptographic strength with a high signal-to-noise ratio in comparison to state-of-the-art techniques.

Adiabatic Trajectory Approximation: A New General Method in the Toolbox of Mixed Quantum/Classical Theory for Collisional Energy Transfer

A new version of the MQCT program is presented, which includes an important addition, adiabatic trajectory approximation (AT-MQCT), in which the equations of motion for the classical and quantum parts of the system are decoupled. This method is much faster, which permits calculations for larger molecular systems and at higher collision energies than was possible before. AT-MQCT is general and can be applied to any molecule + molecule inelastic scattering problem. A benchmark study is presented for H2O + H2O rotational energy transfer, an important asymmetric-top rotor + asymmetric-top rotor collision process, a very difficult problem unamenable to the treatment by other codes that exist in the community. Our results indicate that AT-MQCT represents a reliable computational tool for prediction of collisional energy transfer between the individual rotational states of two molecules, and this is valid for all combinations of state symmetries (such as para and ortho states of each collision partner).

Dissociation Dynamics of Anionic Nitrogen Dioxide in the Low-Lying Resonant States.

Experimental studies of the dynamics near the molecular dissociation threshold are frequently frustrated, due to the small cross sections and the demand for identification of close-lying electronic states or nuclear motions with multiple degrees of freedom. Using the high-resolution anion velocity map imaging technique, here we report a dynamics study of the dissociations of anionic nitrogen dioxide in low-lying resonant states formed by electron attachment [e- + NO2 (X2A1) → NO2- → NO (X2Π) + O- (2P)]. The long-term puzzling issues about the near-threshold dissociations of NO2- are settled. We suggest that three low-lying resonant states (1B1, 3B1, and 3B2) of NO2- contribute to the production of O- at attachment energies of <5 eV. Furthermore, B1 and B2 symmetries of the resonant states lead to different anisotropies of the O- angular distribution. At the relatively high electron attachment energies, a prompt fragmentation in the molecular bent conformation competes with an indirect dissociation in the straightened conformation.

Kondo resonance effects in emergent flat band materials

Macroscopic degrees of freedom that are involved in the transport of carriers through mesoscopic electronic devices are susceptible to the effects of strong many-body correlations. The presence of magnetic impurities in dilute magnetic alloys typically allow for insights into Kondo effect from the scattering of free carriers by localized electron states of the magnetic impurities but this effect is not well understood when there are no d-band electron states. Herein, the signatures of Kondo resonance effect are elucidated in quantum dots derived from a carbon-nanoline embedded monolayer hexagonal boron nitride whose electron states host flat band ferromagnetism as distinct broken symmetry states. Quantum transport state of mesoscopic devices modelled as quantum dots tunnel coupled to metallic leads is computed by direct diagonalization of the Hamiltonian. The possibility of realizing quantum dots with highly tunable electron states in energy interconversion devices is discussed to show the importance of screening effects on single-electron energy levels. The quantum master equation is solved within different formalisms to determine the stationary-state particle and energy currents. Stability diagrams are calculated to show the dependence of the conductance on experimental control variables of the quantum dot device. The computed responses of the stationary-state transport signatures are used to characterize Kondo resonance effects from flat band states of embedded carbon nanoline-based quantum dots. It is found that the local network structure of the hexagonal ring carbon cluster-based quantum dot has a broken particle-hole symmetry in the transport state. This signals the formation of the quasiparticle states expected in second order scattering when the macroscopic “charge” pseudospin symmetry of the tunnelling electron state is broken dynamically due to charging. The results are discussed to show the implications of a vanishing particle-hole symmetry in the carrier transport state of quantum dots for energy conversion applications.

Broken symmetry and competing orders in Weyl semimetal interfaces

We consider interaction-induced broken symmetry states of two Weyl semimetal surfaces with multiple Fermi-arc (FA) states. In the presence of inter- and intra-surface Coulomb interactions, multiple broken symmetries may emerge which coexist and/or compete with one another. Interlayer exciton condensates involving different FA flavors are shown to form, with amplitudes determined by the strength of interactions and the degree of nesting among the arcs. For FA pairs which are well-separated in momentum with strong nesting, the resulting state is a particle-hole analog of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor. Intralayer interactions moreover induce charge density wave (CDW) ordering, so that the most general state of the system is a supersolid. These orderings in principle carry signatures in non-linear behavior and narrow band noise in Coulomb drag transport measurements.

Non-adiabatic coupling in the potential energy surfaces of SO2 molecule.

To investigate the potential energy surfaces and the coupling between the adiabatic states of SO2 molecules, it is necessary to consider the non-adiabatic coupling terms (NACTs), where the Born-Oppenheimer approximation breaks down. In this work, we analyze the conical intersections between 1 1A1 and 1 1B2 states (the A' states in Cs symmetry) and 1 1A2 and 1 1B1 states (the A'' states in Cs symmetry) using NACTs and adiabatic-to-diabatic transformation (ADT) angles. Our results confirm reasonable interaction between 1 1A1 and 1 1B2 states and strong interaction between 1 1A2 and 1 1B1 states.

Unveiling the double triplet nature of the 2Ag state in conjugated stilbenoid compounds to achieve efficient singlet fission.

In this investigation, the excited-state evolution in a series of all-trans stilbenoid compounds, displaying a low-lying dark singlet state of 2Ag-like symmetry nearly degenerate with the bright 1Bu state, was unveiled by employing advanced ultrafast spectroscopies while probing the effect of solvent polarizability. Together with the dual emission, femtosecond transient absorption and broadband fluorescence up-conversion disclosed the double nature of the 2Ag-like state showing both singlet features, a lifetime typical of a singlet and the ability to emit, and a triplet character, exhibiting a triplet-like absorption spectrum. The ultrafast formation (in hundreds of femtoseconds) from the non-relaxed upper singlet state led to the identification of 2Ag as the correlated triplet pair of singlet fission. The spectral difference obtained by comparison of transient absorption peaks of the 2Ag (1TT) and the triplet states was found to be in remarkable agreement with the observed triplet yield and the 1(TT) separation rate constant. Indeed, this spectral shift provided an experimental method to gain qualitative insight into the ease of separation of the 1(TT) and the relative SF efficiency. The highly conjugated polyene-like structures enable the ultrafast formation of the double triplet, but then the large binding energy prevents the triplet separation and thus the effective completion of singlet fission. Even though thermodynamically feasible for all the investigated stilbenoids according to TD-DFT calculations, singlet fission resulted to occur efficiently in the case of 1-(pyridyl-4-ylethenyl)-4-(p-nitrostyryl)benzene and nitro-styrylfuran with the triplet yield reaching 120% and 140%, respectively, triggered by their greatly enhanced intramolecular charge transfer character relative to the other compounds in the series.

Macroeconomic Fundamentals, Economic Growth and Poverty in Ecowas Franc Zone: Does Single Currency Matter?

The paper investigated the role of single currency macroeconomic variables (exchange rate, central government tax and grant revenue, central government fiscal balance, inflation rate, external public debt stock, and gross capital formation) on output, poverty, international trade volume and unemployment in ECOWAS Franc zone. The question was about the state of symmetry of these factors and its effects on economic growth. The core objective was to examine the pattern of relationship these variables have with economic growth. The paper covered the period 1980 to 2019 and countries in the zone. Romer endogenous growth model, optimum currency theory (OCA) and PMG-ARDL methodology were used. From the group coefficients, fiscal balance (0.03) and inflation (0.15); exchange rate (-0.29) and inflation (-4.50); GCF (0.01); and tax/grant revenue (4.10e-10) were significant at the 5% level in the output, poverty, international trade volume and unemployment models, respectively. While the poverty model indicated two OCA groups in the region, the output, international trade and unemployment models showed four OCA groups each. The long run error correction terms in the output, poverty, international trade volume and unemployment models were 0.61, 0.11, 0.10, and 0.093 respectively and significant at the 5% level, meaning divergence from long run equilibrium. A minimum of two OCAs and a maximum of four OCAs were found. The paper therefore concluded that the zone does not fulfill OCA requirements and recommended that appropriate policy mix should be developed to align these single currency macroeconomic factors towards achieving sustainable economic growth in the zone.

Coherent Many-Body Oscillations Induced by a Superposition of Broken Symmetry States in the Wake of a Quantum Phase Transition.

It is now widely accepted that quenches through the critical region of quantum phase transitions result in post-transition states populated with topological defects-analogs of the classical topological defects. However, consequences of the very nonclassical fact that the state after a quench is a superposition of distinct, broken-symmetry vacua with different numbers and locations of defects have remained largely unexplored. We identify coherent quantum oscillations induced by such superpositions in observables complementary to the one involved in symmetry breaking. These oscillations satisfy Kibble-Zurek dynamical scaling laws with the quench rate, with an instantaneous oscillation frequency set primarily by the gap of the system. In addition to the obvious fundamental significance of a superposition of different broken symmetry states, quantum coherent oscillations can be used to verify unitarity and test for imperfections of the experimental implementations of quantum simulators.

Designer meron lattice on the surface of a topological insulator

We present a promising route to realize spontaneous magnetic order on the surface of a 3D topological insulator by applying a superlattice potential. The superlattice potential lowers the symmetry of the surface states and creates tunable van Hove singularities, which, when combined with strong spin-orbit coupling and Coulomb repulsion, give rise to a topological meron lattice spin texture. The periodicity of this designer meron lattice can be tuned by varying the periodicity of the superlattice potential. We employ Ginzburg-Landau theory to classify the different magnetic orders and show that the magnetic transition temperature reaches experimentally accessible values. Our work introduces another direction to realize exotic quantum order by engineering interacting Dirac electrons in a superlattice potential, with promising applications to spintronics.