Symmetric States Research Articles

Experimental construction of a symmetric three-qubit entangled state and its utility in testing the violation of a Bell inequality on an NMR quantum simulator

We designed a quantum circuit to prepare a permutation-symmetric maximally entangled three-qubit state called the state and experimentally created it on an NMR quantum processor. The presence of entanglement in the state was certified by computing two different entanglement measures, namely negativity and concurrence. We used the state in conjunction with a set of maximally incompatible local measurements, to demonstrate the maximal violation of inequality number 26 in Sliwa's classification scheme, which is a tight Bell inequality for the (3, 2, 2) scenario, i.e., the three-party, two-measurement-settings and two-measurement-outcomes scenario.

Jacobi partial waves for a set of 3D noncentral rational scatterers

The common tool of choice for basis expansions for the scattering problem with 3D quantum systems remains the spherical harmonics as eigenfunctions of the Laplace–Beltrami operator on the sphere, with approximations for deviations made around the usually dominant s-wave spherically symmetric state. However, with the growing number of technologically accessible nonspherically symmetric geometries of cold atomic and molecular systems, there is a need to explore as orthonormal bases for partial wave analysis the larger class of weighted Jacobi polynomials, subsuming the spherical harmonics. In particular, the lowest angular state for this bigger class is a toroid instead of a spherical s-orbital. This allows analytic treatment of a wider array of rational angular-dependent potentials which can describe rings and systems with topological constraints such as monopoles. Here, we present exact analytic solutions for the quantum scattering problem by partial wave analysis using the weighted Jacobi polynomials as an expanded basis. We obtain the scattering amplitude, differential and total cross-sections for exactly solvable 3D potentials included in the Smorodinsky-Winternitz noncentral systems with dynamical symmetries. Moreover, this procedure also solves the quantum scattering problem from a novel series of rational trigonometric forms of anisotropic potentials including double ring-shaped configurations.

Exploiting Asymmetric Co States in a Co-N-C Catalyst for an Efficient Oxygen Reduction Reaction

Co-NC catalysts have attracted extensive concerns derived from their high oxygen reduction reaction (ORR) activity, but the catalytic mechanism of Co species with different forms remains controversial. Herein, we prepare Co-NC catalysts with a cobalt nanoparticle-supported and nitrogen-doped carbon structure using the ZIF-67 precursor, in which the Co states in the catalyst present an asymmetric state of an exposed carbon coating (Asy-Co) and a symmetric state of buried carbon (Sy-Co). The acid etching process removed the exposed asymmetric cobalt nanoparticles on the surface. The specific role of cobalt nanoparticles with different forms in the Co-NC catalysts was comprehensively clarified through analyzing the chemical coordination environment by XPS and XAFS. The half-wave potential (E1/2 = 0.83 V) and onset potential (Eon = 1.04 V) of the Co-NC catalysts obtained after acid etching decreased significantly. Thus, the cobalt species removed by the acid etching process offered confirmed contributions to the catalytic activity. This work puts forward an important reference for the design and exploitation of non-noble metal catalysts using symmetry-derived motifs.

Symmetry-protected entanglement in random mixed states

Symmetry is an important property of quantum mechanical systems which may dramatically influence their behavior in and out of equilibrium. In this paper, we study the effect of symmetry on tripartite entanglement properties of typical states in symmetric sectors of Hilbert space. In particular, we consider Abelian symmetries and derive an explicit expression for the logarithmic entanglement negativity of systems with ${\mathbb{Z}}_{N}$ and $\text{U}(1)$ symmetry groups. To this end, we develop a diagrammatic method to incorporate partial transpose within the random matrix theory of symmetric states and formulate a perturbation theory in the inverse of the Hilbert space dimension. We further present entanglement phase diagrams as the subsystem sizes are varied and show that there are qualitative differences between systems with and without symmetries. We also design a quantum circuit to simulate our setup.

Dicke-like superradiance of distant noninteracting atoms

Fully excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954 [Phys. Rev. 93, 99 (1954)]. The burst is characterized by a maximum intensity scaling with the square of the number of atoms $N$ and a temporal width reduced by $N$ compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength $\ensuremath{\lambda}$ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of distant noninteracting atoms with mutual separations much larger than $\ensuremath{\lambda}$. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.

Electrical two-qubit gates within a pair of clock-qubit magnetic molecules

Enhanced coherence in HoW10 molecular spin qubits has been demonstrated by use of clock-transitions (CTs). More recently it was shown that, while operating at the CTs, it was possible to use an electrical field to selectively address HoW10 molecules pointing in a given direction, within a crystal that contains two kinds of identical but inversion-related molecules. Herein we theoretically explore the possibility of employing the electric field to effect entangling two-qubit quantum gates within a 2-qubit Hilbert space resulting from dipolar coupling of two CT-protected HoW10 molecules in a diluted crystal. We estimate the thermal evolution of T1, T2, find that CTs are also optimal operating points from the point of view of phonons, and lay out how to combine a sequence of microwave and electric field pulses to achieve coherent control within a switchable two-qubit operating space between symmetric and asymmetric qubit states that are protected both from spin-bath and from phonon-bath decoherence. This two-qubit gate approach presents an elegant correspondence between physical stimuli and logical operations, meanwhile avoiding any spontaneous unitary evolution of the qubit states. Finally, we found a highly protected 1-qubit subspace resulting from the interaction between two clock molecules.

Floquet interface states between photonic lattices with opposite chirality

We demonstrate interface states between two Floquet-driven photonic lattices having opposite chirality. Symmetrical and antisymmetrical localized states are found at an interface emerging in an otherwise static uniform lattice upon action of mirrored Floquet drives. These states locate near the edges of Floquet zones, highlighting the opening of band gaps initiated from lifted band crossings. They exist in a certain range of the driving frequency, which can be widened by increasing the driving strength. Chiral symmetry of the driven lattices is preferable to realize a large degree of localization of the interface states. We realize such states experimentally and observe different localization behaviors unpredicted in a tight-binding model, yet well understood via a continuum model that is more realistic for the experiment.

Deterministic generation of entanglement states between Silicon-Vacancy centers via acoustic modes.

We propose a scheme to entangle Silicon-Vacancy (SiV) centers embedded in a diamond acoustic waveguide. These SiV centers interact with acoustic modes of the waveguide via strain-induced coupling. Through Morris-Shore transformation, the Hilbert space of this hybrid quantum system can be factorized into a closed subspace in which we can deterministically realize the symmetrical Dicke states between distant SiV centers with high fidelity. In addition, the generation of entangled Dicke states can be controlled by manipulating the strength and frequency of the driving field applied on SiV centers. This protocol provides a promising way to prepare multipartite entanglement in spin-phonon hybrid systems and could have broad applications for future quantum technologies.

Spontaneous symmetry breaking induced by interaction in linearly coupled binary Bose–Einstein condensates

The spontaneous symmetry breaking (SSB) induced by a specific component of a linearly coupled binary Bose–Einstein condensate was analyzed. The model is based on linearly coupled Schrödinger equations with cubic nonlinearity and double-well potential acting on only one of the atomic components. By numerical simulations, symmetric and asymmetric ground states were obtained, and an induced asymmetry in the partner field was observed. In this sense, it is adequately demonstrated that the linear coupling mixing the two-field component (Rabi coupling) promotes the (in)balance between the atomic species, as well as the appearance of the Josephson and SSB phases.

Sb2Se3-assisted reconfigurable broadband Y-junction.

A Y-junction is commonly used in on-chip systems because of its excellent broadband characteristic. However, due to the lack of regulation methods, in most cases Y-junctions are used as passive components. In this work we propose a reconfigurable broadband Y-junction based on phase change material. When Sb2Se3 layers on two branches are at different states, the Y-junction is asymmetric and works as a reconfigurable dual-mode (de)multiplexer. When both Sb2Se3 layers are amorphous, the Y-junction is symmetric and works as a dual-mode 3-dB power splitter. To achieve quasi-adiabatic evolution for both states in a short device length, we propose a segmented fast quasi-adiabatic method. By dividing the gap region into multiple segments and optimizing the geometry and length of each segment, the proposed device achieves bandwidth > 100 nm (crosstalk < -20 dB) in a compact footprint of 19.3 × 3 µm2. The simulation result shows that at center wavelength of 1550 nm, the crosstalk and insertion loss of our device are < -41 dB and <0.12 dB, respectively, under asymmetric mode (de)multiplex state, and the excess loss is within 0.06 dB under symmetric power splitting state. The proposed device may contribute to the realization of a high-bandwidth, flexible mode-division-multiplexing network.

Spin magnetization of magnetic topological surface states in the presence of band asymmetry

In this work we investigate spin magnetization of surface electrons in magnetic topological insulators in the presence of electron–hole band asymmetry. The asymmetry is introduced by quadratic momentum term. The asymmetry in LL spectrum and unique zeroth LL behavior leads to unusual behavior of electron spin magnetization. Electronic magnetization behavior changes from positive to negative depending on zeroth Landau level being electron-like or hole-like. We show that the critical magnetic field at which discontinuity occurs depends both on intrinsic magnetic gap Δ0 and mass term. We show that plateau structure in magnetization depends on interplay of linear and quadratic momentum terms in electronic dispersion as chemical potential is tuned. It is also observed that the plateau structure in our system is unlike conventional oscillatory behavior in 2DEG or plateaus in particle hole symmetric surface states in the absence of mass term.

Einstein-Podolsky-Rosen steering in symmetrical Gaussian states

We have explored quantum Einstein-Podolsky-Rosen steering in symmetric two-mode Gaussian states using Gaussian and non-Gaussian measurements. For Gaussian measurements, we show that steering between the output modes of a symmetric beamsplitter is possible regardless of purity when a threshold input-state quadrature variance compression is achieved. Using the non-Gaussian operators introduced in [1] we show that non-Gaussian measurements can outperform Gaussian measurements for symmetrical states. We also analyze the possibility of asymmetric measurements setups made possible by non-Gaussian measurements and provide examples where such asymmetry is optimal for revealing steering. [1] Ji, SW., Lee, J., Park, J. et al. Quantum steering of Gaussian states via non-Gaussian measurements. Sci Rep 6, 29729 (2016). https://doi.org/10.1038/srep29729

BPS correlators for AdS3/CFT2

The BPS correlators of the symmetric product orbifold SymN(\U0001d54b4) are reproduced from the dual worldsheet theory describing strings on AdS3× S3× \U0001d54b4 with minimal (k = 1) NS-NS flux. More specifically, we show that the worldsheet duals of the symmetric orbifold BPS states can be identified with their lift to the covering surface, thereby making the matching of the correlators essentially manifest. We also argue that the argument can be generalised to arbitrary descendants, using suitable DDF operators on the worldsheet.

Phase transitions as a manifestation of spontaneous unitarity violation

Spontaneous symmetry breaking is well understood under equilibrium conditions as a consequence of the singularity of the thermodynamic limit. How a single global orientation of the order parameter dynamically emerges from an initially symmetric state during a phase transition, however, is not captured by this paradigm. Here, we present a series of symmetry arguments suggesting that singling out a global choice for the ordered state is in fact forbidden under unitary time evolution, even in the presence of an environment and infinitesimal symmetry breaking perturbations. We thus argue that the observation of phase transitions in our everyday world presents a manifestation of the unitarity of quantum dynamics itself being spontaneously broken. We argue that this agrees with the observation that Schrödinger’s time dependent equation is rendered unstable for macroscopic objects owing to the same singular thermodynamic limit that affects equilibrium configurations.

Synchronization and amplification enabled by diversity in nonlinear optical systems and the analogy with converse symmetry breaking for coupled oscillators

Converse symmetry breaking is a phenomenon occurring in populations of coupled oscillators, where stable and phase-locked symmetric states are possible only if the system itself is not symmetric. In this Letter, the analogy of converse symmetry breaking with amplification processes caused by phase and loss asymmetry for signal and idler waves in nonlinear optical systems is presented.

Projections in Various Scenarios and the Impact of Economy, Population, and Technology for Regional Emission Peak and Carbon Neutrality in China.

Owing to the surge in greenhouse gas emissions, climate change is attracting increasing attention worldwide. As the world’s largest carbon emitter, the achievement of emission peak and carbon neutrality by China is seen as a milestone in the global response to the threat. By setting different “emission peak” and “carbon neutrality” paths, this study compares the different pathways taken by China towards regional emission reduction to illustrate China’s possible contribution to global emission reduction, and analyzes the role that China’s economy, population, and technology need to play in this process through the Stochastic Impacts by Regression on Population, Affluence, and Technology model. In terms of path setting, based on actual carbon emissions in various regions from 2000 to 2019 and grid data on land use from 2000 to 2020, the model simulates three emission peak paths to 2030 and two carbon neutrality paths to 2060, thus setting six possible carbon emission trends from 2000 to 2060 in different regions. It is found that the higher the unity of policy objectives at the emission peak stage, the lower the heterogeneity of the inter-regional carbon emission trends. In the carbon neutrality stage, the carbon emissions in the unconstrained symmetrical extension decline state scenario causes the greatest environmental harm. Certain regions must shoulder heavier responsibilities in the realization of carbon neutrality. The economic development level can lead to a rise in carbon emissions at the emission peak stage and inhibit it at the carbon neutrality stage. Furthermore, the dual effects of population scale and its quality level will increase carbon emissions at the emission peak stage and decrease it at the carbon neutrality stage. There will be a time lag between the output of science and technology innovation and its industrialization, while green innovation is a key factor in carbon neutrality. Based on the results, this study puts forward policy suggestions from a macro perspective to better realize China’s carbon emission goals.

Geometric picture for SLOCC classification of pure permutation symmetric three-qubit states

The quantum steering ellipsoid inscribed inside the Bloch sphere offers an elegant geometric visualization of two-qubit states shared between Alice and Bob. The set of Bloch vectors of Bob's qubit, steered by Alice via all possible local measurements on her qubit, constitutes the steering ellipsoid. The steering ellipsoids are shown to be effective in capturing quantum correlation properties, such as monogamy, exhibited by entangled multiqubit systems. We focus here on the canonical ellipsoids of two-qubit states realized by incorporating optimal local filtering operations by Alice and Bob on their respective qubits. Based on these canonical forms we show that the reduced two-qubit states drawn from pure entangled three-qubit permutation symmetric states, which are inequivalent under stochastic local operations and classcial communication (SLOCC), carry distinct geometric signatures. We provide detailed analysis of the SLOCC canonical forms and the associated steering ellipsoids of the reduced two-qubit states extracted from entangled three-qubit pure symmetric states: We arrive at (i) a prolate spheroid centered at the origin of the Bloch sphere -- with longest semiaxis along the z-direction (symmetry axis of the spheroid) equal to 1 -- in the case of pure symmetric three-qubit states constructed by permutation of 3 distinct spinors and (ii) an oblate spheroid centered at $(0,0,1/2)$ inside the Bloch sphere, with fixed semiaxes lengths (1/Sqrt[2],\, 1/Sqrt[2],\, 1/2)), when the three-qubit pure state is constructed via symmetrization of 2 distinct spinors. We also explore volume monogamy relations formulated in terms of the volumes of the steering ellipsoids of the SLOCC inequivalent pure entangled three-qubit symmetric states.

Model-Free Adaptive Iterative Learning Bipartite Containment Control for Multi-Agent Systems.

This paper studies the bipartite containment tracking problem for a class of nonlinear multi-agent systems (MASs), where the interactions among agents can be both cooperative or antagonistic. Firstly, by the dynamic linearization method, we propose a novel model-free adaptive iterative learning control (MFAILC) to solve the bipartite containment problem of MASs. The designed controller only relies on the input and output data of the agent without requiring the model information of MASs. Secondly, we give the convergence condition that the containment error asymptotically converges to zero. The result shows that the output states of all followers will converge to the convex hull formed by the output states of leaders and the symmetric output states of leaders. Finally, the simulation verifies the effectiveness of the proposed method.

Bose-Einstein condensates in quasiperiodic lattices: Bosonic Josephson junction, self-trapping, and multimode dynamics

A Bose-Einstein condensate loaded in a one-dimensional bichromatic optical lattice with constituent sublattices having incommensurate periods is considered. Using the rational approximations for the incommensurate periods, we show that below the mobility edge the localized states are distributed nearly homogeneously in the space and explore the versatility of such potentials. We show that superposition of symmetric and antisymmetric localized states can be used to simulate various physical dynamical regimes, known to occur in double-well and multiwell traps. As examples, we obtain an alternative realization of a bosonic Josephson junction, whose coherent oscillations display beatings or switching in the weakly nonlinear regime, and describe self-trapping and four-mode dynamics, mimicking coherent oscillations and self-trapping in four-well potentials. These phenomena can be observed for different pairs of modes, which are localized due to the interference rather than due to a confining trap. The results obtained using few-mode approximations are compared with the direct numerical simulations of the one-dimensional Gross-Pitaevskii equation. The localized states and the related dynamics are found to persist for long times even in the repulsive condensates. We also described bifurcations of the families of nonlinear modes, the symmetry breaking, and stable minigap solitons.

Topological triplet-superconductivity in spin-1 semimetal

Superconductivity in topological semimetals gives a new paradigm of unconventional superconductors. Their exotic gap structures and topological properties have fascinated searching for material realizations and applications. In this work, we focus on a triple point semimetal where quasiparticle excitations, triple point fermions, carry the effective integer spin-1 in two distinct valleys. Our work demonstrates that the triple point fermion stabilizes inter-valley s-wave spin-triplet pairing. This is due to Fermi statistics, which strictly forbids the formation of inter-valley s-wave spin-singlet pairings. This feature is clearly distinct from the BCS and other multi-band superconductors. We find that two distinct inter-valley s-wave spin-triplet superconductors are allowed which in principle can be controlled by tuning the chemical potential: time-reversal symmetric (sz) state with topologically protected nodal lines and time-reversal broken (sx + isy) state with topologically protected Bogoliubov Fermi surfaces. Our study provides guidance in searching for spin-triplet superconductivity.