Determining the unitary dynamics accessible from finite Hamiltonian resources is a central problem in Hamiltonian engineering and quantum control. Dynamical Lie algebras (DLAs) connect available control Hamiltonians with the reachable dynamics, but their use as a design tool for modifying Hamiltonian generator sets remains less developed. In this work, we develop a finite-dimensional DLA framework for three generator-set operations: composition, invariance, and reduction. For composition, we construct direct sums of component DLAs using spectral projectors on an auxiliary register. For invariance, we analyze when modifications of Pauli-string generating sets preserve the generated Lie algebra, and introduce algebraic diagnostics for added generators. For reduction, we consider compact reductive DLAs and show how projection onto selected simple ideals gives reduced generating sets whose Lie closures are the corresponding ideal sums. We illustrate these results with finite-dimensional applications and numerical studies, including direct-sum dimension addition, central-spin invariance diagnostics, and the relation among DLA reduction, task relevance, and gradient behavior at finite system sizes. The results show how DLA structure can be used to diagnose controllability and guide Hamiltonian generator design under explicit algebraic assumptions.
X-ray coherent diffractive imaging has emerged as a key technique with modern coherent x-ray sources, enabling lensless reconstruction of nanoscale structure and dynamics with high spatial and temporal resolution with even a single x-ray pulse. However, there are many types of nanoscale orderings which are not directly resolvable using linear x-ray contrast mechanisms, for instance the orientation of ferroelectric domains, where systems with identical alignments but different orientations exhibit different topologies. The advent of nonlinear x-ray processes like sum-frequency generation and four-wave mixing raises the possibility of non-linear x-ray imaging, combining the high-resolution and elemental specificity of x-ray imaging with the state selectivity and vector sensitivity of non-linear optical imaging. In this work, we propose a coherent diffractive approach to imaging using x-ray nonlinear processes, leveraging the property of mutual incoherence between different wavelengths to isolate the nonlinear component from the overall diffraction pattern. We numerically demonstrate the approach, and discuss the feasibility of the proposed method in the presence of experimental noise, most relevantly shot noise. This analysis method is applicable in both static and dynamic imaging, including for single-shot imaging, offering a pathway beyond traditional spectroscopy for extreme ultraviolet/x-ray coherent imaging of spatio-temporal dynamics in quantum materials and biological systems.
Here, we develop a compact multilayer magnetic shield for a transportable optical clock, achieving shielding factors of up to $10^{5}$ . To improve the frequency stability of the transportable optical clock, we improved the magnetic-field environment of a transportable $ ^{40}\mathrm{Ca}^{+}$ ion optical clock (TCIOC) using the newly developed magnetic shielding system and reduced the clock-laser frequency noise by transferring the stability of an ultrastable reference laser through an optical frequency comb. These improvements enabled the coherent interrogation time to be extended from $40~\mathrm{ms}$ to $320~\mathrm{ms}$ . A time-interleaved self-comparison yielded a measured short-term fractional frequency instability of $1.6\times10^{-15}/\sqrt{\tau}$ , close to the estimated quantum projection noise-limited instability of $1.18\times10^{-15}/\sqrt{\tau}$ . Meanwhile, the uncertainty contributions associated with the DC second-order Zeeman shift and the servo error were reduced to $1.1\times10^{-21}$ and $4.5\times10^{-19}$ . These results provide a practical basis for further improving the performance of transportable optical clocks.
The Floquet formalism, developed for systems driven periodically in time, is applied to graphene, including the Rashba spin–orbit and Zeeman terms. Employing the high-frequency approximation, we studied Floquet-induced reconstruction of the Dirac spectrum, Poincaré recurrences, and the associated single-particle recurrences, as well as Lissajous curves. We observed single-particle Floquet subharmonic resonances, closed stroboscopic trajectories, and a Floquet-induced topological Lifshitz-like reconstruction of the low-energy spectrum, including anisotropic Dirac-cone deformation and Dirac-cone merging. Our main focus is on periodic time-driving via femtosecond half-cycle laser pulses. We also analyze the quantum metric—the distance between the initial and evolved wave functions—in terms of the participation rates of different bands and commensurate (non-commensurate) properties of the Floquet eigenvalues. In the weak-driving regime, we observe open curves, indicating non-periodic dynamics in the system. Within the considered single-particle Floquet framework, we identify conditions under which the stroboscopic dynamics is dominated by commensurate Floquet phases, leading to quantum Poincaré recurrences, closed Lissajous trajectories, and subharmonic spin oscillations. These effects are interpreted as Floquet time-crystal-like precursors in the sense of single-particle subharmonic dynamics. Within the presented single-particle Floquet framework, Poincaré recurrences and Lissajous resonances provide criteria for closed stroboscopic trajectories and subharmonic Floquet resonances.
We estimate the synchrotron radiation emitted by cosmic-ray muons in a uniform magnetic field, focusing on the photon radiation from $\mu$ eV to meV. Such events can potentially bring backgrounds to the axion dark matter searches. The GEANT4 software package is utilized to simulate the muon tracks in a cylindrical region of interest with an 8 T solenoid magnetic field applied. We further develop an analytical estimation of the angular-frequency-differential synchrotron radiation power spectra in this work as the cosmic-ray muons span a wide range of Lorentz factor $\gamma$ and pitch angle $\alpha$ . We verify that the cosmic-ray muons are not the dominant noise background for the current axion dark matter experiments on the $\mu$ eV scale because of the high quality factor $Q$ and fine energy resolution in the readout. However, without sufficient energy resolution in the detector readout, future broadband axion dark matter experiments will be vulnerable to the synchrotron radiation of these charged particles.
Non-Hermitian topological phases and the non-Hermitian skin effect (NHSE) have attracted significant attention in recent years, yet effectively controlling these phenomena remains challenging. Here, we propose a one-dimensional non-Hermitian Su–Schrieffer–Heeger model implemented on a circuit platform, incorporating a tunable next-nearest-neighbor (NNN) hopping element. We systematically investigate the influence of NNN hopping on both topological properties and the NHSE. By mapping the circuit Laplacian to the Hamiltonian, we analyze the effects of NNN hopping on the admittance spectrum, eigenfrequency spectrum, and spatial impedance distribution. Our results demonstrate that increasing the NNN hopping strength suppresses the NHSE, driving boundary-localized eigenstates to extend into the bulk, a transition quantitatively characterized by the inverse participation ratio. Further analysis using non-Bloch band theory reveals that while NNN hopping does not alter the quantized values of topological invariants, it shifts the critical parameters of topological phase transitions. This work provides a theoretical platform for simulating and controlling non-Hermitian topological states in circuits and establishes a quantitative foundation, through generalized Brillouin zone deformation and non-Bloch invariants, for designing novel non-Hermitian topological devices based on coupling engineering.
Active quantum control at the molecular scale remains a central pursuit in nanochemistry and quantum biology. Here, we demonstrate coherent polarization transfer from a nitrogen-vacancy (NV) center to a radical pair (RP)—a ubiquitous intermediate in chiral-bridge-mediated electron transfer—via dressed-state resonance. While direct energy exchange between the NV center and external spins is typically suppressed by energy conservation, we show that the dressed-state framework overcomes this limitation, enabling efficient control over the RP spin dynamics. Using quantum master equation simulations that incorporate the NV hyperfine Hamiltonian and RP internal interactions, we elucidate the magnetic field effect induced by the NV center. The spatial dependence analysis reveals that effective control with a product yield change of 10% (5%) can be achieved within maximum NV-RP separation ranges of $3.0$ – $4.1~{\mathrm{nm}}$ ( $3.3$ – $4.5~{\mathrm{nm}}$ ) across the vertical, parallel, and randomly oriented NV-RP configurations. These findings establish a pathway for manipulating chemical reactivity using solid-state defects, offering new perspectives for quantum sensing and control in complex molecular systems.
In some transition metal atoms, the special distribution of d -orbital electrons generates a large orbital magnetic moment, thereby exhibiting strong magnetic anisotropy in the crystal field. Experiments such as x -ray magnetic circular dichroism revealed sizable orbital moments in several Mott insulators. However, first-principles calculations using the density functional theory plus Hubbard correction (DFT + U ) sometimes fail to predict the correct orbital moment, due to subtle dependence on the initial occupation matrices. In this work, we have developed a DFT + U methodology for constraining the orbital moment by applying a magnetic field. Our method applies local magnetic field on each magnetic ion individually. In this way, we can establishes the relation between orbital magnetic moments and the total energy for some Mott magnetic materials. One can determine the orbital moments in the ground state from the energy landscape and also can calculate the strength of spin–orbit coupling (SOC) in the magnetic materials. Our calculations confirmed a sizable orbital magnetic moment of the octahedrally coordinated Fe ions in Fe _2 Mo _3 O _8 , which was predicted to be negeligible in previous calculations. We discuss the regulation and influence of electron–electron repulsion, crystal fields and SOC on the orbital moments. This work provides an effective means for in-depth research on the electronic structure and magnetic properties, especially the ground state orbital magnetic moments of atoms in different environments.
Precision measurements of the fundamental properties of trapped antihydrogen in the (ALPHA) experiment at CERN require an accurate determination of the antihdyrogen energy distribution. We introduce a new diagnostic technique, termed Spatio-Temporal Annihilation Mapping (STAM), which measures this distribution by exploiting the dynamics of antihydrogen in adiabatically time-varying magnetic fields. By analyzing the spatial and temporal patterns of annihilations recorded during adiabatic release from magnetic confinement and comparing them with detailed simulations, we infer the underlying energy distributions. STAM enables the simultaneous measurement of axial and transverse energy components, achieving a relative precision of approximately 10% over a mean energy range of $\sim$ 10–100 mK in the ALPHA trap. The technique is applied to both uncooled and laser-cooled antihydrogen populations, with results benchmarked against established laser-based diagnostics. While laser-based methods provide high-resolution measurements of the transverse energy and limited sensitivity to the axial component, an accurate determination of the axial energy remains challenging. In addition to complementing existing techniques, STAM is expected to access energy regimes that are currently inaccessible to laser-based diagnostics due to intrinsic limitations of those methods. These capabilities make STAM broadly applicable to future high-precision spectroscopic and gravitational studies with antihydrogen. Furthermore, STAM provides a novel probe of off-axis magnetic field structures, addressing a critical gap in current magnetometry techniques within the ALPHA experiment.
We experimentally investigate the quench dynamics of a spin–orbit–coupled (SOC) Bose–Einstein condensate and its subsequent thermalization. We measure the damping of momentum oscillations and find that the damping rate increases with SOC strength. Comparing the observed damping to theoretical estimates of spin drag in the absence of SOC, we find comparable order-of-magnitude scales, establishing a reference for dissipative processes involving thermal atoms. We emphasize that this comparison provides a baseline rather than a quantitative description of the SOC system. In addition, we directly measure the final temperature after relaxation and observe a decrease with increasing coupling strength. These results provide experimentally constrained benchmarks for finite-temperature theories of non-equilibrium dynamics in SOC quantum gases.
Criticality is widely regarded as a potential resource to boost the performance of quantum sensing. In existing protocols of criticality-enhanced quantum sensing, the criticality typically originates either from the probe or from the detected system itself. We here propose a scheme for sensing a dissipative reservoir based on the thermal criticality induced by the probe-reservoir interaction at finite temperature. It is revealed that the strong-coupling characteristics of the probe are able to create an additional thermal criticality, which significantly enhances the sensing performance. Our proposed scheme does not require precise dynamical control and is universal to different initial states, as it is built upon the equilibrium state generated by the natural dissipative dynamics of the probe. Expanding the scope of critical metrology, our findings pave a possible route toward high-precision quantum sensing.
Particle-exchange symmetry shapes the counting statistics of many-body systems by giving rise to multiple alternative evolutions whose transition amplitudes interfere. Here, we apply a Fourier transform over the symmetric group $S_N$ to the collection of $N!$ many-body transition amplitudes connecting two states of an $N$-particle system. This provides a decomposition of the counting statistics of many-body interference experiments into contributions associated with distinct irreducible exchange symmetries. As a first application of our formalism, we consider bosons or fermions which are rendered partially distinguishable from one another through unobserved degrees of freedom, and whose state is also subjected to a Fourier analysis. We thereby obtain a systematic description of partial distinguishability, which is both an important experimental noise source and a possible handle for the control of many-body interference. As a second application, we identify mechanisms responsible for completely destructive interference in many-body systems with other exchange symmetries than those of bosons or fermions. For an interferometer implementing the discrete Fourier transform unitary, we predict many instances of such suppressed transitions.
Understanding the dynamical behavior of swarmalators, particularly the transition from disorder to synchronization, constitutes one of the pivotal frontiers in the study of complex systems. We propose an ansatz that successfully decouples the spatial and phase dynamics in the locally coupled chiral swarmalators model, enabling rigorous analytical treatment of this complex system. Within this framework, we systematically examine how the interaction radius affects system synchronization, quantified through an order parameter measuring phase coherence. Our theoretical analysis reveals that increasing the interaction radius $R$ enhances synchronization in both velocity and phase dynamics. This relationship demonstrates that larger interaction networks facilitate more efficient information transfer among heterogeneous oscillators with different intrinsic frequencies. Using a self-consistent approach in the thermodynamic limit, we derive analytical expressions for the order parameter that accurately predict the synchronization transition. These findings provide fundamental insights into synchronization mechanisms in spatially embedded swarmalator systems with applications in understanding biological collective behaviors.
Single crystals of EuPd $ _3$ Si $ _2$ were grown using a high-temperature EuPd-flux method. The material was structurally and chemically characterized by single-crystal x-ray diffraction, powder x-ray diffraction, Laue method and energy-dispersive x-ray spectroscopy. The structural analysis confirmed the orthorhombic crystal structure (space group $Imma$ ) but revealed differences in the lattice parameters and bond distances. The composition is close to the ideal 1:3:2 stoichiometry with an occupation of 7% of the Si sites by Pd. The heat capacity, electrical resistivity, and magnetic susceptibility show two magnetic transitions indicating magnetic ordering below $T_\textrm{N1} = $ 61 K and a spin reorientation at $T_{\textrm{N}\textrm{2}} = $ 40 K. The orthorhombic material shows magnetic anisotropy, with anisotropy constants $K_1 = 7.1 \times 10^5\,\text{J m}^{-3}$ and $K_2 = 4.2 \times 10^5\,\text{J m}^{-3}$ , for field applied along the three main symmetry axes, which is summarized in the temperature-field phase diagrams. The susceptibility data hint to an alignment of the magnetic moments along $[100]$ between $T_\textrm{N1}$ and $T_{\textrm{N}\textrm{2}}$ . Below $T_{\textrm{N}\textrm{2}}$ the magnetic structure changes to an arrangement with moments canted away from $[100]$ . The single crystals investigated in this study are suggested to show antiferromagnetic order below $T_\textrm{N1}$ instead of ferromagnetism that sets in at higher $T_\textrm{C1} = 78\,\textrm{K}$ which might originate from certain differences in the structure, composition or defects that have an impact on the dominant coupling constants of the Ruderman–Kittel–Kasuya–Yosida interaction.
Bound electron–hole pairs called excitons determine the photophysical behavior of semiconducting materials. In this study, we present a combination of electron energy-loss spectroscopy in transmission and optical absorption spectroscopy for the investigation of excitons in bulk 2H-MoTe _2 . The exciton dispersion E ( q ) was measured for momentum transfers oriented along the ΓK and ΓM directions at 20 K. From the extracted dispersion relations, the in-plane exciton effective mass was determined. Our results reveal that for 2H-MoTe _2 the exciton effective mass is anisotropic. In consideration of the complementary optical results the exciton reduced mass, binding energy and radius have been determined.
We show that rotation can strongly amplify the photonic spin Hall effect in a ring Bose–Einstein condensate. For an incident probe beam carrying orbital angular momentum (OAM), the spin-dependent transverse shift of the reflected light is weak in the non-rotating regime but becomes strongly enhanced under rotation because rotation lifts the degeneracy of the condensate mechanical modes via Bragg scattering. The resulting mode splitting produces large photonic spin Hall shifts at ultra-low optical power, with the enhancement increasing with both the condensate winding number $L_p$ and the probe OAM $l$ , while remaining weakly affected by atom–atom interactions. Our findings elucidate a rotation-governed mechanism underlying spin-dependent light transport in hybrid atom–optomechanical systems, thereby highlighting its potential for applications in high-precision rotational sensing.
Abstract Going beyond the conventional classification rule of Altland-Zirnbauer symmetry classes, P T symmetric topological phases are classified by ( P T ) 2 = 1 or − 1 . The interconversion between the two P T -symmetric topological classes is generally difficult due to the constraint of ( P T ) 2 . Here, we propose a scheme to control and interconvert the P T -symmetric topological classes by Floquet engineering. We find that it is the removal of the Z 2 gauge degree of freedom, induced by the π phase difference between different hopping rates, by the periodic driving that leads to such an interconversion. Relaxing the system from the constraint of ( P T ) 2 , rich exotic topological phases, e.g. the coexisting P T -symmetric first-order real Chern insulator and second-order topological insulator not only in different quasienergy gaps, but also in one single gap, are generated. In contrast to conventional Floquet topological phases, our result provides a way to realize exotic topological phases without changing symmetries. It enriches the family of topological phases and gives an insightful guidance for the development of multifunctional quantum devices.
Abstract Recent experiments have discovered superconductivity in the ternary molybdenum pnictide materials A 2 Mo 3 As 3 (A = K, Rb, Cs). In this work, we investigate the superconducting properties of the A 2 Mo 3 As 3 family based on an effective five-band Hubbard model and using the fluctuation exchange approximation. By solving the linearized Eliashberg equation for various interaction parameters, we find that the spin-singlet and spin-triplet pairings dominate as the leading pairing symmetries in the weak and strong electron interaction regimes, respectively. These results are in good agreement with experiments.
Abstract We consider a lattice of d = 6 qudits that supports D ( S 3 ) non-Abelian anyons. We present a method for implementing both braiding and fusion evolutions using only the operators that create and measure anyons, without requiring additional dynamical control. This provides a minimal protocol demonstrating that D ( S 3 ) anyons can generate magic states, thereby establishing their universality for quantum computation. Furthermore, we show that the entire scheme can be encoded in just two qudits, offering a compact blueprint that is inherently scalable and readily implementable in current quantum platforms.
Abstract High-order harmonic (HOH) generation during the interaction of extremely intense electromagnetic (EM) waves in a quantum vacuum is studied within the Heisenberg–Euler formalism. We consider this process in the first nonvanishing order of perturbation theory. The basic expressions are derived for a general geometry, where the polarizations of the various sub-beams forming the focus of the EM beam are virtually identical. Explicit expressions for HOH generation are obtained for 4 π -dipole incoming wave. This beam geometry is optimal for a given incident EM wave power.
