We propose a theoretical model to obtain the photonic spin Hall effect (SHE) in an optomechanical nanocavity using a graphene bilayer as the intracavity medium. In our model, the pump and probe fields coherently drive the first mirror, whereas the second mirror has mechanical oscillation due to the radiation pressure. We show that the right- and left-circular polarization components of the Gaussian probe field striking at an arbitrary incident angle become spatially separate along a direction orthogonal to the plane of incidence. Photonic SHE can be coherently controlled by adjusting the optomechanical interaction, cavity field, and G-mode phonon coupling, as well as G-mode phonon and electronic state interaction. The findings of photonic SHE are equally valid for standard optomechanical systems in the absence of cavity field and G-mode phonon coupling and electronic state interaction. The cavity field and G-mode phonon coupling broadened the detuning range of the probe field to observe the dominant photonic SHE. Adding G-mode phonon and electronic state interaction generates enhanced photonic SHE at three different probe field detunings due to optomechanical-induced transparency being split into three windows. We show that asymmetric photonic SHE can be controlled through cavity field and G-mode phonon coupling and G-mode phonon and electronic state interaction when probe field detuning is nonzero. The photonic SHE in bilayer graphene integrated with an optomechanical cavity may enable further studies of spin-dependent photonic effects and quantum sensing applications.

Quantum beats in superradiance arise from coherent interference between collective emission from independent transitions, fundamentally distinct from single-atom quantum beats. In this work, we report the observation of quantum beats generated from ground-state–Rydberg-state atomic coherences in a cold atomic ensemble. Using phase-matched emission, we observe various time-resolved and time-integrated beating patterns that depend on the storage time between excitation and readout pulses. We develop a detailed model of the readout and emission processes, which quantitatively reproduces all observed beating signatures.

Understanding the physical nature of the D-Wave annealers remains a subject of active investigation. In this study, we analyze the sampling behavior of these systems and explore whether their results can be replicated using quantum and Markovian models. Employing the standard and the fast annealing protocols, we observe that the D-Wave annealers sample states with frequencies matching the Gibbs distribution for sufficiently long annealing times. Using Bloch equation simulations for single-qubit problems and Lindblad and Markovian master equations for two-qubit systems, we compare experimental data with theoretical predictions. Our results provide insights into the role of quantum mechanics in these devices.

We present a method to generate an isolated elliptically polarized short attosecond pulse from the ring-current state of the Ne atom in a chirped infrared (IR) field combined with an ultraviolet (UV) field. We find that the cutoff position of the harmonic spectrum emitted from the ring-current state is extended, but the harmonic efficiency is reduced in a chirped IR field compared with a chirp-free IR field. This harmonic broadening can be well understood by the semiclassical three-step model and the quantum time-frequency analysis. By introducing a UV field into the chirped IR field with a proper chirp parameter, both the efficiency and chirality of harmonic spectrum can be improved. Our analysis indicates that the generation of the elliptically polarized harmonics can be attributed to the asymmetric emission of ionized electrons in the $y$ direction. By optimizing the laser parameters, an isolated 98-as pulse with an ellipticity up to 0.94 is obtained by the broadband elliptically polarized supercontinuum. Our approach provides an effective way to generate and control the sub-100-as isolated elliptically polarized pulses.

The process of photoionization of an atom or molecule in the perturbative regime is described by the dipole matrix element between the initial bound and final continuum states of the active electron. In usual treatments of the photoeffect, the final state is represented by a plane-wave scattering state in which the ejected photoelectron is characterized by a definite linear momentum. We consider the photoeffect in which the ejected photoelectron is described by a vortex scattering state and characterized by a definite projection of its angular momentum on a given vortex axis. Although the plane-wave and vortex transition matrix elements can be expressed in terms of each other, the corresponding cross sections cannot. We develop a theory of the molecular photoeffect with vortex photoelectrons, which includes the introduction and analysis of various vortex photoionization observables and their averaging over molecular orientations. The averaging is essential for treating photoionization of randomly oriented molecules in the gas phase. We show that the averaged vortex differential cross sections reveal new chiral asymmetries caused by the chirality of the vortex photoelectron, which generalize the phenomenon of photoelectron circular dichroism. The theory is illustrated by calculations for the glyceraldehyde molecule described within the molecular zero-range potential model. We also propose and validate by calculations a scheme based on a ring-shaped forked grating which allows, at least in principle, to verify our predictions experimentally.

In the low-energy limit, nonrelativistic particles with short-range interactions exhibit universal behavior that is largely independent of microscopic details. This universality is typically described by effective field theory, in which the two-body interaction is renormalized to a single parameter—the scattering length. For systems of identical bosons, the three-body problem reveals the Efimov effect, a novel phenomenon proposed that necessitates the introduction of an additional three-body parameter. However, the exact relation between this three-body parameter, the coupling constants in the effective field theory, and the binding energies of Efimov states remains unresolved. In this work, we address this question through a comprehensive analysis of the Skorniakov–Ter-Martirosian equation with a finite cutoff. We establish an exact renormalization relation for the three-body parameter and determine its connection to the energies of Efimov bound states. These results are validated through high-precision numerical simulations. We expect our findings to be of fundamental interest across various fields, including atomic, nuclear, condensed matter, and particle physics, and to have broad applications in both few-body and many-body physics.

The far-field intensity distribution of spatiotemporal Laguerre-Gaussian (STLG) modes propagating in free space exhibits a multipetal pattern analogous to that observed in tilted Hermite-Gaussian modes. Here, we show that this phenomenon can be explained by the SU(2) symmetry of spatiotemporal Gaussian modes, which can support the irreducible representation of the SU(2) group and enable the construction of the spatiotemporal model Poincaré sphere. We have also derived analytical expressions for the STLG mode with an arbitrary radial and angular indices propagating in the isotropic media. The propagation dynamics can be understood as a unitary transformation generated by a conserved quantity, where the rotation angle is exactly the intermodal Gouy phase of the spatiotemporal modes in the same order subspace. This spatiotemporal Gouy phase depends on the ellipticity of the wave packets and the group velocity dispersion of the media. The phase, as a function of propagation distance, is categorized into three distinct regimes: normal dispersion, anomalous dispersion, and zero dispersion. Interestingly, in the regime of anomalous dispersion, the nonmonotonic behavior induces both distortion and revival of the intensity distribution, thereby establishing a phase-locked mechanism that is analogous to the Talbot effect.

We propose a non-Hermitian momentum-lattice model based on an atomic ensemble coupled with spatially modulated optical fields. By introducing modulation to the optical fields, we realize a momentum lattice featuring nonreciprocal couplings, long-range interactions, and highly tunable parameters. In this platform, the Brillouin zone emerges in real space, enabling band braiding in the $E\text{−}x$ space, leading to band structures such as unlinks, unknots, Hopf links, and trefoil knots. The resulting band topology is characterized by the discriminant number in one dimension and homotopy classes in two dimensions. Based on the theory called non-Hermitian absorption spectroscopy, we establish a direct correlation between complex band topological structures and spatially resolved absorption spectra. Interestingly, one can take a photo of the band braiding using an optical camera. Moreover, we propose a protocol to implement a three-band non-Hermitian lattice for exploring non-Abelian topology in a synthetic two-dimensional Brillouin torus and discuss its extension to three dimensions.

Differential imaging has garnered significant attention owing to its boundary detection capabilities in image processing. However, to date, there has been scant research investigating the relationship between the differential imaging effect and the topological properties of a one-dimensional (1D) system. In this work, we systematically investigate the multiple-order differential imaging based on two types of topological singularity in 1D photonic crystals (PhCs). For both oblique and normal incidences, we conduct a detailed investigation of differential imaging effect. For the oblique incident cases, the first type of topological singularities support first-order differential imaging in both $x$ and $y$ directions. Meanwhile, based on the second type of topological singularities, ${\partial }^2/\partial x\partial y$-type differential imaging can be achieved. For the normal incident cases, the first type of topological singularities can support radial second-order and fourth-order differential imaging and the second type of topological singularities can support radial fourth-order differential imaging without the need for fine-tuning of the structural parameters. We further demonstrate the realization of these differential imaging effects in the deep-subwavelength region by shifting the first type of topological singularities into this region. This research connects the topological properties of PhCs with optical differential imaging, paving the way for the development of multiple-order differential imaging devices with improved robustness and functionality.

Optical chirality density is a measure of the local handedness of electromagnetic fields. Like energy density, it may be absorbed or scattered through the interaction between light and matter. Here we utilize the conservation of optical chirality to connect the parity and time-reversal symmetries of the intrinsic excitational eigenmodes of a material to those of their associated electromagnetic eigenfields as dictated by Maxwell's equations. To make this connection explicit, we theoretically examine the Born-Kuhn (BK) system, composed of a pair of plasmonic nanorods of variable separation, as a prototypical material model that is both geometrically chiral in its static structure and truly excitationally chiral in its eigenexcitations and eigenfields. By relaying optical chirality metrics of the BK eigenfields back to their underlying sourcing material degrees of freedom, we derive a unique mechanical chirality measure that is related to, but distinct from, other pseudoscalar metrics recently discussed in the literature. Beyond analysis in the absence of sources, we further derive optical chiral extinction, scattering, and absorption cross sections under external drive and discuss their rigorous connection to more common circular dichroism measurements as well as their limitations in comparison to eigenfield chirality metrics. Finally, we investigate the conversion of achiral linearly polarized light into chiral elliptically polarized light through interaction with the BK system, illustrating the conservation of optical chirality in the interaction between light and matter through an analytically tractable example.

Controlling light-matter interactions has been a long-standing goal in quantum optics, particularly through engineering the dispersion relation of the (structured) baths and tailoring the couplings between fields and emitters. We propose a topological cold-atom system with dynamical modulations to realize chiral atom-photon bound states (APBSs) and controllable spatial adiabatic passage (SAP). The system, modeled as a Rice-Mele chain using a double-well lattice and facilitating giant-atom-like nonlocal interaction, exhibits intriguing phenomena such as subradiance and superradiance. We demonstrate that APBSs with tunable chirality can be realized in the bound states in the continuum (BICs) and quasi-BICs and support the decoherence-free interaction via two distinct schemes. We also reveal the dynamical mechanisms for the topologically protected SAP, where the chiral-APBS fidelity during the adiabatic transfer is highly sensitive to the topology. These findings open possibilities for quantum simulation and information processing with cold atoms, particularly through the integration of topologically protected controllable mechanisms.

We propose a genuine two-dimensional chiral waveguide platform based on the hyperbolic surfaces to engineer nonreciprocal interactions and entanglement between quantum emitters. Tuning the dipole polarization allows for maximally chiral coupling between each emitter and the surface plasmon field, resulting in highly directional energy transfer. By employing a master equation approach, we show that the chiral environment not only enables nonreciprocal dipole interactions but also significantly enhances both transient and steady-state entanglement compared with reciprocal systems. The degree of steady-state entanglement is further tunable through dipole polarization, emitter separation, and external driving. Unlike prior implementations constrained by one-dimensional geometries, our fully planar and highly reconfigurable platform provides a scalable route toward integrated quantum photonic networks and on-chip multipartite entanglement.

The interplay between coherence, dissipation, and nonreciprocal interactions plays a crucial role in engineering novel dynamical phases of open quantum systems. Here, we consider two collective spin ensembles, each coupled to its own driven-dissipative bosonic mode, and interacting via a common dissipative bosonic field. By introducing nonreciprocity through asymmetric couplings to the shared field, we demonstrate that quantum coherence can be revived from fully decohered states. This revival signals a transition from a time-translational symmetric phase to a spontaneously time-translation symmetry-broken phase, realizing a continuous time crystal. Remarkably, steady-state entanglement emerges even in regions where macroscopic coherence is absent, underscoring the nontrivial impact of engineered dissipation. The phase transitions are characterized using numerical simulations of the full quantum master equation, mean-field analysis in the thermodynamic limit, and Liouvillian spectral properties. Our work provides a robust framework to realize coherence enhancement, steady-state entanglement, and time-crystalline behavior in driven-dissipative quantum systems.

We determine the necessary and sufficient conditions which ensure that an $N=2m$-particle fermionic or bosonic state has the form $|\mathrm{\Psi }\rangle \propto {\left(A^{†}\right)}^m|0\rangle$, where $A^{†}=\frac{1}{2}{\sum }_{i,j}{A}_{ij}{c}_i^{†}{c}_j^{†}$ is a general pair creation operator. These conditions can be cast as an eigenvalue equation for a modified two-body density matrix and enable an exact reconstruction of the operator $A^{†}$, providing as well a measure of the proximity of a given state to an exact pair condensate. Through a covariance-based formalism, it is also shown that such states are fully characterized by a set of $L$ “conserved” one-body operators which have $|\mathrm{\Psi }\rangle$ as exact eigenstate, with $L$ determined just by the single-particle space dimension involved. The whole set of two-body Hamiltonians having $|\mathrm{\Psi }\rangle$ as exact eigenstate is in this way determined, while a general subset having $|\mathrm{\Psi }\rangle$ as nondegenerate ground state is also identified. Extension to states $\propto f\left(A^{†}\right)|0\rangle$ with $f$ an arbitrary function is also discussed.

Nonrelativistic Kapitza-Dirac scattering of electrons from counterpropagating bichromatic laser waves is studied in the resonant Bragg regime, taking the electron spin into account. We show that the intrinsic field-induced detuning, which arises in the Rabi oscillation dynamics between initial and scattering state of the electron, can be compensated by a suitable adjustment of its incident momentum. Analytical formulas of the optimized electron momentum for spin-dependent three-photon and spin-independent four-photon Kapitza-Dirac scattering are obtained from simplified model systems in reduced dimensionality, which preserve the characteristic properties of the process.

This study investigates the quantum dynamics of a spin-1/2 particle confined to a curved path from the dynamics of a two-dimensional curved thin-layer system incorporating spin connection contributions. We demonstrate that the geodesic curvature, normal curvature, and geodesic torsion govern the emergent non-Abelian gauge potential, while the geodesic and Gaussian curvatures govern the effective scalar potential in the Hamiltonian. The resulting spin precession dynamics induced by the gauge potential are analyzed with and without the adiabatic approximation. Under this approximation, the surface topology is linked to the rotation angle of spin orientation along a surface boundary and to the pseudomagnetic flux. Spin texture evolution along helices illustrates distinct behaviors under geodesic versus nongeodesic propagation. Furthermore, the spin evolution along Viviani's curve exemplifies surface dependence. The curve's topology ensures closure of the spin direction and independence of the spin from the path direction. Our theory establishes a framework for spin-state manipulation via engineered nanostructured channels, enabling topological quantum control strategies.

The geometric measure of entanglement (GME) quantifies how close a multipartite quantum state is to the set of separable states under the Hilbert-Schmidt inner product. The GME can be nonmultiplicative, meaning that the closest product state to two states is entangled across subsystems. In this work, we explore the GME in two families of states: those that are invariant under bilateral orthogonal $(O\otimes O)$ transformations, and mixtures of singlet states. In both cases, a region of GME nonmultiplicativity is identified around the antisymmetric projector state. We employ state-of-the-art numerical optimization methods and models to quantitatively analyze nonmultiplicativity in these states for $d=3$. We also investigate a constrained form of GME that measures closeness to the set of real product states and show that this measure can be nonmultiplicative even for real separable states.

We investigate global locations of Schmidt number witnesses which are outside of the convex set of all bipartite states. Their locations are classified by interiors of faces of the convex set of all states, by considering the line segments from them to the maximally mixed state. In this way, a nonpositive Hermitian matrix of trace 1 is located outside of one and only one face. Faces of the convex set of all states are classified by subspaces, which are range spaces of states belonging to specific faces. For a given subspace, we show that there exist Schmidt number $k+1$ witnesses outside of the face arising from this subspace if and only if every vector in the orthogonal complement of the subspace has Schmidt rank greater than $k$. Once we have Schmidt number $k+1$ witnesses outside of a face, we also have Schmidt number $2,3,\cdots ,k$ witnesses outside of the face.

A constant number of random Clifford measurements allows the classical shadow protocol to perform direct fidelity estimation (DFE) with high precision. However, estimating properties of an unknown quantum state is expected to be more feasible with random Pauli measurements than with random Clifford measurements in the near future. Inspired by the importance sampling technique applied to sampling Pauli measurements for DFE, we show that similar strategies can be derived from classical shadows. Specifically, we describe efficient methods using only local Pauli measurements to perform DFE with Greenberger-Horne-Zeilinger (GHZ), $W$, and Dicke states, establishing tighter bounds (by factors of 14.22 and 16 for GHZ and $W$/Dicke, respectively) on the number of measurements required for desired precision. These protocols are derived by adjusting the distribution of observables. Notably, they require no preprocessing steps other than the sampling algorithms.

Nitrogen-vacancy (NV) centers in nanodiamond offer a promising platform for quantum information processing due to their room-temperature spin coherence and optical addressability. However, scalable quantum processors remain limited by the challenge of achieving strong, controllable interactions between distant NV spins. Here, we propose a scalable architecture utilizing optically levitated nanodiamond arrays, where torsional vibrations mediate the coherent coupling between the embedded NV centers. By optimizing the shape of ellipsoidal nanoparticles, we achieve a light-induced coupling strength exceeding 119 kHz between torsional modes of the distant levitated nanodiamonds, which are two orders of magnitude larger than the typical decoherence rates in this system. This strong interaction, combined with magnetic-field-enabled spin-torsion coupling, establishes an effective interaction between the spatially separated NV centers in the distant nanodiamonds. Numerical simulations confirm that dynamic decoupling can suppress both thermal noise and spin dephasing, enabling two-qubit gates with fidelity exceeding 99%. This work provides a foundation for reconfigurable quantum hybrid systems, with potential applications in rotational sensing and programmable quantum processing.