The behavior of dipolar Bose-Einstein condensates in planar geometries is investigated, focusing on the effects of the polarization orientation. While perpendicular polarization produces a phase diagram with hexagonal, stripes, and honeycomb phases ending at a single critical point, the presence of an in-plane polarization component transforms the critical point into three critical lines, separating two phases at a time and changing radically the appearance of the phase diagram. All transition lines contain first- and second-order regions, while the phase diagram itself shows a resemblance with those displayed by quasi-one-dimensional dipolar systems. Finally, we investigate the effect of introducing an in-plane polarization on the structural properties of the phases and determine the superfluid fraction. Our results show that this process induces an axial deformation on the hexagonal and honeycomb phases, resulting in an anisotropic behavior in the long-distance properties of the system like superfluidity. We expect that the rich phenomenology observed provides motivation for new experiments and theoretical works.

The time-evolving matrix product operator (TEMPO) method is a powerful tool for simulating open system quantum dynamics. Typically, it is used in problems with diagonal system-bath coupling, where analytical expressions for discretized influence functional are available. In this work, we aim to address issues related to off-diagonal coupling by extending the TEMPO algorithm to accommodate arbitrary basis sets. The proposed approach is based on computing the derivative of the discretized path-integral expression of a generalized influence functional when increasing one time step, which yields an equation of motion valid for a nondiagonal basis set and an arbitrary number of noncommuting baths. The generalized influence functional is then obtained by integrating the resulting differential equation. The applicability of the new method is then tested by simulating one- and two-qubit systems coupled to both $Z$- and $X$-type baths.

Quantum dynamics of open continuous variable systems is a multifaceted rapidly evolving field of fundamental and technological significance. An important example is a multimode photonic system coupled to a Markovian bath so that temporal evolution of the density matrix is governed by the master equation of the Lindblad form. Theoretical analysis of the Lindblad dynamics complicated by intermode couplings such as dynamical (coherent) and environment-mediated (incoherent) interactions between the modes can be rather involved, even for exactly soluble models. Our algebraic technique uses the Lie algebra of quadratic combinations of left and right superoperators to simplify both quantitative and qualitative analysis of intermode coupling-induced effects in multimode systems by eliminating jump superoperators and reducing the Lindblad equation to the form governed by the effective non-Hermitian Hamiltonian ${\widehat{H}}_{\mathrm{eff}}$. We show that the spectral properties of the thermal bath Liouvillian are determined by the effective temperature-independent Hamiltonian and employ jump-eliminating transformations for computing its eigenvalues and eigenoperators. It is found that the Liouvillian exceptional points (EPs) are the points in the parameter space where the matrix $H$ associated with ${\widehat{H}}_{\mathrm{eff}}$ is nondiagonalizable. For the case of photonic polarization modes modeled as a bimodal bosonic system, we describe the geometry of EPs and apply our method to study how the intermode-couplings-induced effects such as EPs and temperature influence the dynamics of the speed of evolution that governs the quantum speed limit times of polarization qubit states.

We explore the important task of applying a phase $exp\left(if\right(x\left)\right)$ to a computational basis state $|x\rangle$. The closely related task of rotating a target qubit by an angle depending on $f\left(x\right)$ is also studied. Such operations are key in many quantum subroutines, and frequently $f\left(x\right)$ can be well approximated by a piecewise function; examples range from the application of diagonal Hamiltonian terms (such as the Coulomb interaction) in grid-based many-body simulation to derivative pricing algorithms. Here, we exploit a parallelization of the piecewise approach so that all constituent elementary rotations are performed simultaneously, that is, we achieve a total rotation depth of one. Moreover, we explore the use of recursive catalyst “towers” to implement these elementary rotations efficiently. We find that strategies prioritizing execution speed can achieve circuit depth as low as $O({log}_{2}n+{log}_{2}S)$ for a register of $n$ qubits and a piecewise approximation of $S$ sections (presuming prior preparation of enabling resource states), albeit total qubit count then scales with $S$. In the limit of multiple repetitions of the oracle, we find that catalyst tower approaches have an $O\left(Sn\right)$ $T$-count.

Imbert-Fedorov (IF) shifts refer to transverse tiny displacements of light beams at the interface of two media. Since the IF shifts are a reflection of the light-matter interaction, they can be applied to sense the properties of the medium or light beam. To evaluate the errors of parameters in various kinds of sensors with high precision, quantum metrology based on the SU(1,1) interferometer is expected to improve the measurement accuracy beyond the shot-noise limit (SNL). We propose a theoretical scheme to investigate the IF shifts and incident angle sensitivity for a Laguerre-Gauss beam by introducing a surface-plasmon-resonance (SPR) sensor into the SU(1,1) interferometer. We derived the sensitivity of the IF shifts and incident angle based on the homodyne detection. Meanwhile, the quantum Cramér-Rao bound and SNL of IF shifts and incident angle are obtained in our scheme. Our results demonstrate that the sensitivity of both IF shifts and incident angle can break through the SNL around the SPR angle by injecting two coherent states with large coherent amplitude. Furthermore, it is possible to get the maximal IF shifts and the optimal IF shifts sensitivity simultaneously on the two sides of the SPR angle. Our scheme provides a method for measuring tiny beam shifts and small angular displacement in SPR sensors. The results can be helpful for the development of quantum metrology based on quantum sensors and a deep understanding of light-matter interactions.

The Cu $K$ ionization cross section by electron impact has been measured in the energy range from the $K$-shell threshold to $90\mathrm{keV}$. To this end, a thin Cu film deposited on a thin C backing has been employed. The x rays emitted by the target have been detected by two silicon drift detectors placed at front and back angles with respect to the direction of the incident beam, which allowed us to better assess the peak fit procedure of the $K$ multiplet. A careful analysis of the Cu $K$ x-ray spectra generated by electron bombardment has been conducted, including not only the diagram lines but also the satellite lines and the counts that come from the radiative Auger effect. This enabled us to obtain the $K\alpha$ and $K\beta$ x-ray production cross sections with relative uncertainties of the order of $5\%$, and the $K$-shell ionization cross section with a precision around $7.5\%$. We show that, in most cases, the ionization cross sections reported according to current practice cannot be compared with the available theoretical calculations because the latter do not account for multiple-ionization effects. Our results agree with the distorted-wave Born approximation only when the $K$ x-ray counts from satellite lines, which amount to about $20\%$ of the total, are excluded.

Topological photonic states are important for constructing optical devices immune from structural perturbations, offering a viable solution for robust photonic integrations. Dynamically encircling exceptional points (EPs) of self-intersecting Riemann sheets gives rise to chiral mode transfer, and recently chiral mode converters capable of directionally switching topological photonic states have been constructed in optical waveguide arrays. However, the transmission efficiencies realized in previous studies are inherently low due to path-dependent losses, which hinders their practical application. Here, we proposed to realize efficient chiral topological mode conversion by dynamically encircling the moving EP of the two topological edge modes in lossy waveguide arrays mimicking the non-Hermitian Su-Schrieffer-Heeger lattice via modulation of loss along the propagation direction, which enables reduced average loss in a whole cycle while maintaining the employment of topological properties around an EP. The resultant chiral topological mode converter is highly efficient due to reduced average loss during the passage of EP encirclement, with transfer efficiency as high as $86\%$ in theory with near unity mode purity and considerable transmission $(-2.8\mathrm{dB})$ in simulation with over $92\%$ of the total output energy taken over by the transferred mode. It is also proven to be robust against mild perturbations of coupling strengths and mode mismatch. The efficient and robust chiral topological mode converter will promote the practical applications of topological photonic states, such as broadband optical switches and optical isolators.

Space-time wave packets (STWPs) are pulsed beams that propagate invariantly (without diffraction or dispersion) in linear media. The behavior of STWPs in free space is now well established, and recently their propagation invariance was confirmed in both the normal and anomalous group-velocity dispersion (GVD) regimes. However, rich yet-to-be-observed spectral dynamics have been predicted to occur in the presence of normal GVD, which manifests itself in the reorganization of the spatiotemporal spectrum into distinct structures upon tuning the appropriate optical parameters of the STWP. Indeed, broad varieties of distinct field structures are compatible with propagation invariance in normal GVD, which can be classified in a two-dimensional space parametrized by the group velocity of the STWP and its central axial wave number. Tuning these two parameters gives rise to spatiotemporal spectral reorganization into X-shaped, hyperbolic, parabolic, elliptical, or even spatiotemporally separable spectra. Here, we observe the entire span of spectral reorganization for paraxial STWPs in normally dispersive ZnSe at a wavelength $\sim 1\mu \mathrm{m}$ with on-axis pulse widths $\sim 120$ fs. By tuning the STWP group velocity and central axial wave number while maintaining propagation invariance, we observe transitions in the spatiotemporal spectrum and verify the associated structural changes in the spatiotemporal intensity profile. These results lay the foundations for understanding the potential uses of STWPs in phase-matched nonlinear processes in dispersive media.

We study topological quantum phase transition in a superconducting system via quantum walks. The physical model is composed of a superconducting ququart (a four-level system) employed as the coin and two resonators exploited to encode the positions of the walker in two distinct directions. The topological properties of the quantum evolutions in one- and two-dimensional quantum walks are characterized by topological invariants, namely, the winding number and the Chern number, respectively. Through theoretical analysis, we derive explicit expressions for the critical points of the coin-flip angles, where the topological invariants jump from zero to nonzero integers, signaling the occurrences of topological quantum phase transitions. We also present approaches to measure these topological invariants. Under available control parameters, numerical simulations demonstrate that the measured topological invariants are in accordance with theoretical predictions and are insensitive to the influence of imperfections including systematic errors and decoherence. Moreover, this proposal is flexible and can be implemented across various physical systems, offering valuable insights into exploring topological quantum phase transitions.

Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multistage neural network framework that significantly enhances Hamiltonian learning precision through successive network optimization of residuals. Our approach utilizes time-series data from single-qubit Pauli measurements of random initial states, enabling the estimation of unknown Hamiltonian parameters without prior knowledge of initial states or a specific evolution ansatz. We demonstrate the framework on two-qubit systems, achieving improvement of several orders of magnitude in parameter accuracy, and further extend the method to larger systems by integrating dynamical decoupling techniques. Additionally, the protocol exhibits robustness against experimental noise. This work bridges the gap between scalable Hamiltonian learning and high-precision requirements, offering a practical tool for precise quantum control and metrology.

Quantum entanglement is an essential resource for quantum science and technology. However, entanglement detection and quantification, via typical entanglement measures such as linear entanglement entropy or negativity, can be a very challenging task. Here we propose a protocol to detect bipartite entanglement in a system of $N$ qubits inspired by the concept of monogamy of entanglement, where, given a total system in a pure state with some bipartite entanglement between two subsystems, subsequent unitary evolution and measurement of one of the subsystems may be used to quantify the entanglement between the two. To address the difficulty of detection, we propose to use spin squeezing to quantify the entanglement within the individual subsystem. Knowing that the relation between spin squeezing and some entanglement measures is not one-to-one, we give some suggestions on how a judicious choice of squeezing Hamiltonian can lead to better results in our protocol. For systems with a small number of qubits, we derive analytical results and show how our protocol can work optimally for Greenberger-Horne-Zeilinger (GHZ) states. For larger systems, we show how the accuracy of the protocol can be improved by a proper choice of the squeezing Hamiltonian. Our protocol presents an alternative for entanglement detection in platforms where state tomography is inaccessible or hard to perform. Additionally, the ideas presented here can be extended beyond spin-only systems to expand their applicability.

Measurement-device-independent (MDI) quantum key distribution (QKD) systems are immune to detector side channel attacks. Integrated into existing fiber optical communication lines by means of a dense wavelength division multiplexing technique, they allow one to build secure telecommunication networks of various typologies. The present work focuses on theoretical research of the noise influence caused by spontaneous Raman scattering, four-wave mixing, and linear channel crosstalk on the performance of MDI QKD systems. We consider symmetric and asymmetric system configurations, as well as possible implementation schemes, for discrete- and continuous-variable versions of the protocol. For all cases, the secure key generation rate is calculated to distinguish the features of MDI QKD system operation and optimal conditions when they are most performative.

Exploring strongly correlated spinful states of a few fermionic ultracold atoms in a rapidly rotating trap, an example of which was recently realized for two fermionic ${}^6\mathrm{Li}$ atoms in an optical tweezer, we derive analytical (algebraic) total-spin-eigenstate wave functions through the development and employment of a theoretical platform that integrates exact numerical diagonalization (full configuration interaction, FCI) with symbolic language processing. For such rapid rotations, where the atoms occupy the lowest Landau level (LLL), the obtained algebraic expressions can address the full LLL spectrum in all its complexity, demonstrating that their spatial, spectral, and spin characteristics manifest formation of collectively rotating and vibrating Wigner molecules. The explicitly exhibited analytic wave functions (for two and three spinful ${}^6\mathrm{Li}$ atoms) reproduce precisely the corresponding numerical FCI results and are shown to reach beyond the limited range of applicability of previous Jastrow-type treatments. These results, and their extension to bosonic systems, provide the impetus and analysis tools for future experimental and theoretical simulations of larger mesoscopic systems.

Noise suppression and directional signal enhancement are essential challenges in detecting weak magnetic fields in cavity electrodynamics systems. Traditional schemes struggle to reduce magnonic probe noise but lack directional sensing capabilities. We exploit an innovative and intrinsic squeezing mechanism by leveraging the geometric configuration of an anisotropic ellipsoidal yttrium iron garnet (YIG) sphere and its interaction with internal demagnetization fields. This mechanism can enhance magnetic field signals and suppress noise in the target direction while suppressing sensitivity in nontarget directions to avoid disturbing the target direction, thus generating a directionally selective sensing scheme realizing high-precision detection in complex environments. In particular, the target-direction sensor performance can be optimized by adjusting the YIG sphere's geometry (e.g., aspect ratio) without complex setups, ensuring high feasibility and scalability. Our approach offers greater flexibility and directionality by tuning the YIG sphere's geometry than existing methods. This innovation provides an alternative approach for weak magnetic field detection in cavity magnonics systems, with potential applications in biomedical imaging, quantum sensing, precision measurement, and environmental monitoring.

Recently, Chiao et al. proposed a novel scalar electric Aharonov-Bohm (AB) effect [Phys. Rev. A 107, 042209 (2023)]. They claimed that a quantum system inside a Faraday cage with a time-varying but spatially uniform scalar potential acquires an AB phase, resulting in observable energy-level shifts. This Comment argues that their analysis is flawed: A spatially uniform scalar potential inside the cage, despite external variations, can be gauged away without altering gauge-invariant observables, such as energy differences, thus invalidating their claim. A possible explanation of this seemingly puzzling result is also given.

We respond to the points raised in the preceding Comment [Phys. Rev. A 111, 066203 (2025)] on our recent work [Phys. Rev. A 107, 042209 (2023)], which introduced a theoretical framework for the scalar electric Aharonov-Bohm effect. In this Reply, we take the opportunity to address specific criticisms, by referring to foundational aspects of gauge invariance and time-dependent quantum systems. We explain why the gauging procedure used in the Comment leads to inconsistencies and show that, when applied similarly to the well-established magnetic Aharonov-Bohm effect, it would yield demonstrably incorrect conclusions. Moreover, we highlight the consistency of our results with canonical treatments of the time-dependent Schrödinger equation, and we reaffirm the physicality of energy shifts in field-free regions, an effect observed in the magnetic and predicted in the electric Aharonov-Bohm contexts. We believe that this response contributes to a deeper understanding of the subtleties involved in gauge theory and quantum phase phenomena.

Boundary time crystals exhibit measurement-induced phase transitions in their steady-state entanglement, with critical behavior that depends on the particular unraveling of the Lindblad dynamics. In this work, we investigate another key measure of quantum complexity—nonstabilizerness (or “magic”)—and show that it follows a markedly different pattern. Importantly, in contrast to entanglement, for large system sizes, nonstabilizerness remains invariant under different unraveling schemes—a property we attribute to the inherent permutational symmetry of the model. Although the steady-state stabilizer entropy does not display a genuine phase transition, it exhibits a singular derivative (a cusp) at the mean-field critical point. Furthermore, we demonstrate that finite-size simulations of the average Lindblad evolution fail to capture the asymptotic behavior of nonstabilizerness in the time-crystal phase, while quantum trajectory unravelings correctly reveal its extensive scaling with system size. These findings offer insights into how different quantum resources manifest in open systems.

Electron correlation and higher-order relativistic effects are probed in the evaluation of scalar and tensor static electric dipole (E1) polarizabilities $\left({\alpha }_d\right)$ of several even- and odd-parity states in cesium (Cs) using the Dirac-Hartree-Fock (DHF) method, second-order perturbation theory [MBPT(2)], third-order perturbation theory [MBPT(3)], random phase approximation (RPA), and singles and doubles approximated relativistic coupled-cluster (RCCSD) method. To account for perturbation due to an odd-parity E1 operator on the atomic orbitals, calculations are carried out in the linear response approach. Our final ${\alpha }_d$ values, with the estimated uncertainties, show reasonably good agreement with the previous calculations and available experimental results. Differences among the DHF, MBPT(2), MBPT(3) and RPA results indicate that pair-correlation (PC) effects play major roles compared to the core-polarization (CP) effects in the determination of ${\alpha }_d$ values in Cs. From the differences among the MBPT(3) and RCC results, we find correlations among the PC and CP effects and double CP effects together are also significant in these calculations. Contributions from the Breit interactions are found to be quite large in the high-lying states.