In this work we study the last two hydrogen molecular ion isotopologues, ${\mathrm{DT}}^{+}$ and ${\mathrm{T}}_2^{+}$, for which high-precision calculations have not yet been made. We obtain the nonrelativistic solutions of the Schrödinger equation for the wide range of vibrational states up to the highest possible vibrational $1s{\sigma }_g$ state which are of spectroscopic precision. Transition amplitudes for electric dipole transitions, leading-order relativistic corrections, and coefficients of the effective hyperfine structure Hamiltonians for both ${\mathrm{DT}}^{+}$ and ${\mathrm{T}}_2^{+}$ are also calculated.

This paper investigates shape resonances in the electron-impact ionization of ${\mathrm{CF}}_4$. To this end, scattered-electron–fragment-ion coincidence experiments have been conducted for the molecule, employing an incident electron energy of 1.4 keV and a range of scattering angles from $2.2^{\circ }$ to $6.8^{\circ }$. The ionization spectra of the $C{}^{2}T_2$ ${\left(3t_2\right)}^{-1}$ and $D{}^{2}A_1$ ${\left(4a_1\right)}^{-1}$ channels have been constructed from the scattered-electron–${\mathrm{CF}}_2{}^{+}$-ion coincidence signals obtained. A resonance band at electron energy loss of $E\sim 24\mathrm{eV}$ in the $C{}^{2}T_2$ ionization channel is found to exhibit momentum-transfer dependence characteristic of a dipole-allowed transition and is attributed to the $3t_2\to \varepsilon t_2$ excitation. The spectra of the ionization to the $D{}^{2}A_1$ state manifest a broad peak centered at $E\sim 27\mathrm{eV}$, and its momentum-transfer dependence indicates that this newly identified band arises from a transition to a dipole-forbidden resonance level. The present study demonstrates that angle-resolved $(e,$ $e+\mathrm{ion})$ spectroscopy is a powerful means to investigate shape resonances in the nondipole ionization of molecules, and the outcomes provide a foundation for elucidating the impact of resonance transitions on molecular processes induced by electron impact.

The two-loop electron self-energy correction is one of the most problematic QED effects and, for a long time, was the dominant source of uncertainty in the theoretical prediction of the bound-electron $g$ factor in hydrogenlike ions. A major breakthrough was recently achieved by B. Sikora et al. [Phys. Rev. Lett. 134, 123001 (2025)], who calculated this effect without any expansion in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). In this paper we describe our calculations of one of the most difficult parts of the two-loop self-energy, represented by Feynman diagrams that are treated in the mixed momentum-coordinate representation.

We theoretically investigate strong-field ionization driven by counterrotating two-color laser fields, focusing on the interplay between the amplitude and phase of electron wave packets (EWPs) in shaping photoelectron angular distributions. Using the strong-field approximation (SFA), we disentangle the respective contributions of EWP amplitude and phase and identify an abrupt angular shift of the sideband (SB) peak between the second and third orders in short-range potential systems. This phenomenon originates from a transition in dominance between amplitude and phase modulations, highlighting a significant role of the EWP amplitude that has been largely overlooked in previous studies. Furthermore, we incorporate long-range Coulomb effects using a Coulomb-corrected SFA model and demonstrate that the Coulomb potential amplifies and shifts the phase contribution, inducing notable angular shifts in SB structures. Our results uncover a previously underappreciated impact of amplitude modulation on strong-field photoelectron dynamics.

We investigate the vortex structures and dynamics in two-dimensional uniform Bose quantum liquids, accounting for quantum fluctuation effects via solving the extended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. Using effective potential field analysis and the finite difference method, we establish the conditions for the existence of vortex excitations in such systems. Our results show that vortex excitations require a minimum background density, which is lower than the equilibrium density. As the vortex topological charge increases, this minimum density approaches the equilibrium density. At the critical density, the condensate's healing length remains finite, but the vortex core size diverges—a phenomenon highlighting the distinct properties of quantum liquids compared to gaseous Bose-Einstein condensates. Furthermore, stability analysis reveals that vortex stability depends on the liquid density, confirmed by dynamical evolution under perturbations.

Soliton crystals have multiple self-organized temporal pulses filling the microresonator cavity and achieve high pump-to-comb conversion efficiency, making them of great interest in many potential applications such as communication and meteorology. Optimization of operational parameters such as pump power and coupling rates is a simple method for improving efficiency besides dispersion design. However, soliton number as a freedom has not been extensively investigated before. Here, we systematically investigate the dependence of efficiency on soliton number of soliton crystals, revealing a distinct nonmonotonic relationship. Through soliton number optimization, the system theoretically achieves 100% pump-to-comb conversion efficiency. Based on the model, we successfully achieved 40% efficiency of a $33\times \mathrm{FSR}$ (free spectral range) soliton crystal on a ${\mathrm{MgF}}_2$ platform. This work provides useful insights of efficiency into Kerr soliton microcombs, establishing guiding significance for high-efficiency microcomb generation.

We investigate the scattering of light by a nonlinear, anisotropic slab under conical incidence and arbitrary polarization, within the framework of Maxwell's equations, where the nonlinearities are described by nonlinear susceptibility tensors. We develop a fully tensorial numerical method, free from standard simplifications such as the undepleted pump approximation or scalar field assumptions, based on an iterative scheme where each step is solved via the finite element method. The two-dimensional problem is reduced to one dimension by exploiting symmetry arguments. Energy considerations are also addressed. Several numerical experiments involving a potassium titanyl phosphate (KTP) slab and a lithium niobate $\left({\mathrm{LiNbO}}_3\right)$ photonic crystal are presented, including cases with incident TE and TM waves, as well as a rotation-based study highlighting the anisotropic capabilities of our numerical model. This work provides a practical and general tool to help the optics research community overcome the limitations of existing models. It may facilitate the design of more advanced experiments to test nonlinear optical theories or improve nonlinear devices.

High-quality factor ($Q$ factor) optical resonators constitute the fundamental components of integrated nonlinear photonic devices. On the lithium niobate [${\mathrm{LiNbO}}_3$ (LN)] platform, conventional approaches for achieving high-$Q$ modes typically involve thin-film etching and the deliberate breaking of structural symmetry. However, these methods entail increased fabrication complexity and impose limitations on device scalability and tunability. In this work, we propose an etchless LN metasurface leveraging Fabry-Pérot bound states in the continuum (FP-BICs) to enable efficient second-harmonic generation (SHG). This structure sandwiches an unetched LN thin film between two identical gratings. Using the hybrid coupling model and neglecting the influence of evanescent wave coupling, the approximate film thickness required to support an FP-BIC with an infinite $Q$ factor can be predicted. By detuning the film thickness by 1% from the exact FP-BIC condition, the FP-BIC can be converted into a high-$Q$ quasi-BIC, enabling a high-efficiency SHG of 2.72% under a pump intensity of $100\mathrm{kW}/{\mathrm{cm}}^2$, according to rigorous finite-element simulations. Furthermore, dynamic on-to-off modulation of SHG is demonstrated on this platform by applying an external voltage. This design eliminates the need for etching and symmetry-breaking operations, significantly simplifying the fabrication process and providing a new platform for tunable nonlinear photonics in on-chip light sources and quantum technologies.

Exponential decay is a signature property of a vast class of dynamic systems in atomic, molecular, nuclear, and particle physics. From the perspective of quantum theory, however, exponential decay is a nontrivial behavior that is not obedient to the fundamental bounds that quantum mechanics sets for the evolution of dynamic systems. Here we revisit the question of how the existence and the ubiquity of exponentially decaying systems can be reconciled with and better understood from a perspective of the constitutive principles of quantum mechanics. We show that, contrary to a widespread view, the Mandelstam-Tamm idea of the variance of the evolution Hamiltonian, ${\left(\mathrm{\Delta }E\right)}^2$, as a descriptor of quantum dynamics is fully applicable to exponentially decaying systems. We demonstrate that, with a suitable modification of a physical model of an exponentially decaying system, correcting for an unphysical, infinitely fast onset of quantum evolution, the Mandelstam-Tamm treatment provides a powerful resource for the analysis of exponentially decaying systems, revealing a continuous crossover from the Mandelstam-Tamm-bounded dynamics, unfolding on the short timescale, to exponentially decaying dynamics, which may set in, given a suitable physical setting, at later stages of quantum evolution. In a formalism that we develop, the divergence of $\mathrm{\Delta }E$ is removed, by allowing for a nonzero evolution onset time, leading to quantum dynamics that is in full obedience to the constitutive principles of quantum theory, including the Mandelstam-Tamm bound, the Mandelstam-Tamm energy-time uncertainty, and the Krylov-Fock theorem.

Models for quantum state reduction address the quantum measurement problem by suggesting weak modifications to Schrödinger's equation that have no observable effect at microscopic scales but dominate the dynamics of macroscopic objects. Enforcing linearity of the master equation for such models has long been used as a way of ensuring that modifications to Schrödinger's equation do not introduce a possibility for superluminal signaling. In large classes of quantum-state-reduction models, however, and in particular in models employing correlated noise, formulating a master equation for the quantum state is prohibitively difficult or impossible. Here, we formulate a witness for superluminal signaling that is applicable to generic quantum-state-reduction models, including those involving correlated as well as uncorrelated noise. Surprisingly, application of the witness to known models described by linear master equations shows that they may still admit superluminal signaling, unless a particular locality condition is obeyed. In contrast, we show that the witness introduced here provides a necessary and sufficient condition for excluding superluminal signals under all circumstances. We further apply the witness to several models driven by physical, correlated noise, for which linear master equations are not analytically obtainable, and find that they allow for superluminal signaling. We suggest how specific correlated-noise models may be able to avoid it and that the witness introduced here provides a stringent guide for constructing such models.

We present a framework for simultaneously estimating all four real parameters of a general two-channel unitary $\mathrm{U}\left(2\right)$ with Heisenberg-scaling precision. We derive analytical expressions for the quantum Fisher information matrix and show that all parameters attain the $1/N$ scaling in the precision by using experimentally feasible Gaussian probes, such as two-mode squeezed states or two single-mode squeezed states. Our results extend multiparameter metrology to its most general two-mode setting and establish concrete design principles for experimental implementations of Heisenberg-scaling, multiparameter optical interferometry with experimentally feasible resources. It not only sheds light on the fundamental interface between quantum interference of squeezed light and quantum metrological advantage in multiparameter estimation, but it also provides an important stepping stone towards the development of a wide range of quantum technologies based on distributed quantum metrology in arbitrary optical networks.

Distributed quantum metrology can improve the sensitivity in estimating arbitrary positive-weight linear combinations beyond the classical limit. It is known that multimode entangled states are crucial for distributed metrology. However, strategies to efficiently engineer multimode entangled states and harness them in distributed quantum metrology remains largely unexplored. In this work, we introduce a concept for distributed quantum sensing utilizing nonlinear optical networks. Unlike linear optical networks, nonlinear optical networks utilize optical parametric amplifiers instead of beam splitters for beam splitting. Here, we employ both simultaneous estimation (global) and separate estimation (local) methods to estimate linear combinations and derive the quantum Cramér-Rao bound for the two schemes, respectively. Our findings indicate that the sensitivity of the global strategy surpasses that of the local strategy and reaches the Heisenberg limit. Notably, direct intensity detection saturates the quantum Cramér-Rao bound. Furthermore, we characterize loss effects on measurement sensitivity, revealing the reduction in sensitivity with increasing losses and establishing the conditions for surpassing the standard quantum limit. This scheme can be directly applied to applications such as biological imaging and quantum information processing.

We study temperature estimation using quantum probes, including single-mode initial states and two-mode states generated via stimulated parametric down-conversion in a nonlinear crystal at finite temperature. We explore both transient and equilibrium regimes and compare the performance of Gaussian and non-Gaussian probe states for temperature estimation. In the nonequilibrium regime, we show that single-mode non-Gaussian probe states—such as Fock, odd cat, and Gottesman-Kitaev-Preskill states—can significantly enhance the speed of estimation, particularly at short interaction times. In the two-mode setting, entangled states such as the two-mode squeezed vacuum, NOON state, and entangled cat state can enable access to temperature information at earlier times. In the equilibrium regime, we analyze temperature estimation using two-mode squeezed thermal states, which outperform single-mode strategies. We evaluate practical measurement strategies and find that energy-based observables yield optimal precision, population difference observables provide near-optimal precision, while quadrature-based measurements are suboptimal. The precision gain arises from squeezing, which suppresses fluctuations in the population difference.

The coexistence of quantum information and classical signals within the same fiber link is essential for realizing future quantum networks that utilize the well-established optical fiber infrastructure. In this work, we demonstrate the coexistence of $C$-band energy-time entanglement and $L$-band classical data. By employing wavelength-division multiplexing techniques and polarization management, we achieve quantum entanglement distribution over a 40-km-long fiber carrying $4\mu \mathrm{W}$ of bidirectional received power. Under the highest noise conditions, we obtain a visibility of $84.59\pm 0.68\%$ from Franson interference and calculate a secret key rate of 1.89 kbps using the Bennett-Brassard-Mermin 1992 (BBM92) protocol, showing improved performance compared to an all-$C$-band setup. These results pave the way for large-scale quantum-classical coexistence within existing optical fiber infrastructure.

Quantum optimal control in the presence of decoherence is difficult, particularly when not all Hamiltonian parameters are known precisely, as in quantum sensing applications. In this context, maximizing the sensitivity of the system is the objective, for which the optimal target state or unitary transformations are unknown, especially in the case of multiparameter estimation. Here we investigate the use of reinforcement learning (RL), specifically the soft actor-critic (SAC) algorithm, for problems in quantum optimal control. We adopt a spin-based magnetometer as a benchmarking system for the efficacy of the SAC algorithm. In such systems, the magnitude of a background magnetic field acting on a spin can be determined via projective measurements. The precision of the determined magnitude can be optimized by applying pulses of transverse fields with different strengths. We train an RL agent on numerical simulations of the spin system to determine a transverse-field pulse sequence that optimizes the precision and compare it to existing sensing strategies. We evaluate the agent's performance against various Hamiltonian parameters, including values not seen in training, to investigate the agent's ability to generalize to different situations. We find that the RL agents are sensitive to certain parameters of the system, such as the pulse duration and the purity of the initial state, but overall are able to generalize well, supporting the use of RL in quantum optimal control settings.

Pauli-based computation (PBC) is a universal measurement-based quantum computation model steered by an adaptive sequence of independent and compatible Pauli measurements on separable magic-state qubits. Here, we propose several techniques for reducing the weight of the Pauli measurements and their associated cnot complexity; we also demonstrate how to decrease this model's computational depth. We start by proving new upper bounds on the required weights and computational depth, obtained via a precompilation step. We also propose a heuristic algorithm that can contribute to reductions of over 30% to the average weight of Pauli measurements (and associated cnot count) when simulating and compiling Clifford-dominated random quantum circuits with up to 22 $T$ gates and over 20% for instances with larger $T$ counts. This PBC-compilation scheme, boosted by the heuristic algorithm, outperforms state-of-the-art compilers for the former circuits, reducing the cnot count by 18% to 96% compared with the values achieved by other techniques. In contrast, for the latter circuits with larger $T$ counts, it leads to a number of cnots roughly 30% larger. Finally, inspired by known state-transfer methods, we introduce incPBC, a universal model for quantum computation requiring a larger number of (now incompatible) Pauli measurements of weight at most 2.

The fundamental metrological limits of temperature sensing in open quantum systems remain largely unresolved, particularly regarding the role of non-Gaussian quantum resources. In this paper, we establish analytic bounds on the quantum Fisher information (QFI) for temperature estimation using non-Gaussian states undergoing dissipative bosonic evolution. By focusing on the short-time regime governed by a time-local master equation, we derive precise scaling laws that elucidate when and how non-Gaussian probes decisively outperform Gaussian states under identical energy constraints. Our analysis uncovers a distinct linear-in-time QFI enhancement unique to Fock states, in contrast to the inherently weaker, quadratic scaling of Gaussian probes. These theoretical insights are substantiated through exact numerical simulations and mapped onto experimentally accessible platforms such as circuit QED. Our results not only clarify the quantum thermometric advantage of non-Gaussianity but also chart a realistic pathway toward harnessing it in noisy quantum technologies.

The $2{}^3{S}_1\to 2{}^1{P}_1$ interval in positronium has been measured via microwave spectroscopy. This transition is strictly forbidden by charge conjugation invariance but may be observed in a magnetic field. Extrapolation of the Rabi frequencies obtained from spectral line shapes measured in different fields to the zero field case was used to test for a possible C-violating interaction with Hamiltonian $H_{\mathrm{CV}}$, characterized by the matrix element $M_{\mathrm{CV}}=\langle 2{}^1{P}_1|H_{\mathrm{CV}}|2{}^3{P}_1\rangle$. We obtain $|M_{\mathrm{CV}}|=18.6\pm 6.5\mathrm{MHz}$ and $|M_{\mathrm{CV}}|=37.2\pm 13.4$ MHz for the $M_J=\pm 1\to \pm 1$ and the $M_J=0\to 0$ components, respectively.

Large-scale multiconfigurational calculations are conducted on experimentally significant transitions in Lr I and its lanthanide homologue Lu I, exhibiting good agreement with recent theoretical and experimental results. A single reference calculation is performed, allowing for substitutions from the core within a sufficiently large active set to effectively capture the influence of the core on the valence shells, improving upon previous multiconfigurational calculations. An additional calculation utilizing a multireference set is performed to account for static correlation effects which contribute to the wave function. Reported energies for the two selected transitions are $\mathrm{20\hspace{0.17em}716}\pm 550\mathrm{c}{\mathrm{m}}^{-1}$ and $28587\pm 650\mathrm{c}{\mathrm{m}}^{-1}$ for $7s^{2}8s{}^2{S}_{1/2}\to 7s^{2}7p{}^2{P}_{1/2}^o$ and $7s^{2}7d{}^2{D}_{3/2}\to 7s^{2}7p{}^2{P}_{1/2}^o$, respectively.

The simplified quantum model, originally proposed for collisions with hydrogen, is extended to the case of collisions of different atoms $B+A$ and their ions $B^{+}+A^{-}$. It is shown that the simplified model correctly reproduces experimental data on relative populations of oxygen states in low-energy collisions of ${\mathrm{O}}^{+}$ with ${\mathrm{P}}^{-}/{\mathrm{D}}^{-}/{\mathrm{C}}^{-}/{\mathrm{Si}}^{-}/{\mathrm{O}}^{-}/{\mathrm{S}}^{-}$. The simplified quantum model may be very useful for physically reliable qualitative and quantitative estimations of rate coefficients values of inelastic processes in atom-atom and cation-anion collisions, which are needed for numerical modeling of plasma and gaseous media with temperatures below $\approx 10000\mathrm{K}$. Predictions of the simplified model for ${\mathrm{O}}^{+}+{\mathrm{Na}}^{-},{\mathrm{Li}}^{-},{\mathrm{Ni}}^{-},{\mathrm{I}}^{-},{\mathrm{F}}^{-},{\mathrm{Cl}}^{-}$ low-energy collisions are presented. The equation for the position of the optimal window maximum with respect to the electron binding energy is derived and presented.