We present ab initio calculations of one-electron quantum electrodynamical corrections to the second-order Zeeman splitting for the $1s_{1/2}$, $2s_{1/2}$, and $2p_{1/2}$ states in highly charged hydrogen-like ions. The self-energy correction is evaluated using the rigorous QED approach. The vacuum-polarization correction is evaluated within the electric-loop approximation. Calculations are performed for a wide range of nuclear charge number: $Z=14\text{–}92$.

Strong-field QED (SFQED) probability rates in the locally monochromatic approximation (LMA) have become an indispensable tool for simulations of processes like gamma-ray emission or electron-positron pair production in laser-particle collisions. We revisit the LMA derivation and explicitly demonstrate that it is based on the separation of timescales, neglect of the long-range interference effects, and subsequent averaging over the cycle scale. Doing so, we obtain unambiguously LMA rates for arbitrary polarizations of the plane-wave background. Additionally, we partially restore the finite bandwidth effects that are lost in the LMA derivation. We refer to the bandwidth-restored result as the ${\mathrm{LMA}}^{+}$ and show that it agrees with the full SFQED predictions better than the standard LMA. We use ${\mathrm{LMA}}^{+}$ to address previously inaccessible observables and formulate an additional limitation on the applicability of locally monochromatic approximations in general. We provide analytical results for the angular-integrated ${\mathrm{LMA}}^{+}$ probability rate and the fully differential probability that account for the finite bandwidth effects.

We demonstrate that quantum Lyapunov control provides an effective strategy for enhancing superconducting correlations in the Fermi-Hubbard model without requiring careful parameter tuning. While photoinduced superconductivity is sensitive to the frequency and amplitude of a monochromatic laser pulse, our approach employs a simple feedback-based protocol that prevents the decrease of superconducting correlations once they begin to form. This method enables robust enhancement of pairing across a broad range of initial pumping conditions, eliminating the need for intricate frequency and amplitude optimization. We also show that an alternative implementation, asymptotic quantum control, achieves comparable results. Furthermore, our approach can be adapted to suppress previously induced superconducting correlations, providing bidirectional control over quantum pairing states. These findings suggest practical pathways for manipulating quantum correlations in strongly interacting systems with minimal experimental complexity.

We study the impact of two-color ($\omega$ and $2\omega$) co- and counterrotating ultrashort attosecond laser pulses on nonisotropic atomic targets through the one- and two-photon interference pattern of the photoelectron spectrum. Specifically, we take the ground state of atomic carbon, i.e., $(1s{}^{2}2s{}^{2}2p^2,{}^{3}P{}^e)$ as a prototype. We observe and quantify the strong dependence on the relative carrier-envelope phase (CEP) of the two-color pulses and on the spatial orientation of the electronic target states. Notably, we observe that the photoelectron momentum distributions (PMDs) vary as a function of the CEP due to the interfering two-color one- and two-photon ionization paths. In addition, the PMD region corresponding to one-photon photoionization remains unaffected with varying CEP, depending only on the ellipticity of the pulse, the central photon frequency, and the magnetic quantum number of the initial state. Therefore, comparing the one-photon ionization electron ejection direction following the absorption of a single ($2\omega$) photon with that of the two-photon ionization channel following the absorption of two photons, each with energy $\omega$, we may extract information on the CEP difference between the two pulses.

This study investigates the atomic diffusion process within antirelaxation coated vapor cells using a partially illuminated light-induced atomic desorption (LIAD) scheme. We conducted a comprehensive theoretical analysis to model variation in vapor density during the process and predict the variation in vapor density due to lateral diffusion from the unilluminated region. This implies that under partial illumination, the number density changes follow a triexponential behavior, rather than the biexponential behavior observed under full illumination. In addition, repeated illumination confirmed the existence of lateral diffusion inside the antirelaxation coatings. Additionally, we demonstrated the impact of LIAD on the spin-relaxation time to obtain the intrinsic coating performance variation induced by atomic diffusion. Our study provides deeper insights into the atomic transport phenomena in coated vapor cells, as well as the potential of employing all-optical techniques to manipulate the vapor density and coating properties of coated vapor cells, which are beneficial for applications in quantum sensing and precision measurements.

We investigate the ground state and dynamical properties of ultracold gases in optical lattices with a quasicrystal structure—a scenario inspired by recent experiments on twisted bilayer optical lattices and optical quasicrystals. Our study reveals that the interplay between on-site repulsive interactions and a quasiperiodic potential gives rise to rich physics. At low filling factors, increasing the interaction strength induces a delocalization effect that transforms a Bose-glass (BG) phase, characterized by disconnected superfluid (SF) regions, into a robust SF phase with a percolated network of SF clusters. This transition is quantitatively characterized by monitoring the percolation probability. At higher filling factors, we uncover a striking reentrant behavior: As the on-site interaction increases, the system initially transitions from BG to SF, but a further increase reverses this trend, returning the system to the BG phase. This reentrance is ascribed to an interaction-driven rearrangement of particles, where a once-percolated SF network fragments into isolated SF islands as repulsive interactions dominate. Furthermore, our analysis of quench dynamics demonstrates distinct transient behaviors. Intraphase quenches yield minimal variations in both the percolation probability and the inverse participation ratio (IPR) of the particle-density distribution. In contrast, interphase quenches produce pronounced effects; for instance, a quench from the SF to BG phase is marked by an abrupt loss of global SF connectivity, while a BG-to-SF quench features oscillatory changes in the percolation probability and a gradual decrease in the IPR, eventually stabilizing the SF phase. Our findings unveil the complex interplay between quasiperiodic optical lattice potential and interaction in ultracold Bose gases, offering valuable insights that are highly pertinent to current experimental efforts employing state-of-the-art twisted bilayer and quasicrystalline optical lattice platforms.

In this paper we employ the complex screen method to investigate the dynamic evolution of partially coherent pulses with specified properties as they propagate through a nonlinear Kerr medium. Our results reveal that partially coherent pulses can retain stable pulse characteristics and exhibit enhanced robustness when the source coherence is reduced. Importantly, by adjusting the source pulse properties, the far-zone pulse properties can be effectively predicted and shaped, even in highly nonlinear environments. These findings are of significant importance for applications such as pulse shaping, free-space optical communication, information encryption in nonlinear media. Notably, the results offer valuable insights for mitigating nonlinear effects in light beams within the spatial domain.

This paper describes how resonance spectra and mode profiles can be used to characterize and quantify the mode-shaping effects in open-access plano-concave optical microcavities. The presented semi-analytic theory is based on the application of perturbation theory to the round-trip evolution of the optical field. It includes various mirror-shape and nonparaxial effects and extends the nonparaxial theory presented in [Exter et al., Phys. Rev. A 106, 013501 (2022)] and verified in [Koks et al., Phys. Rev. A 105, 063502 (2022)] to the common case of an anisotropic Gaussian mirror. The presented measurements and analyses of resonance spectra and mode profiles demonstrate how the different mode-shaping effects can be individually distinguished and quantified. Spin-orbit coupling, which is one of the nonparaxial effects, is prominently visible in the intriguing polarization patterns of the resonant modes, while polarization tomography yields the shape-induced birefringence and associated polarization splitting of the fundamental modes.

We propose a hardware-efficient single-photon routing scheme in a synthetic frequency dimension based on a dynamically modulated multimode ring resonator and a driven cyclic three-level superconducting circuit, which effectively models a two-level giant atom coupled to a pair of one-dimensional lattices in the synthetic frequency dimension. The routing dynamics of single-photon wave packets in the frequency dimension are investigated numerically and analytically. Our results show that by tuning the phase of the external field, the photon transmission between the two frequency lattices can be well controlled, thereby determining the propagation direction of photons within the ring resonator. This work presents a feasible scheme for implementing a controllable node in quantum networks, and the predictions of this scheme are well within reach of state-of-the-art experiments.

The motion of a quantum particle in a one-dimensional periodic potential can be described in terms of Bloch wave packets. Like free-particle wave packets, they can propagate without attenuation. Here, we examine this similarity more closely by investigating whether Bloch wave packets can maintain a definite—or nearly definite—momentum direction, a property inherent in free-particle wave packets. This question is particularly relevant to the feasibility of using solid-state-based systems in the search for the first experimental realization of quantum backflow, a quantum interference effect in which a particle's probability density flows in a direction opposite to its momentum.

The Berry phase is a geometric phase that is important in explaining topological quantum phenomena. The Berry phase is also important in nonperturbative phenomena, as the imaginary part of the phase explains the nonperturbative transitions. However, problems arose because the singular perturbation with respect to the Planck constant has not been treated adequately in conventional calculations, where the most serious problem is the arbitrariness of approximate calculations. To solve this problem, we consider the exact WKB approach, which is a mathematical method that treats perturbative expansion with respect to the Planck constant as a rigorous singular perturbation. This method is also a powerful computational tool that makes analytical computation much easier for mathematical software. Using the exact WKB, we analyze the derivation of the dynamical and the geometric exponents in generalized Landau-Zener models, highlighting the differences from other calculational methods. The discontinuity of complex geometric factor is a universal phenomenon that manifests itself in phase transitions, boundaries, particle generation, and topology changes. These phenomena are “nonperturbative” in physics, while mathematically, these discontinuities can be deeply related to the singular structure of complex analysis. The mathematical structure of these phenomena will be revealed by using the exact WKB.

The computation of tunneling splitting in physical systems, such as molecular systems, qubits, and more, is still quite challenging because of its very small magnitude, as compared with the typical vibrational spacing between doublet levels. Thus, it is important to understand and develop methods that can reproduce the physics of the tunneling splitting in a simple and direct way. Herring's formula is probably the most popular expression in this sense. To shed light on the implications of this formula, which was first proposed by Herring [C. Herring, Rev. Mod. Phys. 34, 631 (1962)], we investigate the connection between the two-state approximation, as employed for nonadiabatic-induced tunneling splitting, and the Herring formula, which is relevant to adiabatic tunneling splitting. We show that the two-state approximation and the Herring formula, which may be derived as a weak value of the flux operator and is a derivative result, are identical for a symmetric double well potential. This unveils the physics underlying Herring's formula and provides further justification for the two-state approximation for the nonadiabatic tunneling splitting estimate. We conclude that, when Herring's formula is used with approximate eigenfunctions, it will not be accurate when the two-state approximation is not valid, i.e., when the energy splitting is comparable to the eigenenergy spacing. More generally, Herring's formula will fail when the two-state approximation fails. We also show how the identity between the integral two-state approximation form and Herring's formula may be used to obtain analytic expressions for some nontrivial integrals.

Enhancing the efficiency of quantum heat engines (QHEs) is crucial for advancing fundamental research and quantum technologies. We explore a quantum Stirling cycle using a two-qubit quantum Rabi model with spin-spin coupling as a working medium. We propose parameter optimization strategies to maximize the efficiency of the heat engine, as there are multiple ways for the effective coupling constant to move toward its critical point. In the normal phase, enhancing the temperature ratio of hot-to-cold reservoirs and spin-mode coupling strength can boost QHE efficiency, while increasing the spin-spin coupling strength will reduce the efficiency. In the superradiant phase, when the temperature ratio is held constant, lowering the cold reservoir temperature moves the efficiency closer to the Carnot limit. Furthermore, when the cold reservoir temperature is fixed, increasing the ratio between spin-mode coupling and mode frequency will improve the efficiency. While the spin-spin coupling is fixed, the cycle with a higher-temperature ratio between the hot and cold reservoirs demands a higher ratio between the spin-mode coupling and mode frequency to improve efficiency. Our work deepens the understanding of QHE performance under various conditions and provides operative methods for optimizing the efficiency of QHE.

Quantum network states are multipartite states built from distributing pairwise entanglement among parties and underpin the paradigm of quantum networks for quantum information processing. In this work we introduce the problem of partial distillability in noisy quantum networks. This corresponds to the possibility of distilling by local operations and classical communication an arbitrary pure state for an arbitrary subset of parties starting from a single copy of a quantum network state of an increasing number of parties that share noisy (i.e., mixed) bipartite entangled states. Here, distillation means that the target state is obtained with fidelity as close to 1 as desired, as the size of the network increases when the pairwise entangled links support a constant amount of noise. While we prove an obstruction to multipartite distillation protocols after teleportation with channels with constant noise, we show that partial distillability is indeed possible if certain well-established graph-theoretic parameters that measure the connectivity in the network grow fast enough with its size. We give necessary as well as sufficient conditions for partial distillability in terms of these parameters and we, moreover, provide explicit constructions of networks with partial distillability and a relatively slow connectivity growth.

Nonclassical correlations represent fundamental physical resources that play a crucial role in quantum information processing. In this work, we introduce a generalized nonclassicality quantifier based on metric-adjusted skew information, which aims to characterize the intrinsic nonclassical features of bosonic field states. The proposed nonclassicality quantifier is formally defined as the maximum metric-adjusted skew information between a quantum state and the homodyne rotated quadrature operator, which can effectively reflect the phase-dependent characteristics of the light field and is therefore suitable for capturing nonclassical effects. Notably, our findings reveal that coherent states exhibit a distinct threshold behavior, enabling a precise distinction between classical and nonclassical regimes. Furthermore, through rigorous analysis and comparative evaluation across a set of representative quantum states, we demonstrate that the quantifier not only captures essential nonclassical merits, but also detects entanglement by identifying violations of the additivity property that holds for separable states. As a result, this framework establishes a unified and mathematically rigorous approach for quantifying nonclassicality in both separable and entangled systems, thereby contributing valuable insights to the advancement of quantum resource theories.

The major goal of quantum metrology (QM) is to exploit the quantum resources to raise the measurement precision (MP) as high as possible. While the quantum resources such as squeezing have been widely explored, light-matter interaction systems set up a highly controllable platform applicable for QM in novel pursuit of high MP. However, critical QM by the conventional linear interaction is confronted with the limitation of a local parameter regime, restriction of a low-frequency-limit condition, and the detrimental problem of diverging preparation time of probe state (PTPS). This work shows that mixed interactions by linear and nonlinear light-matter couplings in the presence of bias field can provide various quantum resources, including squeezing, degeneracy lifting, displacement, and quantum phase transition. These resources manifest high sensitivity for QM as demonstrated by analytically obtained critical exponents or exponential behavior of quantum Fisher information. We find that these sensitivity resources can be combined to upgrade the upper bound of MP by many orders over the widely applied squeezing resource. As further advantages in contrast to the linear critical QM, such an upgraded metrology protocol can have a global parameter regime, break the frequency-limit restriction, and avoid the diverging PTPS. Our work paves a way to exploit and combine all the resources in momentum, position, and spin spaces to maximize the MP and expand the applicable conditions simultaneously.

Open quantum walks (OQWs) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for quantum computation and show how we can represent random unitary quantum channels, such as the dephasing and depolarizing channels, in this model. We also develop a simulation protocol with circuit representation for this model, which is heavily inspired by the fact that graphs represent OQWs and are thereby local (meaning that the state in a particular node interacts only with its neighborhood). We obtain asymptotic advantages in the system's dimension, circuit depth, and cnot count compared to other simulation methods.

We introduce an imaginary-time evolution method to evaluate the pure-state constrained-search functional from density-functional theory formulated on finite lattices. Simultaneously, it yields a potential that produces a prescribed density of an eigenstate. Besides being a computational scheme, this allows one to gain theoretical insights into the density-potential mapping. The method can be generalized to the optimization of the expectation value of a general self-adjoint operator on a finite-dimensional Hilbert space under a finite number of expectation-value constraints for commuting self-adjoint operators.