We present an exact solution of the quantum laser master equation using generating functions and confluent Heun equations. By reformulating the evolution of both diagonal and off-diagonal elements of the reduced density matrix, we derive closed-form expressions for the generating functions and identify the full spectrum of decay rates from a two-point connection problem for the confluent Heun equation. This method captures both transient dynamics and steady-state properties without truncation. In the thermodynamic limit of vanishing saturation, the spectrum separates into two analytically tractable eigenvalue families; their intersections mark exceptional points, reflecting nontrivial structure in the system's Liouvillian dynamics. At the lasing threshold, we observe a Liouvillian spectral collapse, signaling a nonequilibrium phase transition. Our results provide a unified, nonperturbative description of laser dynamics across different regimes.

Ontological models, as used in the generalized contextuality literature, play a central role in current research on quantum foundations, providing a framework for defining classicality, constructing classical analogs of key quantum phenomena, and examining the ontology of quantum states. In this work, we show that a counterfactual account of Lüders' rule—which we argue is naturally implied by the mathematical structure of the rule itself—renders such models inherently incompatible with the quantum formalism. This incompatibility arises because the counterfactual update requires ontological models to update their states according to conditional probability, which in turn renders predictions of sequential measurements order-independent. This implies that ontological models, even contextual ones, must either act differently than what we would expect given (this, typically implicitly assumed account of) quantum state update rule, or cannot model quantum behavior.

The bulk-boundary correspondence in Hermitian systems is governed by wave-function topology, whereas in non-Hermitian systems exhibiting the skin effect, it is determined by complex energy topology. In this work, we establish the bulk-boundary correspondence in non-Hermitian class-${\mathrm{D}}^{†}$ topological systems within the framework of wave-function topology. Specifically, we demonstrate that bulk polarization serves as a universal topological invariant, effectively characterizing anisotropic in-gap edge states in Hermitian class-D systems and isotropic in-gap edge states in non-Hermitian class-${\mathrm{D}}^{†}$ systems. Additionally, the spectral winding number determines the localization direction of the isotropic in-gap edge states in class-${\mathrm{D}}^{†}$ systems. By employing the Wilson loop approach to compute the bulk polarization, our work not only restores the bulk-boundary correspondence in non-Hermitian class-${\mathrm{D}}^{†}$ systems, but it also provides valuable insights into the connection between wave-function topology and non-Hermitian band theory.

We generate different orders of quantum coherence in a three-qubit NMR system and study their dynamics in the presence of inherent noise. Robust dynamical decoupling (DD) sequences are applied to preserve the different coherence orders. Initially, DD sequences are implemented simultaneously on all three spins, which effectively protects third-order coherence; however, other coherence orders decay rapidly instead of being preserved. The robust DD sequences were suitably modified in order to preserve other coherence orders. These sequences are applied to the two participating qubits that generate each zero- and second-order coherence, ensuring their effective preservation. In contrast, first-order coherence is preserved more efficiently when DD sequences are applied exclusively on the qubit responsible for generating it. Instead of performing full quantum state tomography, coherence orders are measured directly using single pulses. The robust DD protection schemes are applied to successfully protect two-qubit entanglement in three-qubit star states.

Identifying the best families of quantum error correction (QEC) codes for near-term experiments is key to enabling fault-tolerant quantum computing. Ideally, such codes should have low overhead in qubit number, high physical error thresholds, and moderate requirements on qubit connectivity to simplify experiments, while allowing for high logical error suppression. Quantum low-density parity-check (LDPC) codes have been recently shown to provide a path towards QEC with low qubit overhead and small logical error probabilities. Here, we demonstrate that when the dominant errors are erasures, as can be engineered in different quantum computing architectures, quantum LDPC codes additionally provide high thresholds and even stronger logical error suppression in parameter regimes that are accessible to current experiments. Using large-scale QEC numerical simulations, we benchmark the performance of two families of high-rate quantum LDPC codes, namely the so-called Clifford-deformed La-cross codes and the bivariate bicycle codes, under a noise model strongly biased towards erasure errors. Both codes outperform the surface code by offering up to orders of magnitude lower logical error probabilities. Interestingly, we find that this decrease in the logical error probability may not be accompanied by an increase in the code threshold, as different QEC codes benefit differently from large erasure fractions. While here we focus on neutral atom qubits, the results also hold for other quantum platforms, such as trapped ions and superconducting qubits, for which erasure conversion has been demonstrated.

Anonymous voting enables no one to link a vote and a voter and it has been widely used in contexts such as governmental elections and decision making in groups. In this paper we propose a resource-efficient self-tallying quantum anonymous voting (SQAV) protocol with two-particle entangled states. Similar to the first SQAV protocol with multipartite entangled states [Phys. Rev. A 94, 022333 (2016)], it possesses the properties of privacy, nonreusability, verifiability, fairness, binding, and self-tallying at the same time. We analyze its performance in a noisy quantum network. Our protocol requires $mn\left[1+{log}_2\left(n+1\right)\right]$ qubits to prepare the information states, and its quantum resource cost is lower than that of the first SQAV protocol, where $n^2{log}_{2}m+n{log}_{2}n$ qubits are required to prepare the information states. We also prove the optimality of our quantum resource cost. To be more practical, it is further generalized to the case with three kinds of votes including positive votes, negative votes, and abstaining from voting. Our generalized protocol requires $n\left(2m+1\right)\left[1+{log}_2\left(n+1\right)\right]$ qubits to prepare the information states, which also has lower quantum resource cost than that of the improved SQAV protocol [IEEE Trans. Inf. Forens. Secur. 17, 3264 (2022)], where $n^2{log}_2\left(2m+1\right)+n{log}_{2}n$ qubits are required to prepare the information states. In contrast to multipartite entangled states, two-particle entangled states are relatively easy to prepare, which makes the proposed protocol feasible using current technology.

Code concatenation combines two or more component codes to design larger codes with greater noise resilience. Introducing entanglement assistance to concatenated codes provides a further advantage in terms of improved error rates and beating certain bounds on codes that would otherwise be unbeatable. First, we derive the general expression for the shared entanglement of a concatenated code and show that the number of ebits can depend on the order of concatenating the component entanglement-assisted quantum error-correcting codes (EAQECCs). We further construct families of pairs of EAQECCs such that the number of ebits of the resultant of concatenating the two codes in a given pair is order independent. Second, we derive conditions on code distance under which nonmaximal-entanglement EAQECCs obtained from a classical quaternary Griesmer or Plotkin code saturate the entanglement-assisted (EA) Griesmer or linear EA Plotkin bound, respectively, extending the known result for maximal-entanglement EAQECCs. Furthermore, we present several families of such nonmaximal-entanglement EAQECCs. Third, we derive an EA version of the quantum Griesmer-Rains bound on the number of correctable errors for EAQECCs. Finally, we present families of pairs of EAQECCs such that the violation of the EA Hamming bound by the resultant of concatenating the two codes in a given pair is order dependent.

Building on recent significant interest in entropic uncertainty relations for quantum measurements, this work explores the entropic uncertainty relation for the mutually unbiased equiangular tight frame assigned to quantum $t$-designs. Combining the mathematical structures of quantum measurements with those of quantum designs, uncertainty relations are derived in terms of Tsallis and Rényi $\alpha$ entropies, and rigorous theoretical analysis demonstrates the tightness of the derived entropic lower bounds. Furthermore, a specific relation between quantum design and the index of coincidence is inferred from the information diagrams, which is crucial for deriving the novel entropic uncertainty relation. The results reveal that the entropic lower bounds can be optimized by adjusting the parameters of the quantum $t$-design, broadening the theoretical framework of the entropic uncertainty relation and providing a practical tool for quantum information tasks.

Lightning is a very common natural phenomenon and there has been growing interest in diagnosing lightning plasma. As a major source of lightning spectral emissions, N ii ions have been attracting considerable attention over the past decades [Phys. Rev. Lett. 112, 035001 (2014)]. In this work, we aim to propose a scheme for lightning plasma diagnostics by exploring the alignment of upper levels of strong lightning spectra populated by electron impact excitation, the dominant population mechanism, of N ii ions. To this aim, the magnetic-substate-resolved excitation cross sections of the upper levels are calculated, from which the relevant second- and fourth-rank alignment parameters ${\mathcal{A}}_{20}$ and ${\mathcal{A}}_{40}$ are obtained. It is found that these excited upper levels are highly aligned (that is, the relative population of the magnetic substates significantly deviates from the statistical distribution) at certain impact energies, leading to highly anisotropic and polarized lightning spectral lines. Also, the alignment parameter ${\mathcal{A}}_{20}$ is found to be strongly dependent on the impact energy, whereas such a dependence is relatively weak for ${\mathcal{A}}_{40}$. The strong energy dependence of ${\mathcal{A}}_{20}$ is expected to present strongly energy-dependent angular anisotropy and linear polarization of the lightning spectral lines. In particular, for some of the upper levels the parameter ${\mathcal{A}}_{20}$ undergoes a sign reversal as the impact energy changes, which can qualitatively alter angular anisotropy pattern and polarization behavior of the relevant lightning lines. The discovered strong energy dependence and particularly the sign reversal of the level alignment are expected to serve as a scheme of diagnosing the relevant lightning N ii plasmas such as electron energy and temperature.

Laser ionization spectroscopy was performed on both neutral and singly ionized ${}^{232}\mathrm{Th}$ with the aim of identifying the nuclear-clock isomer in the singly charged ionic state of ${}^{229}\mathrm{Th}$. A search for an efficient laser ionization scheme of ${}^{232}\mathrm{Th}^{+}$ was conducted in an argon-filled gas cell. This revealed a congested spectrum due to collisional quenching effects and the presence of several autoionizing states, one of which has a laser ionization efficiency of at least $1.2\%$. Using a threshold approach, the second ionization potential was determined to be 12.300(9) eV. The subsequent study on atomic ${}^{232}\mathrm{Th}$ validated the threshold approach. Conducting spectroscopy in a hypersonic gas jet suppressed the gas-collision-induced quenching, revealing a Rydberg series that converges to the first ionization potential, determined to be 6.306 879(14) eV. The gas jet also cools down the thorium, allowing for high-resolution laser spectroscopy with a resolution of 240(30) MHz. Using the multiconfigurational Dirac-Hartree-Fock method, the ionization potentials were computed, showing a relative difference of 0.06% and 0.19% between theory and our experimental values for the ionization potentials of $\mathrm{Th}$ and ${\mathrm{Th}}^{+}$, respectively. Further calculations using a pseudorelativistic Hartree-Fock method reveal strong mixing in the used intermediate state at $26113.27{\mathrm{cm}}^{-1}$ of $\mathrm{Th}$. A dedicated fast-extraction gas cell with ${}^{233}\mathrm{U}$ recoil sources was used to study ${}^{229}\mathrm{Th}^{+}$, but no photoionization signal could be observed.

We generate two attosecond pulse trains ($\mathrm{XU}{\mathrm{V}}_{\omega }$ and $\mathrm{XU}{\mathrm{V}}_{2\omega }$) by focusing an infrared (IR, $\omega$) laser pulse and its temporally advanced second harmonic field ($2\omega$) into an argon gas jet. Using the two XUV pulses and another infrared pulse, we perform two types of experiments for electron wave-packet interferences with attosecond time resolution. The delays between three pulses, $\mathrm{XU}{\mathrm{V}}_{2\omega }$, $\mathrm{XU}{\mathrm{V}}_{\omega }$, and IR, are independently controlled. First, at a fixed delay between the $\mathrm{XU}{\mathrm{V}}_{2\omega }$ and the IR pulses, we record the velocity map images of photoelectrons ionized from helium as a function the two XUV pulses. The photoelectron signal intensity is modulated with the period corresponding to the energy separation between the $1s\mathrm{and}4p$ states of helium, 174 as. This indicates that the $4p$ Rydberg state is populated by harmonic 15 ($15\omega$) in both $\mathrm{XU}{\mathrm{V}}_{2\omega }$ and $\mathrm{XU}{\mathrm{V}}_{\omega }$ pulses. Second, we overlap $\mathrm{XU}{\mathrm{V}}_{2\omega }$ with the IR pulse in time and record the VMI images as a function of the two pulses. By analyzing the interference pattern in the VMI images, we find that harmonic 13 (13 $\omega$) from $\mathrm{XU}{\mathrm{V}}_{2\omega }$ is responsible for the generation of the $g$ wave in the ionization continuum. Our method of using two XUV pulses containing different sets of harmonics can simplify attosecond XUV interferometry experiments.

We investigate the effects of attractive Hubbard interaction on two-component fermionic atoms in narrow two-dimensional (2D) energy bands that exhibit Rashba spin-orbit coupling (SOC) in the presence of an applied Zeeman field. This narrow-band 2D spin-orbit-coupled attractive Fermi-Hubbard model can potentially be realized in cold-atom systems in optical lattices with artificially engineered Rashba SOC and Zeeman field. Employing a self-consistent mean-field approximation for the pairing potential, we uncover a complex phase diagram featuring various topological superfluid (TS) phases, dependent on the chemical potential and the Zeeman field. We focus on the pairing potential and the corresponding quasiparticle gap characterizing the TS phases, which are notably small for a wide-band model with quadratic dispersion near the $\mathrm{\Gamma }$ point, as found in earlier work. We identify the parameter regimes that maximize the gap. We find that, while generally the value of the pairing potential increases with the reduction of the fermionic bandwidth, as expected for narrow- or flat-band systems, the magnitude of the topological gap characterizing the TS phases reaches a significantly improved maximum of about $10–12.5\%$ of the interaction strength at finite values of the hopping amplitude, Rashba coupling, and Zeeman field. Our work establishes a robust operating regime for experimenting with topological superfluids in cold-atom optical lattices.

This paper investigates the generation and stabilization of bound states in the continuum (BICs) in a one-dimensional dissipative Floquet lattice. We introduce on-site loss on the two sites neighboring the central hopping defect and analyze the resulting non-Hermitian lattice using Floquet diagonalization and high-frequency expansion. We report the discovery of a stable dark Floquet BIC characterized by a quasienergy with a real part (a value of zero) within the extended band and a vanishing imaginary part, despite the system being purely dissipative. We demonstrate that introducing loss to the two selected sites broadens the parameter window where the BIC exists and effectively protects the BIC against small variations in driving parameters. Our results reveal that increased loss can counterintuitively enhance the stability of the dark Floquet BIC. We further establish that stable dark Floquet BICs can robustly persist even in nonlinear regimes. Our findings provide theoretical support for the experimental realization of stable BICs in dissipative quantum systems.

The atom-cavity system is a versatile platform for emulating light-matter systems and realizing dissipation-induced phases, such as limit cycles (LCs) and time crystals. Here, we study the dynamics of a Bose-Einstein condensate (BEC) inside an optical cavity with transverse pumping and an additional intracavity optical lattice along the cavity axis. Specifically, we explore the theoretical predictions obtained from expanding the atomic field operators of the second-quantized Hamiltonian in two ways: (i) position basis and (ii) single-band Wannier basis. Both bases agree on the existence of most types of static and dynamical phases. However, the large sea of irregular dynamical phase, captured within the position basis, is absent in the Wannier basis. Moreover, we show that they predict different types of LCs due to the inherent limitation of the single-band Wannier expansion, highlighting the importance of including higher energy bands to correctly capture certain phenomena. Using truncated Wigner approximation, we investigate the fragmentation dynamics of the BEC. We demonstrate that both position and Wannier bases qualitatively agree on the photon-mediated fragmentation dynamics of the BEC in the density-wave phase, despite the absence of interatomic interactions. The presence of interatomic interaction leads to further fragmentation, which can only be observed in larger system sizes. Finally, we predict a sudden increase in the fragmentation behavior for larger pump intensities.

The emergence of distinctly subdiffusive scaling in the vicinity of an anomalous nonthermal fixed point is discussed in a quasi-two-dimensional dipolar Bose gas in the superfluid phase, carrying ensembles of vortices and antivortices with zero net angular momentum. The observed scaling behavior reflects coarsening dynamics driven by the mutual annihilation of vortices and antivortices, with the mean interdefect distance growing algebraically over time as ${\ell }_{\text{v}}\left(t\right)\sim t^{\beta }$. A subdiffusive ($\beta <\frac{1}{2}$) exponent $\beta \approx 0.2$ is extracted for various parameter regimes, initial conditions, and dipolar configurations from both scaling occupation-number spectra and the evolution of interdefect distances as well as the corresponding total vortex densities. As vortex-antivortex annihilation progresses, excitations of the background condensate increase. This gives rise to a transition in the scaling behavior at late times, toward a nonthermal fixed point governed by diffusion-type scaling with $\beta \approx \frac{1}{2}$ as expected for the mutual annihilation of well-separated vortex-antivortex dipoles. While the temporal scaling with $\beta$ does not depend significantly on the strength and anisotropy of the dipolar interactions and thus underlines the universality of the anomalous as well as diffusion-type nonthermal fixed points, we find distinctly different vortex patterns resulting in the dipolar case. While in the superfluid with contact interactions only, same-sign vortices tend to cluster and form large-scale eddies, in the dipolar and tilted cases, roton excitations appear to prevent such motion, giving rather rise to a maximization of distances between vortices of either sign.

Advances in technology made it possible to form complex cavities including a set of Bragg gratings and π shifts for distributed feedback (DFB) fiber lasers. This allows for precise control of the mode structure of the cavity. In such lasers, the input pump power defines the gain distribution along the fiber, leading to different lasing regimes. Direct accounting for these effects leads to highly resource-intensive space-time laser models, either to models based on modal decomposition of the field and population inversion associated with a problem of closing the system of variables. We propose a hybrid model that solves the mentioned problems by considering the spatial distribution of the population inversion combined with the field modal decomposition. The spatial field distribution within a single Bragg grating period and corresponding hole burning in the population inversion is characterized by two additional variables describing the population inversion spatial grating. We illustrate the application of the model on an example of $\mathrm{E}{\mathrm{r}}^{3+}$/$\mathrm{Y}{\mathrm{b}}^{3+}$ laser with a cavity including two π shifts. We study the resulting mode dynamics and demonstrate hysteretic behavior of lasing curves. We show that in our example, mode coexistence is observed, whereas an exclusion of the population inversion grating changes the lasing regime to single-mode lasing with one of the modes being suppressed. We hope that the proposed model will find numerous applications in modeling DFB fiber lasers.

Tapered optical fibers (TOFs) with sub-wavelength-diameter waists, known as optical nanofibers, are powerful tools for interfacing quantum emitters and nanophotonics. These applications demand stable polarization of the fiber-guided light field. However, the linear birefringence resulting from Ångström-scale (Å-scale) deviations in the nanofiber's ideally circular cross section can lead to significant polarization changes within mm of light propagation. Here, we experimentally investigate such deviations using two in situ approaches. First, we measure the resonance frequencies of hundreds of flexural modes along the nanofiber, which exhibit splitting due to the noncircular cross section. By analyzing the mean resonance frequencies of each pair and the corresponding frequency splitting, we conclude that the nanofiber can be well described as having an elliptical cross section with a mean radius of $255.2\left(8\right)\mathrm{nm}$, where the semiaxes differ by only about $2\AA$. Second, we monitor the polarization of the guided light field by imaging the light scattered out of the nanofiber and observe a periodic polarization change along it. From the linear birefringence due to the elliptical cross section, we infer a comparable difference in the semiaxes as the first method, and determine the orientation of the polarization eigenaxes. Our work is crucial for any fundamental or applied study that requires a well-controlled interaction between guided light and matter, in particular for quantum memories, frequency conversion, or lasing that require a large interaction length.

We propose a protocol to reduce the linewidth of a weak laser field without power loss based on a quantum squeezing process. By taking advantage of the frequency-dependent noiseless amplification mechanism of the cavity squeezing process, the linewidth of the output field from the cavity can be evidently narrowed in comparison to that of the incident laser field. The reduction effect depends on the strength of the cavity squeezing process, and order-of-magnitude reduction can be made possible in the vicinity of the lasing threshold. Moreover, we find a simple and favorable scaling law for the output field from the cascade system consisting of $M$ identical nonlinear cavities at certain conditions. Our results may be beneficial for a variety of applications where narrow linewidth is crucial, such as quantum metrology and sensing.