The dark-state effect, caused by destructive quantum interference, is an important physical effect in atomic physics and quantum optics. It not only deepens the understanding of light-atom interactions but also has wide applications in quantum physics and quantum information. Therefore, how to efficiently and conveniently determine the number and form of the dark states in multilevel quantum systems with complex transitions is an important and interesting topic in this field. In this work, we present a general theory for determining the dark states in multilevel quantum systems with any coupling configuration using the arrowhead-matrix method. To confirm the dark states in a multilevel system, we first define the upper- and lower-state subspaces, and then diagonalize the Hamiltonians restricted within the two subspaces to obtain the dressed upper and lower states. By further expressing the transitions between the dressed upper and lower states, we can map the multilevel system to a bipartite-graph network, in which the nodes and links are acted by the dressed states and transitions, respectively. Based on the coupling configurations of the network, we can determine the lower dark states with respect to the upper-state subspace. As examples, we analyze the dark states in three-, four-, and five-level quantum systems, for all possible configurations through the classification of the numbers of upper and lower states. Furthermore, we extend the framework to multilevel quantum systems and discuss the existence of dark states in some typical configurations. We also recover the results of the dark-state polaritons in driven three-level systems with the arrowhead-matrix method. Our theory paves the way for manipulating and utilizing the dark states of multilevel quantum systems in atomic physics and quantum optics.

Understanding the origin of phase synchronization between quantum self-sustained oscillators has garnered significant interest in recent years. In this work, we study phase synchronization in three settings: between two continuous-variable oscillators, between two arbitrary quantum spins, and within a hybrid setup involving a spin and an oscillator. We derive a simple and general condition on the elements of the joint density matrix that must be satisfied for them to contribute to the relative phase distribution. In particular, we identify the subset of coherence elements in the joint density matrix that serve as key resources for enabling quantum phase synchronization. Our theory is validated against the previously proposed interaction models known to induce synchronization between the self-sustained oscillators. Moreover, our approach offers valuable insights into the relationship between phase synchronization and various information-theoretic measures.

In quantum many-body systems, characterizing topological phase transitions typically requires complex many-body topological invariants, which are costly to compute and measure. Inspired by quantum reservoir computing, we propose an unsupervised quantum phase detection method based on a many-body localized evolution, enabling efficient identification of phase transitions in the extended Su-Schrieffer-Heeger model. The evolved quantum states produce feature distributions under local measurements, which, after simple postprocessing and dimensionality reduction, naturally cluster according to different Hamiltonian parameters. Numerical simulations show that the evolution combined with local measurements can significantly amplify distinctions between quantum states, providing an efficient means to detect topological phase transitions. Our approach requires neither complex measurements nor full density-matrix reconstruction, making it practical and feasible for noisy intermediate-scale quantum devices.

Contextuality, a fundamental feature distinguishing quantum mechanics from classical theories, has emerged as a vital resource for quantum advantage. While contextuality is well established theoretically, its experimental demonstrations via optimal two-state discrimination remain scarce. Here, we report an experimental study employing a two-path Sagnac interferometer to implement and characterize a contextuality witness. Our results reveal a robust contextuality witness in both noiseless and depolarizing noise cases. Remarkably, controlled introduction of inconclusive rates dynamically enhances noise resilience, revealing a tunable contextuality witness through adjustment of inconclusive rates. Furthermore, we verify quantum randomness under different noise conditions, ensuring robust min-entropy extraction with optimal state discrimination performance. These experimental results advance both fundamental understanding of contextuality as a quantum resource and its practical application in noise-resilient quantum information processing, facilitating the development of more reliable quantum technologies.

Quantum information masking (QIM) refers to the complete transfer of information contained in a single qubit to entanglement, while ensuring that no single qubit contains the original information. In this paper, we theoretically prove the feasibility of single-photon QIM, and experimentally demonstrate that the information of a single qubit can be transformed into the entanglement between different degrees of freedom of a single photon. Unlike conventional methods, our single-photon scheme can switch between the information masking mode and the direct communication mode, which facilitates the construction of integrated quantum masking machines.

In our work we construct a Hamiltonian, whose eigenstates approximate the solutions of the self-consistent Hartree-Fock equations for nonrelativistic atoms and ions. Its eigenvalues are given by completely algebraic expressions and the eigenfunctions are defined by Coulomb wave-function orbitals. Within this approximation we compute the binding energy, ionization potentials, electron density distribution, electron density at the nucleus, and atomic scattering factors of nonrelativistic atoms and ions. The accuracy of our results is comparable with those obtained via the usage of the Hartree-Fock method but does not require solving integrodifferential equations or numerically computing integrals with complex functions. This approach can serve as a good initial approximation for performing more accurate calculations and for the quantitative evaluation of physical parameters that depend on the electron density of atoms. The proposed approach is of interest for various fields of condensed matter physics, plasma physics, and quantum chemistry.

Hyperfine splitting in highly charged ions provides a powerful probe for testing strong-field quantum electrodynamics and investigating nuclear structure. In this work, we theoretically investigate the hyperfine-resolved dielectronic recombination process near to the threshold for selected Li-like highly charged ions. Numerical computations were carried out using a multiconfiguration Dirac-Fock method to address dielectronic recombination resonances for Li-like ions. Our calculations reproduce the previous experimental results of Li-like ${}^{45}\mathrm{Sc}^{18+}$ ions with nuclear spin $I=\frac{7}{2}$ [M. Lestinsky et al., Phys. Rev. Lett. 100, 033001 (2008)]. We further extended the calculation to two highly charged heavy ions, Li-like ${}^{119}\mathrm{Sn}^{47+}$ ($I=\frac{1}{2}$) and ${}^{187}\mathrm{Re}^{72+}$ ($I=\frac{5}{2}$), revealing distinct hyperfine-split dielectronic recombination resonances in the low-energy region. These calculations identify promising candidate ions and provide theoretical guidance for high-resolution dielectronic recombination experiments using the new storage-ring merged-beam technique.

We explore the possibility of forming an oriented polar molecule directly from a pair of colliding atoms. The process comprises the photoassociation and vibrational stabilization along with the molecular orientation. These processes are driven by a single time-dependent, linearly polarized control field and proceed entirely within the electronic ground state, leveraging the presence of a permanent dipole moment. The control field is found by means of an optimal quantum control algorithm with a single target observable given by the restriction of the orientation operator on a subset of bound levels. We consider a rovibrational model system for the collision of the $\mathrm{O}+\mathrm{H}$ atoms and solve directly the time-dependent Schrödinger equation. We show that the optimized field is capable of enhancing the molecular orientation already induced by the photoassociation and vibrational stabilization thus yielding oriented polar molecules that can be useful for many applications.

Close-coupling calculations of electron-atom scattering yield excitation cross sections for atomic eigenstates of relatively small principal quantum number $n\le n_{\max }$ and orbital angular momentum $l\le l_{\max }$ included in the close-coupling expansion. We use the photoionization of the helium system to demonstrate that finite convergent close-coupling calculations can be used to estimate the excitation cross sections of the residual ion to arbitrarily high principal quantum number $n>n_{\max }$ and orbital angular momentum $l>l_{\max }$. In doing so, we demonstrate the utility of the step-function property of the positive-energy state cross sections, together with the negative-energy state cross sections, in determining the desired cross sections for arbitrarily high Rydberg states.

Modern quantum engineering techniques allow for synthesizing quantum systems in exotic lattice geometries, from self-similar fractal networks to negatively curved hyperbolic graphs. We demonstrate that these structures profoundly reshape Bose-Einstein condensation. Fractal lattices dramatically lower the condensation temperature and enhance condensation fluctuations. In a Sierpiński carpet, quasidegeneracies in the tight-binding spectrum fragment the condensate. Hyperbolic lattices, on the other hand, exhibit condensation features similar to regular three-dimensional lattices, despite their embedding in only two dimensions: The critical temperature increases as the system grows, and the temperature dependence of the condensate fraction follows the same power law as for cubic lattices. We explain these similarities through the similarity of the densities of state at low energies. When strong repulsive interactions are included, the gas enters a Mott insulating state. Using a multisite Gutzwiller approach as well as a simple strong-coupling expansion, for the Sierpiński triangle we find a smooth interpolation between the characteristic insulating lobes of one-dimensional and two-dimensional systems. Our findings establish lattice geometry as a powerful tuning parameter for quantum phase phenomena and pave the way for experimental exploration in photonic waveguide arrays and Rydberg-atom tweezer arrays.

We report the realization of a degenerate mixture of ${}^{166}\mathrm{Er}$ and ${}^7\mathrm{Li}$ atoms in their energetically lowest spin states. The two species are sequentially laser cooled and loaded into an optical dipole trap and then transported to a glass cell and simultaneously evaporated to degeneracy. Er serves as the coolant for Li, and we observe efficient sympathetic cooling facilitated by a large interspecies elastic scattering cross section. Three-body losses are found to be small, making this platform promising for the study of interacting mixtures with large mass imbalance.

We study the conditions required to distinguish laser-induced nonlinear quantum electrodynamics effects in vacuum from competing signals due to interactions of laser pulses with ionized residual gas. The latter is inevitably present in vacuum chambers where experiments are performed because the vacuum is never perfect and there is always some residual pressure. The rarefied gas contribution is modeled statistically using the 1D-1V Vlasov-Maxwell system, while vacuum nonlinearities are described within the weak-field expansion of the Heisenberg-Euler effective action. In both cases, photon spectra from wave-mixing processes are evaluated by solving numerically the resulting partial differential equations using a semi-Lagrangian scheme. We consider short pulses in copropagating and counterpropagating configurations, allowing us to identify the laser intensities and vacuum pressures for which the vacuum signal dominates. These results provide quantitative guidance for future all-optical experiments aiming to detect light-by-light scattering in vacuum.

Supercontinuum generation (SCG) on thin-film lithium niobate platforms has opened new opportunities for applications in spectroscopy, metrology, and signal processing. However, the strong material dispersion of lithium niobate limits spectral broadening toward shorter wavelengths, particularly in waveguides without engineered domain structures, thereby restricting efficient SCG in the ultraviolet-to-visible region. Here we propose and theoretically demonstrate a new approach to overcome this limitation by harnessing higher-order waveguide modes. We show that femtosecond pumping near the visible spectrum can excite soliton fission and dispersive wave radiation in higher-order modes, efficiently transferring pump energy toward shorter wavelengths. Numerical simulations reveal that, under appropriate waveguide design and femtosecond pumping at a center wavelength of 860 nm, the excitation of the ${\mathrm{TE}}_{10}$ mode enables broadband SCG spanning 430–1260 nm at a −30 dB level. Our findings offer a simple and effective strategy for chip-scale SCG in the visible regime and pave the way for compact short-wavelength coherent frequency comb sources.

Quantum communication offers a unique framework for unconditional security, where secret key distribution can be used to establish trusted links across insecure networks. We propose a semi-device-independent scheme with two spatially separated mechanical oscillators, indirectly coupled via a lossy optical channel within a cascaded optomechanical setup. This architecture utilizes linearized optomechanical regimes to generate secret key rates through the conditional measurements of the mechanical modes' conjugate variables. It also exhibits asymmetric quantum steering features and position-momentum squeezing under realistic, noise-attenuated transmission conditions. We analyze the achievable key rate in the presence of optical losses and excess noise introduced by untrusted parties, and thermal noise, demonstrating the scheme's potential for secure long-distance communication. This proof-of-principle theoretical approach offers a promising foundation for extending similar schemes in entangled hybrid quantum networks.

Spin-squeezed states play an important role in quantum metrology, as they enhance the measurement precision beyond the standard quantum limit. Here we propose an approach to generating spin-squeezed states in a solid-state platform by coupling an ensemble of nitrogen-vacancy centers to an optical cavity at cryogenic temperature. Through cavity feedback, this setup enables the implementation of an all-to-all interaction (twist-and-turn), facilitating the generation of spin-squeezed states. Our results show that 7.5 dB of squeezing is achievable in the presence of imperfections including dephasing and nonuniform coupling.

The wave function of two identical bosons remains invariant under particle exchange—a fundamental quantum symmetry that underlies Bose-Einstein statistics. We report the experimental observation of bosonic exchange symmetry in the temporal wave function of photon pairs generated via spontaneous four-wave mixing in a three-level cold atomic ensemble. The measured two-photon temporal correlations show excellent agreement with theoretical predictions based on symmetrized bosonic wave functions. In addition, we perform time-resolved two-photon interference to reconstruct the complex temporal wave function. Both the amplitude and phase profiles exhibit clear symmetry under photon exchange, providing a confirmation of bosonic exchange symmetry in the time domain.

Entangled multimode squeezed states of light have a wide variety of applications in quantum information systems, particularly in the generation of non-Gaussian states of light, which are central to continuous-variable quantum computing. Although theoretical approaches exist to model the nonlinear generation of one- and two-mode entangled states of light in ring resonator systems, these approaches are difficult to implement in modeling more complicated many-cavity systems. In this work, we present an efficient and accurate theoretical approach to modeling the generation and propagation of quantum states of light in lossy coupled-cavity systems containing a two- or three-mode nonlinear resonant structure. Our approach is general and computationally viable even in systems with hundreds of modes. We apply our method to the design and modeling of a multimode photonic crystal coupled-cavity system for the generation of entangled squeezed states of light on-chip. The system consists of a three-mode resonant structure coupled to three coupled-resonator optical waveguides (CROWs) in a square lattice silicon photonic crystal slab. The computational speed of the method allows us to efficiently optimize the system such that the signal and idler light in the two output CROWs remains entangled even after propagating tens of cavities down the CROWs.

We analyze the common claim that nonlinear modifications of quantum theory necessarily violate the second law of thermodynamics. We focus on hypothetical extensions of quantum theory that contain readout devices. These black boxes provide a classical description of quantum states without perturbing them. They allow quantum state cloning, though in a way consistent with the relativistic no-signalling principle. We review the existence of such devices in the context of Møller-Rosenfeld semiclassical gravity, which postulates that the gravitational field remains classical and is sourced by the expectation value of a quantum energy-momentum tensor. We show that the definition of information in the models examined in this paper deviates from that given by von Neumann entropy, and that claims of second law violations based on the distinguishability of nonorthogonal states or on violations of uncertainty principles fail to hold in such theories.