Some years ago, to investigate modulational instability using a linear stability analysis, Kondratiev and Lobanov [Phys. Rev. A 101, 013816 (2020)] applied a method that consists of adding complex conjugate equations to a differential system to close up the system self-consistently. It is the aim of this Comment to note and correct the crucial inconsistency found in the method used to investigate the modulational instability in Kondratiev and Lobanov's work.

In this Reply, we address the points raised by Emmanuel Kengne in his Comment on our paper [Phys. Rev. A 101, 013816 (2020)]. Dr. Kengne asserts that the linear stability analysis method applied in the original article is incorrect and proposes an alternative approach. Here, we demonstrate that his considerations are not entirely accurate as the final solution derived from both methods are, in fact, equivalent. Finally, we prove the validity of our method.

Exceptional points featuring enhanced energy response to perturbation hold significant potential in detection and measurement of weak signals. Of particular interest is the existence and property of high-order exceptional points in quantum systems, owing to the capability to provide high-order response to perturbations. We investigate the exceptional points in a system of $n$ identical qubits possessing parity-time-reversal symmetry. We prove that owing to an incomplete coalescence of eigenstates, the highest possible order of exceptional point is $n+1$, which is also the upper bound of the order of energy response to perturbation. More interestingly, by considering an Ising-type interaction, we analytically prove that to achieve an $(m+1)\mathrm{th}$ order response for any $m\le n$, the system must acquire a nontrivial $m$-body interaction. Finally, we propose a Floquet driving scheme to implement an effective multibody Ising-type interaction, which can be realized in trapped ions or superconducting qubits.

Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local realistic hidden-variable theories. Most proofs of Bell's theorem, are based on inequalities. In this paper we present an alternative proof which does not involve inequalities, but only a direct comparison between correlation functions calculated using quantum mechanics on the one hand, and those calculated according to local realistic hidden-variable theories on the other. Our proof is based on a physically motivated use of Fourier series for periodic functions, and confirms that local realistic hidden-variable theories are incompatible with quantum mechanics.

We propose and solve a minimal model of dynamic passage through a second-order phase transition in the presence of symmetry-breaking interactions and no dissipation. Our model generalizes the Hamiltonian dynamics of the Painlevé-2 equation to the case with many degrees of freedom, while maintaining the integrability property. The evolution eventually leads to a highly asymmetric state, no matter how weak the symmetry-breaking parameter of the Hamiltonian is. This suggests a potential mechanism for strong asymmetry in the production of quasiparticles with nearly identical characteristics. The model's integrability also yields exact exponents for the scaling of the density of the nonadiabatically excited quasiparticles.

Quantum architecture search (QAS) has shown significant promise in automating quantum circuit design for variational quantum algorithms (VQAs). However, a central challenge remains in the high computational cost of evaluating the ground-truth performance of numerous circuit architectures during the search process. This challenge is further complicated by factors such as inefficient gradient computation, the barren plateau phenomenon, and frequent data exchange between classical and quantum systems within VQAs, all of which restrict the scalability of QAS for increasingly complex VQAs. In this study, we propose an enhanced QAS framework that integrates a performance predictor trained through self-supervised learning with Bayesian optimization to overcome these computational barriers. To address the challenges of circuit performance evaluation, we develop a graph-isomorphism-network-based predictor pretrained using expressibility prediction, an intrinsic measure of a circuit's capacity to explore the Hilbert space uniformly. This pretraining process creates a structured and smooth latent space, significantly improving the predictor's accuracy and generalizability with minimal labeled data. Furthermore, Bayesian optimization is integrated into the QAS framework to refine the predictor iteratively, concentrating the search on regions containing high-performance circuits and thus accelerating the search process. Simulation results for VQAs involving the variational quantum eigensolver and quantum approximate optimization algorithm demonstrate that the proposed framework achieves faster convergence to optimal circuits and substantially reduces computational costs compared to existing QAS methods.

Common notions of entanglement are based on well-separated subsystems. However, obtaining such independent degrees of freedom is not always possible because of physical constraints. In this work, we explore the notion of entanglement in the context of dependent degrees of freedom. As a physically relevant application, we specifically study quantum correlation features for quasiparticle descriptions. Those are paramount for interacting light-matter systems, utilizing excitations of fermion-boson hybrid modes. By comparing independent and dependent degrees of freedom, we uncover that certain states are nonentangled although they would be entangled when only focusing on the common, independent description, and vice versa. Therefore, insight is provided into the resourcefulness of quantum correlations within the rarely discussed context of dependent degrees of freedom for light-matter links in quantum information applications.

Much of the research in quantum hypothesis testing has focused on simple hypotheses. In practical situations, though, we need to consider more complex, or composite, hypotheses. This paper introduces an approach for testing these composite hypotheses in quantum systems. It combines repeating projective measurements with the quantum Neyman-Pearson test including quantum correlations, which improves the effectiveness of the tests. We also clarify theoretically how the type-II error (false negative) probability of the proposed test behaves asymptotically and show that the proposed test is better at distinguishing hypotheses than traditional approaches. In addition, through numerical calculation, we demonstrate that the proposed test enhances performance in quantum statistical models, where we usually use the classical binomial test. This result shows the practical benefits of applying quantum correlations in hypothesis testing scenarios.

States with a negative Wigner function, a significant subclass of nonclassical states, serve as a valuable resource for various quantum information processing tasks. Here we provide a criterion for detecting such quantum states characterized by a negative Wigner function. Our method relies on evaluating moments of the Wigner function, which involves computing simple functionals and can be implemented in a real experiment without the need for full state tomography or Wigner function reconstruction. We provide explicit examples to support our detection scheme. Further, we propose an experimental method utilizing the mode swap operator to realize these moments in a real experiment.

We propose a versatile quantum sensing protocol based on two dissipatively coupled distant atoms embedded as impurities in a two-dimensional subwavelength atomic array. The array acts analogously to a waveguide or cavity for the emitter light, where a modified decay environment creates cooperative enhancement, allowing for more efficient population transfer. By measuring the population of one of the impurity atoms, it is possible to detect frequency shifts in the emitters' resonance frequencies. We analytically estimate achievable sensitivities as well as the dependence on various system parameters. The proposed protocol is robust against various environmental factors and perturbations, which enhances its applicability in real-world scenarios.

We report on spectroscopy of the low-lying electronic transitions in ${}^{224}\mathrm{Ra}^{+}$. We measured the frequencies of the ${}^{2}S_{1/2}\leftrightarrow {}^{2}P_{1/2}$ cooling transition, the ${}^{2}S_{1/2}\leftrightarrow {}^{2}D_{5/2}$ clock transition, the ${}^{2}D_{3/2}\leftrightarrow {}^{2}P_{3/2}$ electric dipole transition, and the ${}^{2}D_{5/2}\leftrightarrow {}^{2}P_{3/2}$ cleanout transition. From these measurements we calculate the frequencies of the ${}^{2}D_{3/2}\leftrightarrow {}^{2}P_{1/2}$ repump transition, the ${}^{2}S_{1/2}\leftrightarrow {}^{2}D_{3/2}$ electric quadrupole transition, and the ${}^{2}S_{1/2}\leftrightarrow {}^{2}P_{3/2}$ electric dipole transition. The ion's low charge-to-mass ratio and convenient wavelengths make ${}^{224}{\mathrm{Ra}}^{+}$ a promising optical clock candidate.

We theoretically investigate the spin structure of weakly bound diatomic van der Waals molecules formed by two identical bosonic alkali atoms. Our studies were performed using known Born-Oppenheimer potentials while developing a reduced interaction potential model. Such reduced potential models are currently a key for solving certain classes of few-body problems of atoms as they decrease the numerical burden on the computation. Although the reduced potentials are significantly shallower than actual Born-Oppenheimer potentials, they still capture the main properties of the near-threshold bound states, including their spin structure, and the scattering states over a broad range of magnetic fields. At zero magnetic field, we find that the variation in spin structure across different alkali species originates from the interplay between electronic spin exchange and hyperfine interactions. To characterize this competition we introduce a single parameter that is a function of the singlet and triplet scattering lengths, the atomic hyperfine splitting constant, and the molecular binding energy. We show that this parameter can be used to classify the spin structure of vdW molecules for each atomic species.

We present an approach toward generating highly controllable breathers, using an array of staggered optomechanical cavities that feature alternating coupling strengths. Four different types of breather states as well as stable two-soliton states are demonstrated to form in such an optomechanical array, thanks to the interplay between the photon-hopping induced tunneling effect and the photon-phonon coupling in the optomechanical cell. It is seen that both their photonic and phononic wave components manifest quasi-periodic oscillatory patterns and coherent localization. We unveil that such breather dynamics can be well controlled by adjusting the coupling strength, the cavity field decay, and the number of array cells. As a result, we observe an unusual odd-even lattice effect in that stable breathers are only available when the cell number is even. We anticipate that these findings from the staggered optomechanical configuration may expand the realm of cavity optomechanics, yielding promising applications such as on-chip manipulation of light propagation.

Quantum entanglement, as a central concept in quantum theory, plays a crucial role in understanding the fundamentals of quantum mechanics and is widely studied in advanced practical technological applications. We study the behavior of bipartite and tripartite entanglement in a hybrid optoelectromechanical system consisting of a pair of coupled cavities, a large mass membrane, and a low-frequency $LC$ resonator. Within the experimentally achievable parameters, we observe a significant enhancement of the electromechanical entanglement, which directly originates from the electromechanical coupling. We also show that entanglement between subsystems can be manipulated by tuning the cavity-cavity coupling rate. Furthermore, we significantly enhance the robustness of electromechanical entanglement against thermal noise. The enhancement of electromechanical entanglement in this system will facilitate the investigation of quantum theory applications on more macroscopic scales, such as medical imaging, quantum communication, and astronomical signal detection.

We study a system composed of a three-level giant atom (3GA), a waveguide initially in the vacuum state, and a single-mode cavity. The 3GA-cavity system is in a strong-coupling regime, and the distance between the coupling points is comparable to the coherent length of a spontaneously emitted photon. The dynamics of the 3GA and its radiative field in the waveguide for long times are analyzed in each subspace with only one excitation exchanged between the waveguide and the 3GA cavity. Besides the steady value, we also found an oscillatory character of the excited-state population, a signature of oscillating bound states which is generated by the superposition of two bound states in the continuum. The radiative field propagates in the cavitylike geometry formed by the coupling points. When one bound state is emergent, a sinelike interference pattern is visible for the emitted photon distribution in spacetime. An oscillatory character in time and a beat in space for the emitted photon distribution are observed when two bound states are emergent in a subspace. The wavelengths and the periods are controlled by the number of photons in the cavity.

We present a surface plasmon resonance (SPR) system designed to operate without the need for a conventional coupler. The proposed SPR configuration consists of a simple two-layer structure with an upper metal layer and a lower atomic medium. Surface plasmon polaritons (SPPs) are readily excited when the real part of the permittivity of the atomic medium falls below unity, enabling an efficient and streamlined excitation process. The atomic medium dynamics is modulated by external fields, such as pump fields and microwaves, facilitating precise control over SPP excitation. We investigate the influence of the atomic medium, analyzing the lifetimes and propagation lengths for both gold and silver layers, while also addressing realistic factors such as dipole momenta, the potential for structural damage, and manufacturing imperfections. Additionally, we explore the Goos-Hänchen (GH) shift of the reflected light, noting an enhanced GH shift that aligns with optimal SPP excitation. Both negative and positive GH shifts are observed, with their directions and magnitudes modifiable through external parameters. This system provides a straightforward and viable method for SPP generation and controlled SPR and GH shift modulation, presenting significant potential for tunable optical devices in telecommunication. We expect these findings to contribute to the development of advanced systems with improved data transmission capabilities.