Quantum steering ellipsoid formalism provides a faithful representation of all two-qubit states and is useful for obtaining their correlation properties. The steering ellipsoids of two-qubit states that have undergone local operations on both the qubits, in order to bring the state to its canonical form, are the so-called canonical steering ellipsoids. The steering ellipsoids corresponding to the two-qubit subsystems of permutation-symmetric $N$-qubit states are considered here. We construct and analyze the geometric features of the canonical steering ellipsoids corresponding to pure permutation-symmetric $N$-qubit states with two distinct spinors. Depending on the degeneracy of the two spinors in the pure symmetric $N$-qubit state, several families arise which cannot be converted into one another through stochastic local operations and classical communication (SLOCC). The canonical steering ellipsoids of the two-qubit states drawn from the pure symmetric $N$-qubit states with two distinct spinors allow for a geometric visualization of the SLOCC-equivalent class of states. We show that the states belonging to the $W$ class correspond to oblate spheroids centered at $(0,0,1/(N-1))$ with fixed semiaxis lengths $1/\sqrt{N-1}$ and $1/(N-1)$. The states belonging to all other SLOCC-inequivalent families correspond to ellipsoids centered at the origin of the Bloch sphere. We also explore volume monogamy relations of states belonging to these families, mainly the $W$ class of states.

A general form of the photon position operator with commuting components fulfilling some natural axioms is obtained. This operator commutes with the photon helicity operator, is Hermitian with respect to the Białynicki–Birula scalar product, and is defined up to a unitary transformation preserving the transversality condition. It is shown that, using the procedure analogous to the one introduced by T. T. Wu and C. N. Yang for the case of the Dirac magnetic monopole, the photon position operator can be defined by a flat connection in some trivial vector bundle over ${\mathbb{R}}^3\setminus \left\{(0,0,0)\right\}$. This observation enables us to reformulate the quantum mechanics of a single photon on $({\mathbb{R}}^3\setminus \left\{(0,0,0)\right\})\times {\mathbb{C}}^2$.

Weak amplification and other postselection-based metrological protocols can enhance precision while estimating small parameters, outperforming postselection-free protocols. In general, these enhancements are largely constrained because the protocols yielding higher precision are rarely obtained due to a lower probability of successful postselection. It is shown that this precision can further be improved with the help of quantum resources like entanglement and negativity in the quasiprobability distribution. However, these quantum advantages in attaining considerable success probability with large precision are bounded irrespective of any accessible quantum resources. The advantage is being considered only within the scope of postselected metrology. Here we derive a bound of these advantages in postselected metrology, establishing a connection with weak value optimization where the latter can be understood in terms of the geometric phase. We introduce a scheme that saturates the bound, yielding anomalously large precision. Moreover, we prove that these advantages can be achieved with positive quasiprobability distribution. We also provide an optimal metrological scheme using a three-level nondegenerate quantum system.

The task of a telecloning protocol is to send an arbitrary qubit possessed by a sender to multiple receivers. Instead of performing Bell measurement at the sender's node, if one applies unsharp measurement, we show that the shared state can further be recycled for a certain number of telecloning protocol. Specifically, in case of a single sender and two receivers, the maximum attempting number, which is defined as the maximum number of rounds used by the channel to obtain quantum advantage in the fidelity, turns out to be 3 both for optimal and nonoptimal shared states for telecloning while the maximal number reduces to 2 in case of three receivers. Although the original telecloning with quantum advantage is possible for arbitrary numbers of receivers, we report that the recycling of resources is not possible in telecloning involving a single sender and more than three receivers, thereby demonstrating a no-go theorem. We also connect the maximal achievable fidelities in each round with the bipartite entanglement content of the reduced state between the sender and one of the receivers as well as with the monogamy score of entanglement.

Trapped ions driven by electromagnetic radiation constitute one of the most developed quantum technologies to date. The scenarios range from proof-of-principle experiments to on-chip integration for quantum information units. In most cases, these systems have operated in a regime where the magnitude of the ion-radiation coupling constant is much smaller than the trap and electronic transition frequencies. This regime allows the use of simple effective Hamiltonians based on the validity of the rotating-wave approximation. However, novel trap and cavity designs now permit regimes in which the trap frequency and the ion-radiation coupling constant are commensurate. This opens up new avenues for faster quantum gates and state transfers from the ion to a photon and other quantum operations. From the theoretical side, however, there is not yet much known in terms of models and applications that go beyond the weak-driving scenario. In this work, we present two main results in the scenario of stronger driving. First, we revisit a known protocol to reconstruct the motional Wigner function and expand it to stronger-driving lasers. This extension is not trivial because the original protocol makes use of effective Hamiltonians valid only for weak driving. The use of stronger fields or faster operations is desirable since experimental reconstruction methods of that kind are usually hindered by decoherence. We then present a model that allows the analytical treatment of stronger driving and that works well for nonresonant interactions, which are generally out of the reach of previous models.

We study ionization of atoms in strong elliptically polarized laser fields numerically and analytically. We focus on the effects of laser ellipticity on the offset angle in the photoelectron momentum distribution. This angle is considered to encode the time information of tunneling ionization in attoclock experiments. The calculated offset angle increases with the decrease of ellipticity, but the momentum along the major axis of laser polarization related to this angle changes slowly, in agreement with experiments. With a Coulomb-included strong-field model, the scaling laws for the ellipticity dependence of this angle and relevant momentum components are obtained, and the ellipticity dependence of Coulomb-induced ionization time lag encoded in this angle is also addressed.

Magnetic gradiometers have wide practical and academic applications, and two important types of field gradient observables are the total field gradient and field gradient tensor. However, measurements of the field gradient tensor have not been the focus of previous researches on atomic magnetic gradiometers. In this work, we develop an atomic magnetic gradiometer based on two separately optically pumped atomic ensembles in a Herriott-cavity-assisted atomic cell. This gradiometer shows versatile operation modes and functions, and we demonstrate them in measurements of both types of field gradient observables.

The study of high-order harmonic generation in liquid-state materials is still in its infancy. Quantitative models are highly required to understand the mechanisms. Here we develop a semiclassical method to investigate the ultrafast electron dynamics in liquids under monochromatic and two-color laser fields in momentum space. By assuming that different $k$ values are decoupled, we construct a quasienergy band for the liquid model and give the group velocity of the ionized electrons under the driving field. It successfully predicts the caustic enhancement of the liquid harmonic spectrum. We also find that the cutoff of the liquid harmonic spectrum is determined by the $k$-dependent band gap. Our results provide a different perspective for analyzing the nonlinear and nonperturbative liquid-state harmonic generation.

We propose a scheme for the quantum simulation of quantum link models in two-dimensional lattices. Our approach considers spinor dipolar gases on a suitably shaped lattice, where the dynamics of particles in the different hyperfine levels of the gas takes place in one-dimensional chains coupled by the dipolar interactions. We show that at least four levels are needed. The present scheme does not require any particular fine-tuning of the parameters. We perform the derivation of the parameters of the quantum link models by means of two different approaches, a nonperturbative one tied to angular-momentum conservation, and a perturbative one. A comparison with other schemes for $(2+1)$-dimensional quantum link models present in the literature is discussed. Finally, the extension to three-dimensional lattices is presented, and its subtleties are pointed out.

We propose a multidimensional discrete-time quantum walk (DTQW), whose continuum limit is an extended multidimensional Dirac equation, which can be further mapped to the Schrödinger equation. We show in two ways that our DTQW is an excellent measure to investigate the two-dimensional (2D) extended Dirac Hamiltonian and higher-order topological materials. First, we show that the dynamics of our DTQW resembles that of a 2D Schrödinger harmonic oscillator. Second, we find in our DTQW topological features of the extended Dirac system. By manipulating the coin operators, we can generate not only standard edge states but also corner states.

We investigate the relation between the amount of entanglement localized on a chosen subsystem of a multiqubit system via local measurements on the rest of the system, and the bipartite entanglement that is lost during this measurement process. We study a number of paradigmatic pure states, including the generalized Greenberger–Horne–Zeilinger (GHZ), the generalized $W$ (gW), Dicke, and the generalized Dicke states. For the generalized GHZ and $W$ states, we analytically derive bounds on localizable entanglement in terms of the entanglement present in the system prior to the measurement. Also, for the Dicke and the generalized Dicke states, we demonstrate that with increasing system size, localizable entanglement tends to be equal to the bipartite entanglement present in the system over a specific partition before measurement. We extend the investigation numerically in the case of arbitrary multiqubit pure states. We also analytically determine the modification of these results, including the proposed bounds, in situations where these pure states are subjected to single-qubit phase-flip noise on all qubits. Additionally, we study one-dimensional paradigmatic quantum spin models, namely, the transverse-field XY model and the XXZ model in an external field, and numerically demonstrate a cubic dependence of the localized entanglement on the lost entanglement. We show that this relation is robust even in the presence of disorder in the strength of the external field.

Entangled states are self-evidently important to a wide range of applications in quantum communication and quantum information processing. We propose an efficient and convenient two-step protocol for generating Bell states and NOON states of two microwave resonators from merely coherent states. In particular, we derive an effective Hamiltonian for resonators coupled to a superconducting $\mathrm{\Lambda }$-type qutrit in the dispersive regime. By the excitation-number-dependent Stark shifts of the qutrit transition frequencies, we are able to individually control the amplitudes of specified Fock states of the resonators associated with relevant qutrit transition, using carefully tailored microwave drive signals. Thereby an arbitrary bipartite entangled state in Fock space can be generated by a typical evolution-and-measurement procedure. We analyze the undesired state transitions and the robustness of our protocol against the systematic errors from the microwave driving intensity and frequency, the quantum decoherence of all components, and the crosstalk of two resonators. In addition, we demonstrate that our protocol can be extended to a similar scenario with a $\mathrm{\Xi }$-type qutrit.

Joint Gaussian measurements of two quantum systems are important for quantum communication between remote parties and are often used in continuous-variable teleportation or entanglement-swapping protocols. Many of the errors in real-world implementations can be modeled by independent Gaussian error channels acting prior to measurement. In this work we study independent single-mode Gaussian error channels on two modes $\mathsf{A}$ and $\mathsf{B}$ that take place prior to a joint Gaussian measurement. We determine the set of pairs of such channels that render all Gaussian measurements separable and therefore unsuitable for entanglement swapping or teleportation of arbitrary input states. For example, if the error channels are loss with parameters $l_{\mathsf{A}}$ and $l_{\mathsf{B}}$ followed by added noise with parameters $n_{\mathsf{A}}$ and $n_{\mathsf{B}}$, then all Gaussian measurements are separable if and only if $l_{\mathsf{A}}+l_{\mathsf{B}}+n_{\mathsf{A}}+n_{\mathsf{B}}\ge 1$.

In this work we report state-of-the-art theoretical calculations of the dipole polarizability of the argon atom. Frequency dependence of the polarizability is taken into account by means of the dispersion coefficients (Cauchy coefficients), which is sufficient for experimentally relevant wavelengths below the first resonant frequency. In the proposed theoretical framework, all known physical effects including the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size corrections are accounted for. We obtained ${\alpha }_0=11.0775\left(19\right)$ for the static polarizability and ${\alpha }_2=27.976\left(15\right)$ and ${\alpha }_4=95.02\left(11\right)$ for the second and fourth dispersion coefficients, respectively. The result obtained for the static polarizability agrees (within the estimated uncertainty) with the most recent experimental data [C. Gaiser and B. Fellmuth, Phys. Rev. Lett. 120, 123203 (2018)] but is less accurate. The dispersion coefficients determined in this work appear to be the most accurate in the literature, improving by more than an order of magnitude upon previous estimates. By combining the experimentally determined value of the static polarizability with the dispersion coefficients from our calculations, the polarizability of argon can be calculated with accuracy of around $10\mathrm{ppm}$ for wavelengths above roughly $450\mathrm{nm}$. This result is important from the point of view of quantum metrology, especially for a new pressure standard based on thermophysical properties of gaseous argon. Additionally, in this work we calculate the static magnetic susceptibility of argon, which relates the refractive index of dilute argon gas with its pressure. While our results for this quantity are less accurate than in the case of the polarizability, they can provide, via the Lorenz-Lorentz formula, the best available theoretical estimate of the refractive index of argon.

The bound-state QED approach is applied to calculations of the $2p_{3/2}\to 2s$ transition energies in He-, Li-, and Be-like uranium. For ${\mathrm{U}}^{90+}$ and ${\mathrm{U}}^{89+}$, standard perturbation theory for a single level is employed, while the calculations of ${\mathrm{U}}^{88+}$ have required its counterpart for quasidegenerate levels. The utilized approach merges the rigorous QED treatment up to the second order of perturbation theory with the higher-order electron-correlation contributions evaluated within the Breit approximation. The higher-order screened QED effects are estimated by means of the model-QED operator. The nuclear recoil, nuclear polarization, and nuclear deformation effects are taken into account as well. Along with the transition energies, their pairwise differences are calculated. The comprehensive analysis of the uncertainties due to uncalculated effects is carried out, and the most accurate theoretical predictions, which are in perfect agreement with available experimental data, are obtained.

The finite-nuclear-size (FNS) effect has a large contribution to atomic spectral properties, especially for heavy nuclei. By adopting the microscopic nuclear charge-density distributions obtained from the relativistic continuum Hartree-Bogoliubov (RCHB) theory, we systematically investigate the FNS corrections to atomic energy levels and bound-electron $g$ factors of hydrogenlike ions with nuclear charge up to 118. The comparison of the present numerical calculations with the predictions from empirical nuclear charge models, the nonrelativistic Skyrme-Hartree-Fock calculations, and the results based on experimental charge densities indicate that both the nuclear charge radius and the detailed shape of the charge-density distribution play important roles in determining the FNS corrections. The variation of FNS corrections to energy levels and $g$ factors with respect to the nuclear charge are investigated for the several lowest bound states of hydrogenlike ions. It is shown that they both increase by orders of magnitude with increasing nuclear charge, while the ratio between them has a relatively weak dependence on the nuclear charge. The FNS corrections to the $s_{1/2}$ and $p_{1/2}$ bound-state energies from the RCHB calculations are generally in good agreement with the analytical estimations by Shabaev [V. M. Shabaev, J. Phys. B 26, 1103 (1993)] based on the homogeneously charged sphere nuclear model, with the discrepancy indicating the distinct contribution of microscopic nuclear structure to the FNS effects.

Tampering resonant rare-gas clusters with nonresonant atoms has been shown to significantly decrease in the final ionization of the resonant atoms [J. Phys. B: At., Mol. Opt. Phys. 41, 181001 (2008)], but not their transient ionization [Phys. Rev. Lett. 112, 183401 (2014)]. In this paper, we explain the details of the charge transfer mechanism from the resonant to nonresonant atoms. We have applied our model to the interaction of an ultraintense x-ray laser tuned to the center of xenon's giant 4d resonance with core-shell argon-xenon clusters. Our results are in agreement with previous experimental results of the disintegration products, and the transient states. Also, our model predicts that the resonant xenon is quickly ionized by the laser. The freed electrons then collisionally ionized the outer argon atoms before recombining with the inner xenon ions to reduce their final charge state. We find that unlike homogeneous clusters whose behavior is governed by the number of atoms, the behavior of core-shell heterogeneous clusters is well predicted by the ratio of resonant to nonresonant atoms.

In recent years, electric field measurement techniques based on Rydberg atoms have shown unique advantages in high sensitivity and wideband applications and miniaturization. The Rydberg atom receiver senses the electromagnetic signal using the quantum coherence effect, which overcomes the inherent defects of traditional electronic receivers in terms of thermal noise, insertion loss of microwave devices, and the use of wavelength-dependent antennas, thus providing the Rydberg atomic receivers the potential to become the next generation of microwave receivers. For some particular application scenarios such as radar and communication, superheterodyne reception is a critical technical approach, and the linear dynamic range is an essential factor in evaluating the performance of the superheterodyne receivers. It is challenging to promote the Rydberg atomic receiver without figuring out the influence of system parameters on the linear dynamic range. This paper starts with the response mechanism of the Rydberg atomic superheterodyne receiver, and a theoretical model is established to simulate the atom-microwave responses. Then the harmonics' generation mechanism is discussed, and the atomic linear dynamic range under different probe light Rabi frequencies is studied further. Furthermore, a method to evaluate the antiblocking performance of the system is proposed. This work is expected to provide theoretical guidance for the design and performance optimization of the Rydberg atomic superheterodyne receiver.

We theoretically consider effectively one-dimensional quantum droplets in a symmetric Bose-Bose mixture confined in a parabolic trap. We systematically investigate ground and excited families of localized trapped modes which bifurcate from eigenstates of the quantum harmonic oscillator as the number of particles departs from zero. Families of nonlinear modes have nonmonotonous behavior of chemical potential on the number of particles and feature bistability regions. Excited states are unstable close to the linear limit, but become stable when the number of particles is large enough. In the limit of large density, we derive a modified Thomas-Fermi distribution. Smoothly decreasing the trapping strength down to zero, one can dynamically transform the ground-state solution to the solitonlike quantum droplet, while excited trapped states break in several moving quantum droplets.

We investigate the thermal Casimir-Polder (CP) potential of ${}^{87}\mathrm{Rb}$ atoms in Rydberg $nS$-states near single- and double-layer graphene, and briefly look into the lifetimes near graphene-hexagonal boron nitride (hBN) multilayered structures. The dependence of the CP potential on parameters such as atom-surface distance, temperature, principal quantum number $n$, and graphene Fermi energy are explored. Through large-scale numerical simulations, we show that, in the nonretarded regime, the CP potential is dominated by the nonresonant and evanescent-wave terms which are monotonic, and that, in the retarded regime, the CP potential exhibits spatial oscillations. We identify that the most important contributions to the resonant component of the CP potential come from the $nS\text{−}nP$ and $nS\text{−}(n-1)P$ transitions. Scaling of the CP potential as a function of the principal quantum number and temperature is obtained. A heterostructure comprising hexagonal boron nitride layers sandwiched between two graphene layers is also studied. When the boron nitride layer is sufficiently thin, the CP potential can be weakened by changing the Fermi energy of the top graphene layer. Our study provides insights for understanding and controlling CP potentials experienced by Rydberg atoms near single- and multilayer graphene-based van der Waals heterostructures.