Quantum repeater networks are a fundamental of any future quantum internet and long-distance quantum communications. The entangled quantum nodes can communicate through several different levels of entanglement, leading to a heterogeneous, multilevel network structure. The level of entanglement between the quantum nodes determines the hop distance and the probability of the existence of an entangled link in the network. Here, we define a decentralized routing for entangled quantum networks. The proposed method allows an efficient routing to find the shortest paths in entangled quantum networks by using only local knowledge of the quantum nodes. We give bounds on the maximum value of the total number of entangled links of a path. The proposed scheme can be directly applied in practical quantum communications and quantum networking scenarios.

We consider the problem of one-sided device-independent self-testing of any pure entangled two-qubit state based on steering inequalities which certify the presence of quantum steering. In particular, we note that in the 2-2-2 steering scenario (involving two parties, two measurement settings per party, and two outcomes per measurement setting), the maximal violation of a fine-grained steering inequality can be used to witness certain extremal steerable correlations, which certify all pure two-qubit entangled states. We demonstrate that the violation of the analogous Clauser-Horne-Shimony-Holt inequality of steering or the nonvanishing value of a quantity constructed using a correlation function called mutual predictability, together with the maximal violation of the fine-grained steering inequality, can be used to self-test any pure entangled two-qubit state in a one-sided device-independent way.

By local measurements on party $A$ of a system $\mathit{AB}$ and classical communication between its two parties, one can achieve a nonlocal advantage of quantum coherence (NAQC) on party $B$. For the $l_1$ norm of coherence and the relative entropy of coherence, we generalized the framework of NAQC for two qubits and derived the criteria which capture NAQC in the ($d\times d$)-dimensional states when $d$ is a power of a prime. We also presented a framework for formulating NAQC and showed through explicit examples its capacity for capturing the NAQC states. Moreover, we proved that any bipartite state with NAQC is quantum entangled; thus the obtained criteria can also be used as an entanglement witness.

The original formulation [M. Piris, Phys. Rev. Lett. 119, 063002 (2017)] of the natural-orbital-functional second-order-Møller-Plesset (NOF-MP2) method is based on the MP2 that uses the canonical Hartree-Fock molecular orbitals. The current work presents a reformulation of the dynamic energy correction based on the orbital-invariant MP2, which allows one to attain both dynamic and static correlations even for those systems with strong orbital localizability and significant multiconfigurational character. To improve the reference Slater determinant formed with natural orbitals, the natural orbital functional that generates them is also modified to take into account only the interpair static correction. This more general NOF-MP2 is able to dissociate properly noble-gas dimers, which remain as nonbound species within the canonical formulation. Test calculations in a selected set of 30 polyatomic molecules demonstrate a substantial improvement not only of the relative energies, but also of the total energies calculated with the NOF-MP2 method.

We present high-resolution data of the single-excitation spectrum of protactinium, reaching slightly beyond the first-ionization threshold. Within this work, more than 1500 energy levels are recorded in different excitation energy ranges below $50000{\mathrm{cm}}^{-1}$. Our experimental results show that the tabulated data in the literature severely underestimate the density of states particularly regarding the highly excited spectral range.

Recently, spectroscopic investigations of the protactinium atom applying resonant laser ionization spectroscopy revealed high-resolution data of the single-excitation spectrum of protactinium, reaching slightly beyond the first ionization potential [P. Naubereit et al., preceding paper, Phys. Rev. A 98, 022505 (2018)]. The more than 1500 recently detected energy levels contain several complete sequences of levels. In this work we study the spectral fluctuations of these data exhibiting clear signatures of intrinsic quantum chaos within the protactinium atom. In order to obtain an estimate on possibly missing levels, simulations were performed based on large ensembles of random matrices from the Gaussian orthogonal ensemble. Our experimental results show that tabulated data in the literature are far from completeness and atomic structure calculations severely underestimate the density of states in the spectral range of highly excited states. However, the statistical analysis of our data as well as of the data from literature and calculations predict a level statistics close to that of fully developed chaos at energies well below the single-ionization threshold.

The role of electron correlation in the hyperfine structure of alkali metals and alkaline earth metal monopositive ions in their ground electronic configuration is investigated using the Z-vector method in a relativistic coupled-cluster regime within the singles and doubles approximation. The systematic effects of core-correlating functions, polarization of core electrons, and high-lying virtual functions on core electrons correlation are studied. The study reveals that the core-correlating function plays a significant role in core polarization and thus is very important for precise calculation of the wave function near the nuclear region. The inner-core electrons (1s-2p) require very high virtual energy functions for proper correlation. Therefore, the all-electron correlation treatment and the inclusion of higher-energy virtual functions are the key factors for precise calculation of the hyperfine structure constant of atoms. Our calculated values are in excellent agreement with the available experimental values, which also implies that the wave function produced by the Z-vector method is accurate enough for further calculation of the parity- and time-reversal symmetry-violating properties in atoms and molecules.

Simultaneous ionization and excitation of helium by electron impact is studied through ejected electron angle integrated double-differential cross sections (DDCSs) as a function of ionized electron energy using the four-body distorted wave model. Results are presented for different alignments of the $2p0$ magnetic substate of the $\mathrm{H}{\mathrm{e}}^{+}$ ion, and alignment effects observed in fully differential cross sections are shown to persist in the DDCS. Examination of the DDCS for different orientations leads to a determination of anisotropy parameters and phase angles between substate amplitudes as a function of ejected electron energy.

We derive a variation equation for a time-dependent effective potential that is local both in time and in space and show that this potential generates and propagates spin orbitals with which a many-particle, time-dependent, multiconfigurational wave function $\mathrm{\Psi }\left(t\right)$ is constructed. Within this approach, the wave function and the effective potential are determined simultaneously in a self-consistent manner both in time-independent and in time-dependent cases. We also derive an equation that determines a real-valued effective potential and show that the equation establishes a relation among the first-order and second-order reduced density matrices and the electron repulsion integrals in the spin-orbital representation. By introducing the first-order density equation, we show that the variation equation for the effective potential can be simplified for an exact wave function. We also show that we can derive an effective potential with which a ground-state wave function that fulfills the Brillouin-Brueckner condition is constructed and that we can derive the effective potential proposed by Slater, with which a ground-state wave function represented by the multiconfiguration expansion is calculated, when an additional constraint is imposed on the varitation equation.

Based on the two-dimensional mean-field equations for pancake-shaped dipolar Bose-Einstein condensates in a rotating frame, for both attractive and repulsive dipole-dipole interaction (DDI) as well as arbitrary polarization direction, we study the profiles of the single vortex state and show how the critical rotational frequency changes with the $s$-wave contact interaction strength, DDI strength, and polarization angle. In addition, we find numerically that at the “magic angle” $\vartheta =arccos(\sqrt{3}/3)$, the critical rotational frequency is almost independent of the DDI strength. By numerically solving the dipolar Gross-Pitaevskii equation at high rotation speed, we identify different patterns of vortex lattices which strongly depend on the polarization direction. As a result, we undergo a study of vortex lattice structures for the whole regime of polarization direction and find evidence that the vortex lattice orientation tends to be aligned to the dipole polarization axis for positive DDI strength and to the perpendicular direction of the dipole axis for negative DDI strength.

By employing the equivalent of a knife-edge measurement for matter waves, we are able to characterize ultralow-momentum widths. We measure a momentum width corresponding to an effective temperature of $0.9\pm 0.2$ nK, limited only by our cooling performance. To achieve similar resolution using standard methods would require hundreds of milliseconds of expansion or Bragg beams with tens of Hz frequency stability. Furthermore, we show evidence of tunneling in a one-dimensional system when the “knife-edge” barrier is spatially thin. This method is a useful tool for atomic interferometry and for other areas in cold-atom physics where a robust and precise technique for characterizing the momentum distribution is crucial.

We present a systematic theoretical investigation of second-harmonic generation (SHG) in a subwavelength lithium niobate (LN) single-crystal thin-film waveguide with birefringence in permittivity and refractive index and strong anisotropy in the nonlinear susceptibility ${\chi }^{\left(2\right)}$. In a macroscopic birefringence LN crystal, the birefringence phase matching scheme that makes use of the refractive index management between the extraordinary light (EL) and ordinary light (OL) is dominantly used to ensure high-efficiency SHG. Yet, this scenario needs significant modification in a subwavelength LN thin film, where one should instead consider the waveguide modes of fundamental wave (FW) and second-harmonic wave (SHW) to participate in the SHG process. To this end, we first analytically solve and calculate the dispersion and modal profile of optical waveguide modes supported in the birefringence LN planar waveguide in a broad bandwidth ranging from ultraviolet to infrared regimes for TM (EL-like) and TE (OL-like) polarization states and at different waveguide thicknesses. Then we systematically examine the phase matching conditions that are necessary for high-efficiency energy conversion from FW waveguide mode to SHW waveguide mode via SHG. We find several modal phase matching schemes by exploiting the versatile freedoms of the FW and SHW waveguide mode number and polarization, and the waveguide thickness and symmetry. Yet modal phase matching only takes place at very limited discrete wavelengths of FW pump light. Under the modal phase matching condition, we derive the nonlinear coupled mode theory from Maxwell's equations and calculate the conversion efficiency of SHG, and find that the efficiency of SHG is determined by the nonlinear coupling coefficients that are closely associated with the modal profile overlap extent and mode transition strength between FW mode and SHW mode, and the involved nonlinear coefficient components of ${\chi }^{\left(2\right)}$. Finally, we have analytically derived the explicit formula that allows for direct calculation of the SHG efficiency as a function of the interaction length of FW mode and SHW mode, the nonlinear coupling coefficient, and the FW pump intensity, for both the small signal and general large signal situations. Our analytical theory and formulation can greatly facilitate the deep understanding of nonlinear optical interaction physics and provide a convenient tool for accurate quantitative evaluation of the SHG energy conversion efficiency of a pump laser in nanoscale LN single-crystal thin films. This analytical theory can also benefit for the design of nanoscale nonlinear optical devices based on the material platform of LN and other nonlinear crystal thin films.

We discuss level splitting and sideband transitions induced by a modulated coupling between a superconducting quantum circuit and a nanomechanical resonator. First, we show how to achieve an unconventional time-dependent longitudinal coupling between a flux (transmon) qubit and the resonator. Considering a sinusoidal modulation of the coupling strength, we find that a first-order sideband transition can be split into two. Moreover, under the driving of a red-detuned field, we discuss the optical response of the qubit for a resonant probe field. We show that level splitting induced by modulating this longitudinal coupling can enable two-color electromagnetically induced transparency (EIT), in addition to single-color EIT. In contrast to standard predictions of two-color EIT in atomic systems, we apply here only a single drive (control) field. The monochromatic modulation of the coupling strength is equivalent to employing two eigenfrequency-tunable mechanical resonators. Both drive-probe detuning for single-color EIT and the distance between transparent windows for two-color EIT can be adjusted by tuning the modulation frequency of the coupling.

The nonlinear interaction of two temporally separated solitons inside optical fibers has been studied in the scalar case in which both solitons remain linearly polarized during their mutual interaction. Here we consider two arbitrarily polarized vector solitons inside birefringent optical fibers where they interact nonlinearly. We develop a general formalism based on two coupled nonlinear Schrödinger equations that include both the Raman and the Kerr nonlinearities. We use it to study how the two vector solitons evolve in the temporal, spectral, and polarization domains in optical fibers exhibiting no, medium, or large birefringence. The attractive force that leads to collisions of two in-phase solitons in isotropic fibers is affected considerably by the fiber's birefringence. In particular, no collisions occur even in the case of medium birefringence. Rather, the two vector solitons exchange energy as they approach each other and then move away from each other. Moreover, considerably energy is shed in the form of dispersive waves. Polarization of the two solitons is found to be affected considerably by the fiber nonlinearity in the case of medium birefringence but linear effects dominate its evolution in fibers with large birefringence.

The correlations of certain entangled quantum states can be fully reproduced via a local model. We discuss in detail the practical implementation of an algorithm for constructing local models for entangled states, recently introduced by Hirsch et al. [Phys. Rev. Lett. 117, 190402 (2016)] and Cavalcanti et al. [Phys. Rev. Lett. 117, 190401 (2016)]. The method allows one to construct both local hidden state (LHS) and local hidden variable (LHV) models, and can be applied to arbitrary entangled states in principle. Here, we develop a systematic implementation of the algorithm, discussing the choice of the free parameters. For the case of two-qubit states, we design a ready-to-use procedure. This allows us to construct LHS models (for projective measurements) that are almost optimal, as we show for Bell diagonal states, for which the optimal model has recently been derived. Finally, we show how to construct fully analytical local models, based on the output of the convex optimization procedure.

The Casimir force between two parallel thick plates, one perfectly dielectric, the other purely magnetic, was calculated long ago by Boyer [T. H. Boyer, Phys. Rev. A 9, 2078 (1974)]. Its most characteristic property is that it is repulsive. The problem of this repulsive behavior is actually delicate and counterintuitive. In the present paper we analyze the problem by first considering the simple harmonic oscillator model introduced by us earlier [J. S. Høye et al., Phys. Rev. E 67, 056116 (2003); Phys. Rev. A 94, 032113 (2016)]. Extension of this model shows how the repulsive behavior can be understood on a microscopic basis, due to the duality between canonical and mechanical momenta in the presence of the electromagnetic vector potential. This duality corresponds to the transverse magnetic and transverse electric modes in electrodynamics. We analyze the generalized Boyer case where the permittivities and permeabilities of the parallel plates are arbitrary. In this respect we first find the induced interaction between a pair of particles with given electric and magnetic polarizabilities and then find it for a pair of parallel plates. The method used for our evaluations is the statistical mechanical one that we introduced and applied earlier. Whether the pair of particles or plates attract or repel each other depends on their polarizabilities or permittivities and permeabilities respectively. For equal particles or equal plates there is always attraction.

A combined experimental and theoretical study of superelastic electron collisions from laser-aligned magnesium atoms for a range of collision energies from 35 to 55 eV is presented. ${}^{24}\mathrm{Mg}$ atoms were excited from the $3{}^{1}S_0$ ground state to the $3{}^{1}P_1$ excited state using continuous-wave linearly polarized laser radiation at ∼285 nm. Electrons of well-defined energy $E_{\mathrm{inc}}$ then deexcited the targets, and the superelastically scattered electrons emerging from the collision were detected as a function of scattering angle and laser polarization. Results for alignment of the target by the electron beam are presented for a range of scattering angles, for outgoing energies from $E_{\mathrm{out}}=35$ to $55\mathrm{eV}$. The agreement between the measurements and the results of the convergent close-coupling theory are encouraging, but some discrepancies remain.

In the usual optomechanical cooling, even if the system has no thermal component, it still has a quantum limit—known as the quantum backaction limit (QBL)—on the minimum phonon number related to shot noise. By studying the side-band cooling regime in optomechanical systems (OMSs), we find that the cooling can be improved significantly when the frequency modulation (FM) that can suppress the Stokes heating processes is introduced into the system. We analyze and demonstrate the reasons of the phonon number below the QBL redefined in the whole stable region of the standard OMSs. The above analyses are further checked by numerically solving the differential equations of second-order moments derived from the quantum master equation with broad system parameters, ranging from weak coupling to ultrastrong coupling and resolved-side-band to unresolved-side-band regimes. Comparing with the cases of those without FM, the stable ground-state cooling can also be achieved even in the conventional unstable region.

We calculate signals of real photon-photon scattering in the collision of three laser pulses. Taking goal parameters from the Station of Extreme Light at the upcoming Shanghai Coherent Light Source, we consider two scenarios: (i) the collision of three optical pulses; (ii) the collision of an XFEL with two optical pulses. Our analysis uses the infinite Rayleigh-length approximation from previous work and is benchmarked against full numerical results. Although experimentally more difficult to perform, we find that colliding three laser pulses offers certain advantages in the detection of scattered photons by separating their frequency, momentum, and polarization from the background.