We present a detailed investigation of the supermultiplet structures for the intrashell resonances of ${\mathrm{H}}^{-}$, classified according to their approximate quantum numbers. The resonance energies and widths are calculated by employing the complex-scaling method with configuration-interaction basis functions, and our results are compared with previous available calculations. The complete $I$-supermultiplet structures are constructed for the intrashell resonances associated with the H ($N=2,$ 3, and 4) thresholds. They include the doubly excited states of ${\mathrm{H}}^{-}$ with a variety of configuration symmetries showing both Feshbach and shape types. It is found that the ${\mathrm{H}}^{-}$ ($N=4$) supermultiplet has upper portions exceeding the H ($N=5$) threshold. This phenomenon should be useful in predicting the supermultiplet structures associated with higher-lying thresholds.

The energy spectrum, atom-dimer scattering length, and atom-trimer scattering length for systems of three and four ultracold atoms with $\delta$-function interactions in one dimension are presented as a function of the relative mass ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat three-body (“HHL”) systems of one light and two heavy atoms, as well as four-body (“HHHL”) systems of one light and three heavy atoms. Zero-range interactions of arbitrary strength are assumed between different atoms, but the heavy atoms are assumed to be noninteracting among themselves. Fermionic and bosonic heavy atoms with both positive and negative parity are considered.

In this work, we define single-particle potentials for a positron and a positronium atom interacting with light atoms (H, He, Li, and Be) by inverting a single-particle Schrödinger equation. For this purpose, we use accurate energies and positron densities obtained from the many-body wave function of the corresponding positronic systems. The introduced potentials describe the exact correlations for the calculated systems including the formation of a positronium atom. We show that the scattering lengths and the low-energy $s$-wave phase shifts from accurate many-body calculations are well accounted for by the introduced potential. We also calculate self-consistent two-component density-functional-theory positron potentials and densities for the bound positronic systems within the local-density approximation. They are in a very good agreement with the many-body results, provided that the finite-positron-density electron-positron correlation potential is used, and they can also describe systems comprising a positronium atom. We argue that the introduced single-particle positron potentials defined for single molecules are transferable to the condensed phase when the intermolecular interactions are weak. When this condition is fulfilled, the total positron potential can be constructed in a good approximation as the superposition of the molecular potentials.

We investigate theoretically the ionization dynamics of $\text{H}\left(2s\right)$ and $\text{H}(2p$${}_0)$ by short midinfrared laser pulses in the over-barrier ionization (OBI) regime. Through the numerical solution to the time-dependent Schrödinger equation, we calculate the differential and angular distributions of photoelectrons as well as the total ionization probability. In a wide range of laser intensities and wavelengths, significant differences are found between the $\text{H}\left(2s\right)$ and $\text{H}(2p$${}_0)$ states in both the differential and total ionization yields. Analysis of the excitation dynamics reveals that both the low-lying excited states and the Rydberg states are significantly populated for a 1200-nm laser. As the laser wavelength gradually increases to 2100 nm, the population on the low-lying excited state drastically decreases. We observe the population of the Rydberg states oscillates as a function of the laser peak intensity, which gradually disappears when the Keldysh parameter $\gamma$ decreases. As the laser intensity increases further, the total ionization probability and the population of the Rydberg states stay almost the same, which is related to the partial stabilization phenomena recently confirmed in experiments. In the deep OBI regime, we find that this kind of ionization suppression is more obvious in the 2$s$ state than in the 2$p$${}_0$ state. We also compare the transverse momentum distributions of the electrons ionized from the two states and find the effect of the Coulomb potential is stronger in the 2$p$${}_0$ state than that in the 2$s$ state, which is due to the different initial electron distributions.

We investigate the drag force on a moving impurity in a spin-orbit-coupled Bose-Einstein condensate. We prove rigorously that the superfluid critical velocity is zero when the impurity moves in all directions but one, in contrast to the case of liquid helium and superconductor, where it is finite in all directions. We also find that when the impurity moves in all directions except the two special ones, the drag force has nonzero transverse component with a small velocity. When the velocity becomes large and the states of the upper band are also excited, the transverse force becomes very small due to opposite contributions of the two bands. The characteristics of the superfluid critical velocity and the transverse force are results of the order-by-disorder mechanism in spin-orbit-coupled boson systems.

The existence regimes and dynamics of soliton molecules in dispersion-managed (DM) optical fibers have been studied. Initially we develop a variational approximation to describe the periodic dynamics of a soliton molecule within each unit cell of the dispersion map. The obtained system of coupled equations for the pulse width and chirp allows to find the parameters of DM soliton molecules for the given dispersion map and pulse energy. Then by means of a scaling transformation and averaging procedure we reduce the original nonlinear Schrödinger equation (NLSE) with piecewise-constant periodic dispersion to its counterpart with constant coefficients and additional parabolic potential. The obtained averaged NLSE with expulsive potential can explain the essential features of solitons and soliton molecules in DM fibers related to their energy loss during propagation. Also, the model of averaged NLSE predicts the instability of the temporal position of the soliton, which may lead to difficulty in holding the pulse in the middle of its time slot. All numerical simulations are performed using the parameters of the existing DM fiber setup and illustrated via pertinent examples.

Electron vortex beams have been predicted to enable atomic scale magnetic information measurement, via transfer of orbital angular momentum. Research so far has focused on developing production techniques and applications of these beams. However, methods to measure the outgoing orbital angular momentum distribution are also a crucial requirement towards this goal. Here, we use a method to obtain the orbital angular momentum decomposition of an electron beam, using a multipinhole interferometer. We demonstrate both its ability to accurately measure orbital angular momentum distribution, and its experimental limitations when used in a transmission electron microscope.

In this preliminary Brief Report we explore a method for examining relativistic effects in one-electron molecules that avoids the evaluation of multicenter integrals. Here the Dirac equation for a simplified version of the ${{\mathrm{H}}_2}^{+}$ ion is solved exactly for the ground-state Schrödinger and Dirac energy levels. The model consists of representing the electron-proton Coulomb interaction as a projection operator onto a linear subspace of Hilbert space.

We argue for an operational requirement that all state-dependent measures of disturbance should satisfy. Motivated by this natural criterion, we prove that in any $d$-dimensional Hilbert space and for any pair of noncommuting operators, $A$ and $B$, there exists a set of at least $2^{d-1}$ zero-noise, zero-disturbance (ZNZD) states, for which the first observable can be measured without noise and the second will not be disturbed. Moreover, we show that it is possible to construct such ZNZD states for which the expectation value of the commutator $[A,B]$ does not vanish. Therefore any state-dependent error-disturbance relation, based on the expectation value of the commutator as a lower bound, must violate the operational requirement. We also discuss Ozawa's state-dependent error-disturbance relation in light of our results and show that the disturbance measure used in this relation exhibits unphysical properties. We conclude that the trade-off is inevitable only between state-independent measures of error and disturbance.

State and measurement tomography make assumptions about the experimental states or measurements. These assumptions are often not justified because state preparation and measurement errors are unavoidable in practice. Here we describe how the Gram matrix associated with the states and measurement operators can be estimated via semidefinite programming if the states and the measurements are so-called globally completable. This is, for instance, the case if the unknown measurements are known to be projective and nondegenerate. The computed Gram matrix determines the states, and the measurement operators uniquely up to simultaneous rotations in the space of Hermitian matrices. We prove the reliability of the proposed method in the limit of a large number of independent measurement repetitions.

Detection of radiation signals is at the heart of precision metrology and sensing. In this article we show how the fluctuations in photon-counting signals can be exploited to optimally extract information about the physical parameters that govern the dynamics of the emitter. For a simple two-level emitter subject to photon counting, we show that the Fisher information and the Cramér-Rao sensitivity bound based on the full detection record can be evaluated from the waiting-time distribution in the fluorescence signal which can, in turn, be calculated for both perfect and imperfect detectors by a quantum trajectory analysis. We provide an optimal estimator achieving that bound.

Observables with a continuous spectrum are known to fundamentally differ from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for discrete variables have been translated to continuous ones, this is not the case in general. Here we show that it is possible to manipulate, detect, and classify continuous-variable states using observables with a continuous spectrum revealing properties and symmetries which are analogous to finite discrete systems. Our approach leads to an operational way to define, and adapt, to arbitrary continuous quantum systems, quantum protocols, and algorithms developed for discrete systems.

We propose a scheme for transferring entanglement from one photonic degree of freedom to another through Raman interactions between a photon pair in cavity modes and atomic ensemble. The condition for deterministically generating the entanglement encoded in frequency or both frequency and polarization is obtained. The scheme could be immune to the photon loss originating from cavity-mode damping, spontaneous emission, and the dephasing due to atomic thermal motion. For current techniques, there are no major difficulties for this scheme to be realized experimentally.

We extend the recent result of a bipartite Bell singlet [A. W. Carr and M. Saffman, Phys. Rev. Lett. 111, 033607 (2013)] to a stationary three-dimensional entanglement between two-individual neutral Rydberg atoms. This proposal makes full use of the coherent dynamics provided by a Rydberg-mediated interaction and the dissipative factor originating from the spontaneous emission of a Rydberg state. The numerical simulation of the master equation reveals that both the target state negativity $\mathcal{N}\left({\widehat{\rho }}_{\infty }\right)$ and fidelity $\mathcal{F}\left({\widehat{\rho }}_{\infty }\right)$ can exceed 99.90%. Furthermore, a steady three-atom singlet state $|S_3\rangle$ is also achievable based on the same mechanism.

We provide a recurrent construction of entanglement witnesses for a bipartite systems living in a Hilbert space corresponding to $2N$ qubits ($N$ qubits in each subsystem). Our construction provides a method of generalization of the Robertson map that naturally meshes with $2N$-qubit systems, i.e., its structure respects the $2^{2N}$ growth of the state space. We prove that for $N>1$ these witnesses are indecomposable and optimal. As a byproduct we provide a family of PPT (Positive Partial Transpose) entangled states.

Density functional approximations to the exchange-correlation energy of the Kohn-Sham theory, such as the local density approximation and generalized gradient approximations, lack the well-known integer discontinuity, a feature that is critical to describe molecular dissociation correctly. Moreover, standard approximations to the exchange-correlation energy also fail to yield the correct linear dependence of the ground-state energy on the number of electrons when this is a noninteger number obtained from the grand canonical ensemble statistics. We present a formal framework to restore the integer discontinuity of any density functional approximation. Our formalism derives from a formula for the exact energy functional and a constrained search functional that recovers the linear dependence of the energy on the number of electrons.

Total and partial fluorescence yield (PFY) $L$-edge x-ray absorption spectra differ from the transmission x-ray absorption spectra (XAS) through state-dependent fluorescence yield across the XAS. For $3d^1$ to $3d^9$ in octahedral symmetry we apply simulations of PFY and XAS and show how the atomic $2p3d$ Coulomb exchange parameter $G_{pd}$ governs the differences in the $L_3/(L_2+L_3$) branching ratio between PFY and XAS. $G_{pd}$ orders the XAS final states following Hund's rules creating a strong state-dependent fluorescence decay strength variation across the XAS leading to the differences between PFY and XAS.

Widths of $K{L}_{2,3}$ atomic levels for Ca, Fe, and Zn have been calculated in a fully relativistic way using the extensive multiconfiguration Dirac-Fock and modified Dirac-Hartree-Slater calculations. The study of de-excitation of the $K^{-1}{L}_{2,3}^{-1}$ hole state has been presented. Additionally, the approximation to $K{L}_{2,3}$ level widths has been examined.

We consider the interaction between a spherical plasma sheet and a planar plasma sheet due to the vacuum fluctuations of electromagnetic fields. We derive the TGTG formula for the Casimir interaction energy and study its asymptotic behaviors. In the small separation regime, we confirm the proximity force approximation and calculate the first correction beyond the proximity force approximation. This study has potential application to model Casimir interaction between objects made of materials that can be modeled by plasma sheets such as graphene sheets.

The collision cross section that controls thermalization of gas mixtures is the transport cross section ${\sigma }_{\eta }^{\left(1\right)}$ and not the elastic cross section ${\sigma }_{\mathrm{el}}$. The two are the same for pure $s$-wave scattering but not when higher partial waves contribute. We investigate the differences between them for prototype atomic mixtures and show that the distinction is important at energies above $100\mu \mathrm{K}$ for LiYb and $3\mu \mathrm{K}$ for RbYb and RbCs. For simple systems, both ${\sigma }_{\eta }^{\left(1\right)}$ and ${\sigma }_{\mathrm{el}}$ follow universal energy dependence that depends only on the $s$-wave scattering length when expressed in reduced length and energy units.