The hyperspherical harmonic basis is used to describe bound states in an $A$-body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this representation, the matrix elements between the basis elements are simple, and the potential energy is presented in a compact form well suited for numerical implementation. The basis is neither symmetrized nor antisymmetrized, as required in the case of identical particles; however, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it and the identification of the physical states is possible, as it will be shown in specific cases. We have in mind applications to atomic, molecular, and nuclear few-body systems in which symmetry-breaking terms are present in the Hamiltonian; their inclusion is straightforward in the present method. As an example, we solve the case of three and four particles interacting through a short-range central interaction and Coulomb potential.

X-ray atomic absorption of iodine in the energy region of the $K$ edge is determined from the absorption of iodine vapor at temperatures up to $1000°\text{C}$ with appreciable dissociation of the molecular species. Kinetics of dissociation, relevant for isolation of the absorption of the atomic species, is discussed. The atomic signal is obtained as a linear combination of the highest-temperature absorption spectra at two vapor densities; the coefficients of the combination are determined from extended x-ray absorption fine structure (EXAFS) analysis of the molecular signal. Photoexcitation channels are identified in the $K$-edge profile and in the spectral features originating from multielectron excitations. The applicability of the atomic absorption as the true absorption background for EXAFS analysis is demonstrated.

Ultracold atoms are increasingly used for high-precision experiments that can be utilized to extract accurate scattering properties. This results in a stronger need to improve on the accuracy of interatomic potentials, and in particular the usually rather inaccurate inner-range potentials. A boundary condition for this short range can be conveniently given via the accumulated phase method. However, in this approach one should satisfy three conditions, two of which are in principle conflicting, and the validity of these approximations comes under stress when higher precision is required. We show that a better compromise between the two is possible by allowing for an adiabatic change in the hyperfine mixing of singlet and triplet states for interatomic distances smaller than the separation radius. Results we presented previously in a brief publication using this method show a high precision and extend the set of predicted quantities. The purpose of this paper is to describe its background. A mass-scaling approach to relate accumulated phase parameters in a combined analysis of isotopically related atom pairs is described in detail and its accuracy is estimated, taking into account both Born-Oppenheimer and Wentzel-Kramers-Brillouin breakdown. We demonstrate how numbers of singlet and triplet bound states follow from the mass scaling.

The $R$-matrix method is used to calculate the elastic integral, differential, momentum transfer cross sections, and the excitation cross sections from the ground state $X{{}^{2}A}_1$ to the five low-lying electronically excited states $A{{}^{2}B}_1$, $B{{}^{2}B}_2$, $C{{}^{2}A}_2$, ${{}^{4}A}_2$, and ${{}^{4}B}_2$ of the ${\text{NO}}_2$ radical. Twenty-one target states are included in the close-coupling expansion of the scattering system, where each target state is represented by configuration-interaction wave function. The calculations give two shape resonances of ${{}^{3}B}_1$ and ${{}^{1}B}_1$ symmetries located at 1.18 and 2.33 eV, respectively, with a common configuration $6a_{1}2b_1$. We also detect eight core-excited shape resonances and one Feshbach resonance. Partial elastic, total, and electronic excitation cross sections are presented and compared with the limited previous work. The dissociative nature of the ${{}^{3}B}_1$ and ${{}^{1}B}_1$ shape resonances is explored by performing scattering calculations in which one N-O bond is stretched while the other bond and the bonding angle are frozen. These resonances support dissociative attachment yielding NO and ${\text{O}}^{-}$ in their respective ground states.

We investigate in detail the focusing of a circularly polarized Laguerre-Gaussian laser beam [$\hslash \ell$ orbital angular momentum per photon; $\sigma =1\left(-1\right)$ for left- (right-) handed polarization] by a high-numerical-aperture objective. The diffraction-limited focused beam has unexpected properties resulting from a strong interplay between the angular spatial structure and the local polarization in the nonparaxial regime. In the region near the beam axis, and provided that $\left|\ell \right|\ge 2$ and $\ell$ and $\sigma$ have opposite signs, the energy locally counterpropagates and the projection of the electric field onto the focal plane counter-rotates with respect to the circular polarization of the incident beam. We explicitly show that the total angular momentum flux per unit power is conserved after focusing, as expected by rotational symmetry, but the spin and orbital separate contributions change.

An engineering technique using continuous quantum measurement in conjunction with feed forward is proposed to improve indistinguishability of a single-photon source. The technique involves continuous monitoring of the state of the emitter, processing the noisy output signal with a simple linear estimation algorithm, and feed forward to control a variable delay at the output. In the weak-coupling regime, the information gained by monitoring the state of the emitter is used to reduce the time uncertainty inherent in photon emission from the source, which improves the indistinguishability of the emitted photons.

Optical signals obtained by the material response to classical laser fields are given by nonlinear response functions which can be expressed by sums over various quantum pathways of matter. We show that some pathways can be selected by using nonclassical fields, through the entanglement of photon and material pathways, which affects the power-law dependence on the incoming field intensity. Spectrally overlapping stimulated Raman scattering and two-photon-absorption pathways in a pump-probe experiment are separated by controlling the degree of entanglement of pairs of incoming photons. Pathway selectivity opens up new avenues for mapping photon into material entanglement. New material information, otherwise erased by interferences among pathways, is revealed.

We propose a scheme enabling the universal coupling of angular momentum of $N$ remote noninteracting qubits using linear optical tools only. Our system consists of $N$ single-photon emitters in a $\Lambda$ configuration that are entangled among their long-lived ground-state qubits through suitably designed measurements of the emitted photons. In this manner, we present an experimentally feasible algorithm that is able to generate any of the $2^N$ symmetric and nonsymmetric total angular momentum eigenstates spanning the Hilbert space of the $N$-qubit compound.

The cold atom on a two-dimensional square optical lattice is studied within the hard-core boson Hubbard model with an alternating potential. In terms of the quantum Monte Carlo method, it is shown explicitly that a supersolid phase emerges due to the presence of the alternating potential. For the weak alternating potential, the supersolid state appears for the whole range of hard-core boson densities except the half-filling case, where the system is a Mott insulator. However, for the strong alternating potential, besides the supersolid and Mott insulating states, a charge-density wave phase appears.

Global conservation laws imply superselection rules (SSRs) which restrict the operations that are possible on any given state. Imposing the additional constraint of local operations and classical communication forbids the transfer of quantum systems between spatially separated sites. In the case of particle conservation this imposes a SSR for local particle number. That is, the coherences between subspaces of fixed particle number at each site are not accessible and any state is therefore equivalent to its projection onto these subspaces. The accessible entanglement under the SSR is less than (or equal to) that available in the absence of the SSR. An ancilla can be used as a reference system to increase the amount of accessible entanglement. We examine the relationship between local-particle-number uncertainty and the accessible entanglement and consider the optimal reference states for recovering entanglement from certain systems. In particular we derive the optimal ancilla state for extracting entanglement for a single-shared particle and make steps toward the optimum for general systems. We also show that a reference for phase angle is fundamentally different to a reference for the SSR associated with particle conservation.

We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the detection operators associated with the two different conclusive outcomes does not exceed unity, we obtain a general solution. As an application, we consider the discrimination of two mixed qubit states. Moreover, for the case of higher-rank detection operators we give a solution for particular states. The relation of the optimized measurement to other discrimination schemes is also discussed.

A suitable NMR experiment in a one-dimensional dipolar coupled spin system allows one to reduce the natural many-body dynamics into effective one-body dynamics. We verify this in a polycrystalline sample of hydroxyapatite (HAp) by monitoring the excitation of NMR many-body superposition states: the multiple-quantum coherences. The observed effective one-dimensionality of HAp relies on the quasi-one-dimensional structure of the dipolar coupled network that, as we show here, is dynamically enhanced by the quantum Zeno effect. Decoherence is also probed through a Loschmidt echo experiment, where the time reversal is implemented on the double-quantum Hamiltonian, ${\mathcal{H}}_{DQ}\propto I_i^{+}{I}_j^{+}+I_i^{-}{I}_j^{-}$. We contrast the decoherence of adamantane, a standard three-dimensional system, with that of HAp. While the first shows an abrupt Fermi-type decay, HAp presents a smooth exponential law.

Wavelengths, transition rates, and line strengths are calculated for the multipole (E1, M1, E2, M2, and E3) transitions between the excited $\left[\mathrm{Xe}\right]4f^{13}ns$, $\left[\mathrm{Xe}\right]4f^{13}nd$, and $\left[\mathrm{Xe}\right]4f^{13}np$ and the ground $\left[\mathrm{Xe}\right]4f^{14}$ state in Yb III ion with the nuclear charge $Z=70$ $(\left[\mathrm{Xe}\right]=\left[\mathrm{Ni}\right]4s^{2}4p^{6}4d^{10}5s^{2}5p^6)$. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in this hole-particle system. This method is based on the relativistic many-body perturbation theory that agrees with multiconfiguration Dirac-Fock calculations in lowest-order, includes all second-order correlation corrections, and includes corrections from negative energy states. The calculations start from a $\left[\mathrm{Xe}\right]4d^{14}$ Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. Evaluated multipole matrix elements for transitions from excited states into the ground states and transitions between excited states are used to determine the lifetime of the 20 $\left[\mathrm{Xe}\right]4f^{13}5d\left(J\right)$ levels, four $\left[\mathrm{Xe}\right]4f^{13}6s\left(J\right)$ levels, 12 $\left[\mathrm{Xe}\right]4f^{13}6p\left(J\right)$ levels, and four $\left[\mathrm{Xe}\right]4f^{13}7s\left(J\right)$ levels.

We propose an easy to use model for interacting atoms in an optical lattice. This model allows for the whole range of weakly to strongly interacting atoms, and it includes the coupling between relative and center-of-mass motions via anharmonic lattice terms. We apply this model to a high-precision spin-dynamics experiment, and we discuss the corrections due to atomic interactions and the anharmonic coupling. Under suitable experimental conditions, energy can be transferred between the relative and center-of-mass motions, and this allows for creation of Feshbach molecules in excited lattice bands.

The $M$-shell ionization in high-$Z$ atoms by ${\text{O}}^{q+}$ ions have been studied systematically in the energy range of 8.0–35.2 MeV in order to verify the available theoretical approaches describing the $M$-shell ionization by charged particles in asymmetric collisions. The measured $M$ x-ray spectra were analyzed taking into account the effects of x-ray line shifting and broadening caused by the multiple ionization in the $M$ and $N$ shells. The $M$-subshell ionization cross sections, derived by using the $M$-shell decay rates modified for the multiple ionization effects, have been compared with the theoretical predictions based on the plane-wave Born approximation (PWBA), the semiclassical approximation (SCA), and the binary-encounter approximation (BEA). In the PWBA approach two theoretical calculations were considered: the energy-loss Coulomb deflection perturbed stationary state relativistic (ECPSSR) theory and its recent modification called the energy-loss Coulomb deflection united and separated atoms relativistic (ECUSAR) theory, which corrects a description of the electron binding effect to account for the united and separated atoms (USA) electron binding energy limits. In the SCA calculations performed with relativistic hydrogenic wave functions the binding effect was included in the limiting cases of separated-atom (SA) and united-atom (UA) limits. The measured $M$-subshell ionization cross sections are the best reproduced by the SCA-UA calculations, with exception of the $M_{2,3}\left(3p\right)$-subshell cross sections which are strongly enhanced and cannot be reproduced by the discussed calculations.

We perform quantum-mechanically exact calculations of resonances in the spectrum of the hydrogen atom in crossed external fields and establish a close connection between the classical transition state in phase space and features in the quantum spectrum. By varying the external field strengths, structures are revealed which are surprisingly similar to the quantized energy levels of the classical electron motion in the vicinity of the saddle point obtained with an approximation of the potential. The results give clear evidence for signatures of the transition state in quantum spectra.

We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely, a Mott insulator in the paramagnetic and antiferromagnetic phases, and a putative $d$-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultracold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We argue that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are easier to observe in the attractive Hubbard mode as a band insulator of Cooper pairs and superfluid phase, respectively. The putative $d$-wave superfluid phase of the repulsive Hubbard model doped away from half filling is related to a $d$-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to “quantum simulate” the Hubbard model in an optical lattice over the simulation of the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.

We propose a scheme for realizing controlled multiqubit quantum phase gates via the adiabatic evolution for trapped ions. Leveraging on the adiabatic operation, the scheme is tolerant to ambient noise and insensitive to the randomness of moderate fluctuations in experimental parameters. In our scheme, the ions are illuminated by lasers tuned to the first lower vibrational sideband or quasiresonant transition, the vibrational mode is not utilized as a data bus, and dark state evolution is required. The required gate operation time does not increase with the increasing number of qubits. This leads to a more efficient implementation of multiqubit gates than that of a series of one-qubit and two-qubit operations for quantum circuits and quantum algorithms.

We investigate the question of optimal input ensembles for memory channels and construct a rather large class of Pauli channels with correlated noise, which can be studied analytically with regard to the entanglement of their optimal input ensembles. In a more detailed study of a subclass of these channels, the complete phase diagram of the two-qubit channel, which shows three distinct phases, is obtained. While increasing the correlation generally changes the optimal state from separable to maximally entangled states, this is done via an intermediate region where both separable and maximally entangled states are optimal. A more concrete model, based on random rotations of the error operators which mimic the behavior of this subclass of channels, is also presented.

We derive analytical upper bounds for the entanglement of generalized Greenberger-Horne-Zeilinger states coupled to locally depolarizing and dephasing environments and for local thermal baths of arbitrary temperature. These bounds apply for any convex quantifier of entanglement, and exponential entanglement decay with the number of constituent particles is found. The bounds are tight for depolarizing and dephasing channels. We also show that randomly generated initial states tend to violate these bounds and that this discrepancy grows with the number of particles.