A one-dimensional model of bosons with repulsive short-range interactions, solved analytically by Lieb and Liniger many years ago, predicts the existence of two branches of elementary excitations. One of them represents Bogoliubov phonons; the other, as suggested by some authors, might be related to dark solitons. On the other hand, it has been already demonstrated within the framework of the classical field approximation that a quasi-one-dimensional interacting Bose gas at equilibrium exhibits excitations which are phonons and dark solitons. By showing that for lower temperatures statistical distributions of dark solitons obtained within the classical field approximation are well represented by the distributions of quasiparticles of the second kind derived from fully quantum description, we demonstrate that type II excitations in the Lieb-Liniger model are, indeed, quantum solitons.

Dynamics of solitons in a one-dimensional trap with motionless and moving walls is studied by the example of bright solitons of an atomic Bose-Einstein condensate. Newton-type equations of the soliton's center motion are proposed and analyzed, and regimes of periodic, almost-periodic, and deterministically chaotic dynamics are presented. The predictions based on these approximate equations are in excellent agreement with that based on the Gross-Pitaevskii equation in the case of sufficiently narrow and slow solitons.

We study quantum coherence properties of a dilute gas at temperatures above, but not much above, the transition temperature of Bose-Einstein condensation. In such a gas, a small proportion of the atoms may possess coherence lengths longer than the mean neighboring-atomic distance, implying the existence of quantum coherence greater than that expected for thermal atoms. Conjecturing that a part of this proportion of the atoms may lie in a coherently condensed state, some unexplained experimental results [D. E. Miller et al., Phys. Rev. A 71, 043615 (2005)] can be explained.

We report on the production of a degenerate Fermi gas of ${}^{53}\mathrm{Cr}$ atoms, polarized in the state $F=9/2, m_F=-9/2$, by sympathetic cooling with bosonic $S=3,m_S=-3 {}^{52}\mathrm{Cr}$ atoms. We load in an optical dipole trap $3\times {10}^4{}^{53}\mathrm{Cr}$ atoms with ${10}^6 {}^{52}\mathrm{Cr}$ atoms. Despite the initial small number of fermionic atoms, we reach a final temperature of $T\simeq 0.6\times T_f$ (Fermi temperature), with up to ${10}^3 {}^{53}\mathrm{Cr}$ atoms. This surprisingly efficient evaporation stems from an interisotope scattering length $|a_{BF}|=80(\pm 10)a_B$ (Bohr radius) which is small enough to reduce evaporative losses of the fermionic isotope, but large enough to assure thermalization.

We show that the origin of the nonequivalence of Hamiltonians in different representations is a change of the form of the time-derivative operator at a time-dependent unitary transformation. This nonequivalence does not lead to an ambiguity of the energy expectation values of a particle in nonstationary fields but assigns the basic representation. It has been explicitly or implicitly supposed in previous investigations that this representation is the Dirac one. We prove the alternative assertion about the basic role of the Foldy-Wouthuysen representation. We also derive the general equation for the energy expectation values in the Dirac representation. As an example, we consider a spin-1/2 particle with anomalous magnetic and electric dipole moments in strong time-dependent electromagnetic fields. We apply the obtained results to a spin-1/2 particle in a plane monochromatic electromagnetic wave and give an example of the exact Foldy-Wouthuysen transformation in the nonstationary case.

The multipartite entangled state has drawn broad attention for both foundations of quantum mechanics and applications in quantum information processing. Here, we study the spatially separated $N$-partite continuous-variable Greenberger-Horne-Zeilinger–like states, which can be produced by a linear optical network with squeezed light and $N-1$ beamsplitters. We investigate the properties of multipartite Einstein-Podolsky-Rosen steering possessed by those states, and find that the steering of a given quantum mode is allowed when not less than half of the modes within the states take part in the steering group. This is certified by the detection of the correlation between position and momentum quadratures of the steered mode and a combination of quadratures of other modes inside the steering group. The steering is evidenced by the high correlation where the steering group can infer the quadratures of the steered mode to high precision, i.e., below the quantum limit for the position and momentum quadratures of the steered quantum mode. We also examine the influence of inefficiency on the multipartite steering, and derive the threshold of the loss tolerance. Furthermore, we discuss the collective $N$-partite steering induced by the asymmetric loss on beams, which exists when a given quantum mode can only be steered by all the remaining $N-1$ modes collaboratively. The present multipartite steering correlation may have potential applications in certain quantum information tasks where the issue of trust is important, such as one-sided device-independent quantum secret sharing.

Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of constructing a joint probability distribution for all values of all the different properties observed in Bell inequality tests. Physically, the impossibility of measuring such a distribution experimentally, as a set of relative frequencies, is due to the quantum back-action of projective measurements. Weakly coupling to a quantum probe, however, produces minimal back-action, and so enables a weak measurement of the projector of one observable, followed by a projective measurement of a noncommuting observable. By this technique it is possible to empirically measure weak-valued probabilities for all of the values of the observables relevant to a Bell test. The marginals of this joint distribution, which we experimentally determine, reproduces all of the observable quantum statistics including a violation of the Bell inequality, which we independently measure. This is possible because our distribution, like the weak values for projectors on which it is built, is not constrained to the interval $[0,1]$. It was first pointed out by Feynman that, for explaining singlet-state correlations within “a [local] hidden variable view of nature … everything works fine if we permit negative probabilities.” However, there are infinitely many such theories. Our method, involving “weak-valued probabilities,” singles out a unique set of probabilities, and moreover does so empirically.

The “Lewis-Riesenfeld phases” which play a crucial role in constructing shortcuts to adiabaticity may be a resource for the implementation of quantum phase gates. By combining “Lewis-Riesenfeld invariants” with “quantum Zeno dynamics,” we propose an effective scheme of rapidly implementing $\pi$ phase gates via constructing shortcuts to adiabatic passage in a two-distant-atom-cavity system. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity is discussed. It is noted that this scheme is insensitive to both error sources. Additionally, a creation of $N$-atom cluster states is put forward as a typical example of the applications of the fast and noise-resistant phase gates. The study results show that the shortcuts idea is not only applicable in other logic gates with different systems, but also propagable for many quantum information tasks.

Based on the mutually unbiased bases, the mutually unbiased measurements and the general symmetric informationally complete positive-operator-valued measures, we propose three separability criteria for $d$-dimensional bipartite quantum systems, which are more powerful than the corresponding ones introduced previously [C. Spengler, M. Huber, S. Brierley, T. Adaktylos, and B. C. Hiesmayr, Phys. Rev. A 86, 022311 (2012); B. Chen, T. Ma, and S. M. Fei, Phys. Rev. A 89, 064302 (2014); and B. Chen, T. Li, and S. M. Fei, arXiv:1406.7820v1 [quant-ph] (2014)]. Some states such as Werner states and Bell-diagonal states are used to further illustrate the efficiency of the presented criteria.

The radiative lifetime of the $4s^{2}4p^4{}^1{S}_0$ metastable state in $\mathrm{K}{\mathrm{r}}^{2+}$ ions has been experimentally determined using an electrostatic ion trap of the ion-beam storage type. The radiative lifetime was obtained by measuring the number of 350-nm photons emitted during the ${}^1{S}_0{\to }^3{P}_1$ magnetic dipole transition of $\mathrm{K}{\mathrm{r}}^{2+}$ as a function of the storage time. The storage lifetime of the $\mathrm{K}{\mathrm{r}}^{2+}$ beam in the trap, which is a correction term in the determination of the radiative lifetime, was measured by detecting Kr neutrals produced by electron capture collisions with residual gases in the trap. We have obtained a lifetime value of $17.4\pm 0.4\mathrm{ms}$, which is larger than the previous experimental results, but consistent with theoretical predictions.

The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method has shown promise in calculating electronic dynamics in molecules driven by strong and high-energy lasers. It must incorporate restricted configuration spaces (meaning that a particular combination of Slater determinants is used, instead of full configuration interaction) to be applied to big systems. Two different Ansätze are used to determine the essential term in the equations. The first Ansatz is the Lagrangian variational principle. The explicit, complete MCTDHF equations of motion, satisfying that principle, for arbitrary configuration spaces, are given. The property that a restricted configuration list must satisfy in order for the Lagrangian and McLachlan variational principles to give different results is identified. The second Ansatz keeps the density matrix block diagonal among equivalent orbitals, in a generalization of the method of Worth [J. Chem. Phys. 112, 8322 (2000)]. The methods perform well in calculating the dynamics of Be and ${\mathrm{BC}}^{2+}$ subject to ultrafast, ultrastrong lasers in severely truncated Hilbert spaces, although they exhibit differing degrees of numerical stability as implemented.

In this paper we present results of ab initio calculations for the beryllium dimer with a basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled-cluster correction for inner-shell effects. We have developed STO basis sets, ranging in quality from double to sextuple $\zeta$, which are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order ${\alpha }^2$ are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the electronic binding energy of the beryllium dimer is determined to be $929.0\pm 1.9{\text{cm}}^{-1}$, in a very good agreement with the recent experimental value.

Calculation of the differential cross section for dielectronic recombination with one-electron uranium within the framework of quantum electrodynamics is presented. The dielectronic recombination of nonpolarized and polarized incident electrons is considered. The polarization of the emitted photon is investigated. The contributions of the Breit interaction and the interference of the photon multipoles are studied.

A first principles study of the dynamics of ${}^6\mathrm{Li}\left({}^{2}S\right)+{}^6\mathrm{Li}{}^{174}\mathrm{Yb}\left({}^2{\Sigma }^{+}\right){\to }^6{\mathrm{Li}}_2{(}^1{\Sigma }^{+})\hspace{0.17em}+\hspace{0.17em}{}^{174}\mathrm{Yb}({}^{1}S)$ reaction is presented at cold and ultracold temperatures. The computations involve determination and analytic fitting of a three-dimensional potential energy surface for the ${\mathrm{Li}}_2\mathrm{Yb}$ system and quantum dynamics calculations of varying complexities, ranging from exact quantum dynamics within the close-coupling scheme, to statistical quantum treatment, and universal models. It is demonstrated that the two simplified methods yield zero-temperature limiting reaction rate coefficients in reasonable agreement with the full close-coupling calculations. The effect of the three-body term in the interaction potential is explored by comparing quantum dynamics results from a pairwise potential that neglects the three-body term to that derived from the full interaction potential. Inclusion of the three-body term in the close-coupling calculations was found to reduce the limiting rate coefficients by a factor of two. The reaction exoergicity populates vibrational levels as high as $v=19$ of the ${}^6\mathrm{Li}{}_2$ molecule in the limit of zero collision energy. Product vibrational distributions from the close-coupling calculations reveal sensitivity to inclusion of three-body forces in the interaction potential. Overall, the results indicate that a simplified model based on the long-range potential is able to yield reliable values of the total reaction rate coefficient in the ultracold limit but a more rigorous approach based on statistical quantum or quantum close-coupling methods is desirable when product rovibrational distribution is required.

We present measurements of the total elastic and resonant charge-exchange ion-atom collision rate coefficient $k_{\mathrm{ia}}$ of cold sodium (Na) with optically dark low-energy ${\mathrm{Na}}^{+}$ ions in a hybrid ion-neutral trap. To determine $k_{\mathrm{ia}}$, we measured the trap loading and loss rates from both a Na magneto-optical trap (MOT) and a linear radio-frequency quadrupole Paul trap. We found the total rate coefficient to be $7.4\pm 1.9\times {10}^{-8}{\mathrm{cm}}^3/\mathrm{s}$ for the type-I Na MOT immersed within an $\approx 140-\mathrm{K}$ ion cloud and $1.10\pm 0.25\times {10}^{-7}{\mathrm{cm}}^3/\mathrm{s}$ for the type-II Na MOT within an $\approx 1070-\mathrm{K}$ ion cloud. Our measurements show excellent agreement with previously reported theoretical fully quantal ab initio calculations. In the process of determining the total rate coefficient, we demonstrate that a MOT can be used to probe an optically dark ion cloud's spatial distribution within a hybrid trap.

The resonant process of dielectronic recombination (DR) has been applied as a spectroscopic tool to investigate intra-$L$-shell excitations $2s-2p_j$ in Li-like ${}^{136}{\text{Xe}}^{51}+$. The experiments were carried out at the electron cooler of the Experimental Storage Ring of the GSI-Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany. The observed center-of-mass energy range (0–505 eV) covers all resonances associated with the $2s+e^{-}\to {\left(2p_{1/2}n{l}_j\right)}_J$ and ${\left(2p_{3/2}n{l}_j\right)}_J$ DR processes. Energies and strengths of isolated $2p_{1/2}n$ and $2p_{3/2}n$ DR-resonance groups were obtained for principal quantum numbers $n$ up to 43 and 36, respectively. The $2s-2p_{1/2}$ and $2s-2p_{3/2}$ excitation energies were deduced to be 119.816(42) eV and 492.174(52) eV. The excitation energies are compared with previous measurements of other groups and with recent QED calculations. In addition, the experimental spectra and extracted resonance strengths are compared with multiconfiguration Dirac-Fock calculations. Measurements and theory are found to be in good agreement with each other.

Photoionization of neutral atomic sulfur in the ground and metastable states was studied experimentally at a photon energy resolution of 44 meV (full width at half maximum). Relative cross section measurements were recorded by using tunable vacuum ultraviolet radiation in the energy range 9–30 eV obtained from a laser-produced plasma and the atomic species were generated by photolysis of molecular precursors. Photoionization of this atom is characterized by multiple Rydberg series of autoionizing resonances superimposed on a direct photoionization continuum. A wealth of resonance features observed in the experimental spectra are spectroscopically assigned and their energies and quantum defects tabulated. The cross section measurements are compared with state-of-the-art theoretical cross section calculations obtained from the Dirac Coulomb $R$-matrix method. Resonance series in the spectra are identified and compared, indicating similar features in both the theoretical and experimental spectra.

A generalized double-well-basis coupled representation is proposed to investigate excitation spectra and thermodynamics of bosonic atoms in double-well optical superlattices. In the hard-core limit and with a filling factor of one, excitations describing the creation of pairs of a doubly occupied state and a simultaneous empty state, and those from a symmetric singly occupied state to an antisymmetric state are carefully analyzed and their excitation spectra are calculated within mean-field theory. Based on the hard-core statistics, the equilibrium properties such as heat capacity and particle populations are studied in detail. The cases with other filling factors are also briefly discussed.

Motivated by recent cold-atom experiments in optical lattices, we consider a lattice version of the Landau-Zener problem. Every single site is described by a Landau-Zener problem, but due to particle tunneling between neighboring lattice sites this on-site single-particle Landau-Zener dynamics couples to the particle motion within the lattice. The lattice, apart from having a dephasing effect on single-site Landau-Zener transitions, also implies, in the presence of a confining trap, an intersite particle flow induced by the Landau-Zener sweeping. This gives rise to an interplay between intra- and intersite dynamics. The adiabaticity constraint is therefore not simply given by the standard one, the Hamiltonian rate of change relative to the gap of the on-site problem. In experimentally realistic situations, the full system evolution is well described by Franck-Condon physics; e.g., nonadiabatic excitations are predominantly external ones characterized by large phononic vibrations in the atomic cloud, while internal excitations are very weak as close-to-perfect on-site transitions take place.

We obtain analytically two kinds of inhomogeneous spin domain configurations endowed with time-dependent periodic domain walls in spin-1 Bose-Einstein condensate, which result from the positive and negative quadratic Zeeman effects, respectively. It is shown analytically that the topological defects are given by the unmagnetized atoms, at which the order parameter is of polar phase, but besides them, the order parameter is of axisymmetry-broken phase. The quadratic Zeeman effect can be tuned to induce the dynamical phase transition of the spin domain, and its sign can affect the topological structure of the spin pattern. These features arise from the axisymmetry breaking due to the pointwise-different population exchange between the sublevels determined uniquely by the quadratic Zeeman effects. The related experimental observations for the spin-1 ${}^{87}\mathrm{Rb}$ and ${}^{23}\mathrm{Na}$ condensates are also discussed.