We propose an efficient technique for creation and manipulation of entangled states and for construction of arbitrary many-particle unitary transformations in a linear ion trap. We show that, under suitable conditions on the laser pulse areas and detunings, the propagator within the single-excitation manifold has the form of a Householder reflection (HR). We demonstrate that a single HR is sufficient to create an entangled $W$-type state or to transfer one entangled state into another. An arbitrary $N$-dimensional unitary transformation can be constructed by at most $N-1$ HRs, i.e., significantly faster than $O\left(N^2\right)$ steps in previous proposals, which makes this technique less sensitive to heating and other types of decoherence. We present examples of synthesis of quantum Fourier transforms for four, five, and six ions, which are constructed using only two, three, and four HRs, respectively.

We investigate upper and lower bounds on the entropy of entanglement of a superposition of bipartite states as a function of the individual states in the superposition. In particular, we extend the results by Gour [Phys. Rev. A 76, 052320 (2007)] to superpositions of several states rather than just two. We then investigate the entanglement in a subspace as a function of its basis states: we find upper bounds for the largest entanglement in a subspace and demonstrate that no such lower bound for the smallest entanglement exists. Finally, we consider entanglement of superpositions using measures of entanglement other than the entropy of entanglement.

We consider two-mode squeezed states which are parametrized by the squeezing parameter and the phase. We present a scheme for teleporting such entangled states of continuous variables from Alice to Bob. Our protocol is operationalized through the creation of a four-mode entangled state shared by Alice and Bob using linear amplifiers and beam splitters. Teleportation of the entangled state proceeds with local operations and the classical communication of four bits. We compute the fidelity of teleportation and find that it exhibits a trade-off with the magnitude of entanglement of the resultant teleported state.

The N $1s$ near edge x-ray absorption fine structure spectra of acrylonitrile gas are accurately reproduced by a complete ab initio multidimensional vibrational analysis. The role of ${\pi }^{\ast }$-orbital localization and hybridization on vibrations accompanying core excitation is discussed. Transition to the ${\pi }_{\perp }^{\ast }\left(\text{C}=\text{C}-\text{C}\equiv \text{N}\right)$ delocalized orbital excites mostly stretching vibrations of the whole spinal column of the molecule. Promoting a core electron to the localized ${\pi }_{\parallel }^{\ast }\left(\text{C}\equiv \text{N}\right)$ produces $\text{C}\equiv \text{N}$ stretching vibration combined with two strong bending modes of the $\text{C}-\text{C}\equiv \text{N}$ end of the molecule, related to the change of carbon hybridization.

The spin-exchange effect in spin-polarized electron collisions with unpolarized open-shell molecules ${\text{O}}_2$, ${\text{B}}_2$, ${\text{S}}_2$, and ${\text{Si}}_2$, has been studied by the $R$-matrix method with the fixed-bond approximation. All of these molecules have ${{}^3\Sigma }_g^{-}$ symmetry in their ground states. Usual integrated cross sections with unpolarized electrons have also been studied. We used the complete active space self-consistent field orbitals and put more than ten target electronic states in the $R$-matrix models. In electron ${\text{O}}_2$ elastic collisions, calculated polarization fractions agree well with the experimental results, especially around the ${{}^4\Sigma }_u^{-}$ resonance. In $e{\text{-B}}_2$, ${\text{S}}_2$, and ${\text{Si}}_2$ elastic collisions, larger spin-exchange effect is observed compared to the $e{\text{-O}}_2$ elastic collisions. In all four cases, spin-exchange effect becomes prominent near resonances. This association of resonance and magnitude of the spin-exchange effect was studied by explicitly removing the resonance configurations from the $R$-matrix calculations. In general, spin-exchange effect is larger in $e{\text{-B}}_2$ collisions than in $e{\text{-S}}_2$ and ${\text{Si}}_2$ collisions, and is smallest in $e{\text{-O}}_2$ collisions.

Starting from a system of $N$ radial Schrödinger equations with a vanishing potential and finite threshold differences between the channels, a coupled $N\times N$ exactly solvable potential model is obtained with the help of a single nonconservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as does its Jost matrix. It depends on $N\left(N+1\right)/2$ unconstrained parameters and on one upper-bounded parameter, the factorization energy. A detailed study of the model is done for the $2\times 2$ case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has zero, one, or two bound states, and zero or one resonance; a compact formula for the open-channel scattering length is obtained. As a first physical application, exactly solvable $2\times 2$ atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interacts with a bound or virtual state close to threshold, which results in a large background scattering length.

We devise a theory of x-ray absorption by symmetric-top molecules which are aligned by an intense optical laser. Initially, the density matrix of the system is composed of the electronic ground state of the molecules and a thermal ensemble of rigid-rotor eigenstates. We formulate equations of motion of the two-color (laser plus x rays) rotational-electronic problem. The interaction with the laser is assumed to be nonresonant; it is described by an electric dipole polarizability tensor. X-ray absorption is approximated as a one-photon process. It is shown that the equations can be separated such that the interaction with the laser can be treated independently of the x rays. The laser-only density matrix is propagated numerically. After each time step, the x-ray absorption is calculated. We apply our theory to study adiabatic alignment of bromine molecules $\left({\text{Br}}_2\right)$. The required dynamic polarizabilities are determined using the ab initio linear response methods coupled-cluster singles (CCS), second-order approximate coupled-cluster singles and doubles (CC2), and coupled-cluster singles and doubles (CCSD). For the description of x-ray absorption on the ${\sigma }_{g}1s\to {\sigma }_{u}4p$ resonance, a parameter-free two-level model is used for the electronic structure of the molecules. Our theory opens up novel perspectives for the quantum control of x-ray radiation.

A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in an optical lattice. Inelastic scattering processes between the two atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived that describes tunneling of single fermions, tunneling of fermionic pairs, and an exchange of fermionic spins. Low-energy states of this Hamiltonian are a Néel state for strong effective repulsion, dimer states for moderate interaction, and a density wave of paired fermions for strong effective attraction.

We study a simple model of $N$-component fermions with contact interactions which describes fermionic atoms with $N=2F+1$ hyperfine states loaded into a one-dimensional optical lattice. We show by means of analytical and numerical approaches that, for attractive interaction, a quasi-long-range molecular superfluid phase emerges at low density. In such a phase, the pairing instability is strongly suppressed and the leading instability is formed from bound states made of $N$ fermions. At small density, the molecular superfluid phase is generic and exists for a wide range of attractive contact interactions without an $\mathrm{SU}\left(N\right)$ symmetry between the hyperfine states.

Pulsed field ionization has been used for state selective detection of Rydberg atoms in many contexts, and it has been generally assumed that field ionization is an isolated atom process. While this assumption is valid for room temperature atoms, in which all interatomic interactions are transient, it is not good for the frozen Rydberg gas, in which the same interactions are omnipresent. We describe field ionization of cold Rb atoms in which the dipole-dipole interaction between pairs of atoms alters the field ionization.

We describe a three-dimensional model of the magneto-optical trap (MOT) for the simplest case of (1+3)-level atoms. The atomic density matrix equations are solved up to eighth order in the Rabi frequency and compared with experimental observations. We propose that coherences between the excited state sublevels can largely explain the dependence of the atomic temperature on detuning and light intensity.

We study the influence of three laser beams on the center-of-mass motion of cold atoms with internal energy levels in a tripod configuration. We show that, as for electrons in graphene, the atomic motion can be equivalent to the dynamics of ultrarelativistic two-component Dirac fermions. We propose and analyze an experimental setup for observing such a quasirelativistic motion of ultracold atoms. We demonstrate that the atoms can experience negative refraction and focusing by Veselago-type lenses. We also show how the chiral nature of the atomic motion manifests itself as an oscillation of the atomic internal state population, which depends strongly on the direction of the center-of-mass motion. For certain directions an atom remains in its initial state, whereas for other directions the populations undergo oscillations between a pair of internal states.

A quantum holonomy reflects the curvature of some underlying structure of quantum-mechanical systems, such as that associated with quantum states. Here, we extend the notion of holonomy to families of quantum channels, i.e., trace-preserving completely positive maps. By the use of the Jamiołkowski isomorphism, we show that the proposed channel holonomy is related to the Uhlmann holonomy. The general theory is illustrated for specific examples. We put forward a physical realization of the channel holonomy in terms of interferometry. This enables us to identify a gauge-invariant physical object that directly relates to the channel holonomy. Parallel transport condition and concomitant gauge structure are delineated in the case of smoothly parametrized families of channels. Finally, we point out that interferometer tests that have been carried out in the past to confirm the $4\pi$ rotation symmetry of the neutron spin can be viewed as early experimental realizations of the channel holonomy.

Boson-fermion pairing is considered in a discrete environment of bosons and fully spin-polarized fermions, coupled via an attractive Bose-Fermi Hubbard Hamiltonian in one dimension. The results of the $T$-matrix approximation for particles of equal mass and at double half-filling are compared with the results of exact diagonalization and with quantum Monte Carlo results. Satisfactory agreement for most quantities is found. The appearance of a stable, weak-coupling pairing mode is also confirmed.

We develop the work of Christandl et al. [Phys. Rev. A 71, 032312 (2005)], to show how a $d$-hypercube homogenous network can be dressed by additional links to perfectly route quantum information between any given input and output nodes in a duration that is independent of the routing chosen and, surprisingly, the size of the network.

The dependence of transition frequencies on the fine-structure constant $\alpha =e^2∕\hslash c$ is calculated for several many-electron systems which are used or planned to be used in laboratory searches for time variation of the fine-structure constant. In systems with a large number of electrons in open shells (from 11 to 15) the relative effects of the variation may be strongly enhanced. For the transitions which were considered before the results are in good agreement with previous calculations.

We have calculated $S$-wave resonances in the positron-sodium system using the stabilization method in the framework of hyperspherical coordinates. Resonances below the $\mathrm{Ps}(n=2)$ threshold have been investigated. We have located all the previously known $S$-wave resonances by Kar and Ho [Eur. Phys. J. D 35, 453 (2005)] and Ward et al. [J. Phys. B 22, 3763 (1989)] and observed relatively good agreement for the resonance positions. In addition, two new higher-lying resonances associated with the $\mathrm{Ps}(n=2)$ threshold are found to be at energies of $-0.06656$ and $-0.06353\text{a.u.}$

A systematic investigation of the absolute total detachment cross sections of atomic negative ions is presented and a simple semiclassical model developed based on the experimental findings. The total electron detachment process for several anion species, namely ${\text{C}}^{-}$, ${\text{O}}^{-}$, ${\text{F}}^{-}$, ${\text{S}}^{-}$, ${\text{Si}}^{-}$, ${\text{Cl}}^{-}$, ${\text{Ge}}^{-}$, and ${\text{Na}}^{-}$, in collisions with He, Ne, and Ar, in the velocity range of 0.2–1.8 a.u., were studied. In the intermediate-velocity regime the experimental data are well reproduced by the proposed model, which assumes independent contributions from the outermost quasifree electron and from the neutral core atom of the negative ion.

Using a pump-probe scheme with controllable time-delay in the range of $0–73\mathrm{fs}$, we have solved from first principles the time-dependent Schrödinger equation (TDSE) describing a hyper-fast excitation process that involves both the discrete and the continuous spectrum of the three-electron atomic negative ion, ${\mathrm{He}}^{-}$. Two approaches were implemented, both using state-specific wave functions for two multiply excited discrete states (the initial state, ${\mathrm{He}}^{-}1s2s2p{}^{4}P^o$, and the final state, ${\mathrm{He}}^{-}2p^3{}^{4}S^o$), and one intermediate state which is a shape resonance (${\mathrm{He}}^{-}1s2p^2{}^{4}P$, including the underlying continuum of scattering states. The wavelengths of the two pulses connecting resonantly the states are in the infrared $\left(10080\mathrm{\AA }\right)$ and in the soft x-ray region $\left(323\mathrm{\AA }\right)$. The first approach is analytic and solves the TDSE to first order in perturbation theory. This is acceptable for weak pulses whose duration is of the order of a few tens of femtoseconds. The second approach solves the TDSE nonperturbatively, via the state-specific expansion approach. A series of computations have produced time-dependent probabilities for preparing the triply excited bound state ${\mathrm{He}}^{-}2p^3{}^{4}S^o$ for various combinations of the duration of the two pulses. Apart from providing the first such quantitative data, the results suggest the appearance of effects of short-time nonexponential decay of resonances when it becomes possible to monitor excitation with time-delayed short pulses.

Recent advances in ultracold atomic Fermi gases make it possible to achieve a fermionic superfluid with multiple spin components. In this context, any mean-field description is expected to fail, owing to the presence of tightly bound clusters or molecules that consist of more than two particles. Here we present a detailed study of a strongly interacting multicomponent Fermi gas in a highly elongated or quasi-one-dimensional harmonic trap, which could be readily obtained in experiment. By using the exact Bethe ansatz solution and a local density approximation treatment of the harmonic trap, we investigate the equation of state of the multicomponent Fermi gas in both a homogeneous and trapped environment, as well as the density profiles and low-energy collective modes. The binding energy of multicomponent bound clusters is also given. We show that there is a peak in the collective mode frequency at the critical density for a deconfining transition to a many-body state that is analogous to the quark color superconductor state expected in neutron stars.