We demonstrate tunable control of the group velocity of a weak probe pulse from subluminal to superluminal. The model is an extended $\Lambda$-type system with two extra control fields and an extra energy level. Phase variation of one of the control fields imparts the tunability in the group velocity along with other interesting spectral behavior in the absorption spectrum.

Grover’s quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of $N$ items laid out in $d$ spatial dimensions can be searched in time of order $\sqrt{N}$ for $d>2$, and in time of order $\sqrt{N}\text{poly}\left(\log N\right)$ for $d=2$. We consider an alternative search algorithm based on a continuous-time quantum walk on a graph. The case of the complete graph gives the continuous-time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that $\sqrt{N}$ speedup can also be achieved on the hypercube. We show that full $\sqrt{N}$ speedup can be achieved on a $d$-dimensional periodic lattice for $d>4$. In $d=4$, the quantum walk search algorithm takes time of order $\sqrt{N}\text{poly}\left(\log N\right)$, and in $d<4$, the algorithm does not provide substantial speedup.

Multiqubit logical gates are proposed as implementations of logical operations on $N$ qubits realized physically by the local manipulation of qubits before and after the one-time evolution of an Ising chain. This construction avoids complicated tuning of the interactions between qubits. The general rules of the action of multiqubit logical gates are derived by decomposing the process into the product of two-qubit logical operations. The formalism is demonstrated by the construction of a special type of multiqubit logical gate that is simulated by a quantum circuit composed of controlled-NOT gates.

We present a derivation of the partial-wave expansions of the exact, time-independent, single-particle Green function for an arbitrary potential taken from a wide class typical of atomic and molecular systems, whose expansion in spherical harmonics about some point is given. The Green-function expansions are expressed in terms of matrix solutions, one regular at the origin and one at infinity, of the coupled radial Schrödinger equations related to that potential, and a constant, Wronskian-type matrix constructed from them. Expansions are developed for both positive energies, relevant to scattering states, and negative energies, where we elucidate the mathematical condition for bound states.

A hydrogen atom moving across a magnetic field is considered in a wide region of magnitudes of magnetic field and atom momentum. We solve the Schrödinger equation of the system numerically using an imaginary time method and find wave functions of the lowest states of atom. We calculate the energy and the mean electron-nucleus separation as a function of atom momentum and magnetic field. All the results obtained could be summarized as a phase diagram on the “atom-momentum – magnetic-field” plane. There are transformations of wave-function structure at critical values of atom momentum and magnetic field that result in a specific behavior of dependencies of energy and mean interparticle separation on the atom momentum $P.$ We discuss a transition from the Zeeman regime to the high magnetic field regime. A qualitative analysis of the complicated behavior of wave functions vs $P$ based on the effective potential examination is given. We analyze a sharp transition at the critical momentum from a Coulomb-type state polarized due to atom motion to a strongly decentered (Landau-type) state at low magnetic fields. A crossover occurring at intermediate magnetic fields is also studied.

Divergence-free pseudo-potentials for spatially even- and odd-wave interactions in spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bose mapping method is used to relate the effectively one-dimensional fermionic many-body problem to that of a spinor Bose gas. Depending on the relative magnitudes of the even- and odd-wave interactions, the $N$-atom ground state may have total spin $S=0$, $S=N∕2$, and possibly also intermediate values, the case $S=N∕2$ applying near a $p$-wave Feshbach resonance, where the $N$-fermion ground state is space-antisymmetric and spin-symmetric. In this case the fermionic ground state maps to the spinless bosonic Lieb-Liniger gas. An external magnetic field with a longitudinal gradient causes a Stern-Gerlach spatial separation of the corresponding trapped Fermi gas with respect to various values of $S_z$.

We propose an optical ring interferometer to observe environment-induced spatial decoherence of massive objects. The object is held in a harmonic trap and scatters light between degenerate modes of a ring cavity. The output signal of the interferometer permits to monitor the spatial width of the object’s wave function. It shows oscillations that arise from coherences between energy eigenstates and that reveal the difference between pure spatial decoherence and that coinciding with energy transfer and heating. Our method is designed to work with a wide variety of masses, ranging from the atomic scale to nanofabricated structures. We give a thorough discussion of its experimental feasibility.

Maximally entangled states should maximally violate the Bell inequality. It is proved that all two-qubit states that maximally violate the Bell-Clauser-Horne-Shimony-Holt inequality are exactly Bell states and the states obtained from them by local transformations. The proof is obtained by using the certain algebraic properties that Pauli’s matrices satisfy. The argument is extended to the three-qubit system. Since all states obtained by local transformations of a maximally entangled state are equally valid entangled states, we thus give the characterizations of maximally entangled states in both the two-qubit and three-qubit systems in terms of the Bell inequality.

The dependence of the relativistic correlation energy in the ground states of helium isoelectronic series ions on the atomic number, for $1⩽Z⩽118$, is investigated. The correctness of the results derived from large-scale Hylleraas configuration-interaction calculations has been confirmed by analyzing the results of numerical multiconfiguration Dirac-Fock calculations. In particular, the relativistic correlation energy is a nonmonotonic function of $Z$. It has a minimum at $Z=20$ and a maximum at $Z=68$ and rapidly decreases for larger $Z$ values.

Electron-impact excitation of the CO molecule has been investigated by use of a crossed beam double trochoidal electron spectrometer. Forward and backward scattered electrons from the ${}^2\Pi$ resonance are analyzed. In order to separate these two contributions, electron beam modulation and time-of-flight detection of scattered electrons have been introduced. Backward electrons are additionally delayed in time by introduction of a decelerator device. The operation of this device is tested by a measurement performed on the ${}^2\Pi _g$ resonance in ${\mathrm{N}}_2$ molecule. The ratio of forward-to-backward scattered electrons from the ${}^2\Pi$ resonance in CO is found to be equal to 1, and thus the angular distribution of scattered electrons to be symmetric relative to 90°. This conclusion is compared to existing angular distribution measurements and theoretical predictions.

We present a scheme to teleport an entanglement of zero- and one-photon states from one cavity to another. The scheme, which has 100% success probability, relies on two perfect and identical bimodal cavities, a collection of two kinds of two-level atoms, a three-level atom in a ladder configuration driven by a classical field, Ramsey zones, and selective atomic-state detectors.

We present an efficient scheme for the controlled generation of pure two-qubit states possessing any desired degree of entanglement and a prescribed symmetry. This is achieved in two-qubit-cavity QED systems (e.g., cold-trapped ions and flying atoms) via on-resonance ion- or atom-cavity couplings, which are time dependent and asymmetric, yielding a trapping vacuum state condition which does not arise for identical couplings. A duality in the role of the coupling ratio yields states with a given concurrence but opposing symmetries. Both the trapping state condition and the resulting entanglement power are robust against decoherence channels.

We show theoretically that concurrent interactions in a second-order nonlinear medium placed inside an optical resonator can generate multipartite entanglement between the resonator modes. We show that there is a mathematical connection between this system and van Loock and Braunstein’s proposal for entangling $N$ continuous quantum optical variables by interfering with the outputs of $N$ degenerate optical parametric amplifiers (OPA) at a $N$-port beam splitter. Our configuration, however, requires only one nondegenerate OPA and no interferometer. In a preliminary experimental study, we observe the concurrence of the appropriate interactions in periodically poled ${\mathrm{RbTiOAsO}}_4$.

This paper discusses the relationship between the Wigner function, along with other related quasiprobability distribution functions, and the probability density distribution function constructed from the wave function of the Schrödinger equation in quantum phase space, as formulated by Torres-Vega and Frederick (TF). At the same time, a general approach in solving the wave function of the Schrödinger equation of TF quantum phase space theory is proposed. The relationship of the wave functions between the TF quantum phase space representation and the coordinate or momentum representation is thus revealed.

We consider the question of competition between leptonic and hadronic annihilation in matter-antimatter interaction. The rate of direct positron-electron annihilation in cold hydrogen-antihydrogen collisions has been calculated. The presence of leptonic annihilation introduces an absorptive, imaginary component to the hydrogen-antihydrogen scattering length; this component is $1.4\times {10}^{-4}\mathrm{a.u.}$ for the singlet state of the leptonic spins, and $1.2\times {10}^{-7}\mathrm{a.u.}$ for the triplet state. Leptonic annihilation is shown to be about 3 orders of magnitude slower than proton-antiproton annihilation.

The results of simulations of antihydrogen formation in a Penning trap are reported. The antihydrogen atoms are formed by three-body capture. We find that the arrested nature of the three-body capture in the trap greatly reduces the expected binding energy of the antihydrogen. Typically, the formed antihydrogen has larger velocity along the magnetic field than across the field and a binding energy below $k_{B}T$.

Available theoretical total and differential cross sections for the ionization of argon atoms by energetic proton impact are discussed and compared with our present calculations. The results depend sensitively on the model potential used for the description of the unperturbed atomic orbitals. Remarkable post-prior discrepancies are found when the electron-target interactions are calculated with respect to different potentials for the initial and final channels, respectively. Not only the orthogonality between bound and continuum wave functions, but also the correct asymptotic behavior of the exchange part of the potential is crucial for a satisfactory description of the experimental data.

Measured cross sections for electron-impact ionization of excited $\mathrm{Xe}$ atoms are not presently available. Therefore, we combine in this work the formalisms of the binary encounter approximation and Sommerfeld’s quantization of atomic orbits and derive from first-principles cross sections for ionization of excited atoms by electrons of low and moderate energies (up to a few hundred $\mathrm{eV}$). The approach of this work can be used to calculate the cross sections for electron-impact ionization of excited atoms and atomic ions other than xenon.

Atomic and electronic structures of the electronically magic $\mathrm{Na}_{59}{}^{+}$ cluster are investigated using density functional theory and an ab initio pseudopotential. Two atomically closed-shell structures are found, but none of these “double-magic” structures is the global ground state at $T=0$. Simulated annealing with ab initio molecular dynamics yields a more stable amorphous, but “spherical” atomic structure that closely resembles structures obtained from a simple classical model of 59 point charges in a spherical harmonic well. This indicates that the sodium ions arrange into a structure that is dictated by a stiff spherical background of the closed 58-electron configuration. Upon heating, this cluster melts already at about $175\mathrm{K}$ displaying a minute latent heat of $2.3\mathrm{meV}∕\text{atom}$. The simulated photoelectron spectrum at $260\mathrm{K}$ reproduces the $1g$, $2p$, and $1f$ peaks observed previously in the experiment.

Self-phase-modulation-induced spectral broadening of laser pulses in air-guided modes of hollow photonic-crystal fibers (PCFs) is shown to allow the creation of fiber-optic limiters for high-intensity ultrashort laser pulses. The performance of PCF limiters is analyzed in terms of elementary theory of self-phase modulation. Experiments performed with 100 fs microjoule pulses of $800\mathrm{nm}$ $\mathrm{Ti}$:sapphire laser radiation demonstrate the potential of hollow PCFs as limiters for $10\mathrm{MW}$ ultrashort laser pulses and show the possibility to switch the limiting level of output radiation energy by guiding femtosecond pulses in different PCF modes.