We consider the implementation of an arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as quantum remote control. We investigate protocols that achieve this using local operations, classical communication, and shared entanglement. Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that the required resources are, necessarily, those needed for implementation by bidirectional state teleportation.

An alternative numerical solution of the Hartree-Fock integro-differential equations is reported that consists of reformulating the self-consistent ansatz as a nonlinear set of coupled Schrödinger and Poisson equations. In the simple case of helium, this yields an amazingly simple dynamical system whose statistical properties are constrained by the virial theorem. This approach leads to an equation of state for helium at zero temperature and very high densities, covering the whole range of astrophysical interest, up to the pressure ionization phase transition that is predicted around 44 Mbar by the present model.

Relativistic multireference many-body perturbation theory is employed to calculate the energy spectra, magnetic-dipole, and electric-quadrupole transition probabilities of the lowest ${}^3{P}_J$ fine-structure states of ions in the silicon isoelectronic sequence. Theoretical lifetimes of the ${}^3{P}_{1,2}$ states are evaluated and compared with recent experiments.

We describe the patterns of creation and splitting of planar closed orbits of electrons in hydrogen atoms in crossed electric and magnetic fields. These orbits lie in the plane perpendicular to the magnetic field, and they start and end at the nucleus. Using a Poincaré map to study the regular motions, we observe that the bifurcations of planar closed orbits fall into an ordered sequence as energy changes: a “tangent bifurcation” creates one closed orbit that splits into two; subsequently, one of them becomes periodic, and splits by a “pitchfork bifurcation” into two periodic orbits and one closed orbit. Based on these calculations, we classify the closed orbits that are involved in a sequence of bifurcations in a family, and we name the family by the winding ratio of the periodic orbits in the family. To understand this ordered sequence of bifurcations, we create a simple integrable Hamiltonian as a model of the Poincaré map. This model gives a simple interpretation of the sequence of the bifurcations. The model contains only general assumptions, so we expect that such sequences of bifurcations of closed orbits will be commonly found in physical systems.

A theory of free precession in selective reflection is presented. In contrast to standard theories of free precession in which transmission signals decay in a time on the order of the inverse of the inhomogeneous width, the selective reflection signal decays in a time of order of the inverse of the homogeneous width. Both short-pulse excitation and continuous-wave (cw) excitation are considered. In the case of cw excitation, it is possible to observe beating between the contributions to the signal that are first and third order in the amplitude of the excitation field.

We report on measurements of the cross section for photoionization of Rb atoms in the highly excited ${5D}_{5/2}$ level at wavelengths ranging from 1064 to 532 nm (photoelectron energies of 0.175 to 1.34 eV). We efficiently populate the ${5D}_{5/2}$ level using coherent two-photon excitation of trapped atoms with pulses in the counterintuitive order. The absolute photoionization cross sections are then measured via the increased loss of atoms from the magneto-optical trap when it is illuminated by the photoionizing light. Our results are in good agreement with new calculations based on the valence-electron parametric potential method.

We derive the frequency of precession and conditions for stability for a quantized vortex in a single-component and a two-component Bose-Einstein condensate. The frequency of precession is proportional to the gradient of the free energy with respect to displacement of the vortex core. In a two-component system, it is possible to achieve a local minimum in the free energy at the center of the trap. The presence of such a minimum implies the existence of a region of energetic stability where the vortex cannot escape and where one may be able to generate a persistent current.

We investigate the energy spectrum structure of a system of two (identical) interacting bosonic wells occupied by N bosons within the Schwinger realization of the angular momentum. This picture enables us to recognize the symmetry properties of the system Hamiltonian H and to use them for characterizing the energy eigenstates. Also, it allows for the derivation of the single-boson picture that is shown to be the background picture naturally involved by the secular equation for H. After deriving the corresponding eigenvalue equation, we recast it in a recursive N-dependent form that suggests a way to generate the level doublets (characterizing the H spectrum) via suitable inner parameters. Finally, we show how the presence of doublets in the spectrum allows us to recover, in the classical limit, the symmetry-breaking effect that characterizes the system classically.

We describe a method to create superposition states from a mixed state of a harmonic oscillator. If the initial state is described by a thermal state, then the resulting superposition state will be a “hot” superposition state. Such a state can be distinguished from a statistical mixture by its coherence properties. Here we suggest how to demonstrate the coherence of the superposition state by observing interference fringes when the two parts of the wave packet are overlapped. In the case of the mixed superposition state, a partial overlap may not be sufficient to observe the presence of fringes. We introduce therefore the idea of a coherence length for the wave packet and demonstrate its relevance for interferometry of mixed states. We illustrate our ideas with the example of superposition states for the motion of a single trapped ion.

Dark resonances with widths below 30 Hz have been observed in a rubidium cell filled with neon as buffer gas at room temperature. We compare an approximate analytic solution of a Λ system to our data and show that under our experimental conditions the presence of the buffer gas reduces the power broadening of the dark resonances by two orders of magnitude. We also present numerical calculations that take into account the thermal motion and velocity-changing collisions with the buffer-gas atoms. The resulting dark-resonance features exhibit strong Dicke-type narrowing effects and thereby explain the elimination of Doppler shifts and Doppler broadening, leading to observation of a single ultranarrow dark line.

Self-rotation (SR) of elliptically polarized light resonant with atoms in a collision-free vapor is investigated experimentally and theoretically. Results of density matrix calculations are compared to measurements of SR on the Rb $D1\mathrm{}$ and $D2\mathrm{}$ lines. It is noted that SR effects involving individual hyperfine transitions are suppressed due to Doppler broadening, and so previously unrecognized effects arising from the interaction of light with multiple hyperfine transitions can become dominant.

A scheme is proposed for the teleportation of atomic states within cavities. The scheme is insensitive to the cavity field states and cavity decay. The teleportation may be achieved in a simple way. We show how the idea can be used to generate multiatom entangled states. In order to entangle n atoms, we require $n-1$ cavities and allow the first cavity to exchange energy with the environment. The other $n-2$ cavities are always in the vacuum state and thus the cavity decay is suppressed.

The purpose of this paper is to suggest a scheme, which can be realized with today’s technology and could be used for entangling a probe to a photon qubit based on polarization. Using this probe, a translucent or a coherent eavesdropping can be performed.

We present a technique in which the total internal quantum state of an atom may be reconstructed via the measurement of the momentum transferred to an atom following its interaction with a near resonant traveling-wave laser beam. We present measurements that demonstrate the feasibility of the technique.

This paper is devoted to the development of a rigorous theory of angular-momentum relaxation. It is shown that by incorporating quantum-dynamical semigroups in the quantum Markovian master equation, the theory becomes mathematically sound. The expansion of the initial relaxation process in terms of primary relaxation processes of rank l offers a clearer view of the relaxation process structure. A close look at experimental procedure (the system Hilbert space structure, symmetry of the environment, and multipolarities of the system-environment interaction) gives all the information needed to simplify the structure of the relaxation equation and renders it a powerful tool for considering specific physical effects. The quantum Markovian master equation in the state multipole representation is obtained and the physical meaning of the parameters involved is found. The general approach is used for the study of a Zeeman multiplet. The relaxation rates as functions of the spectral densities of correlations (describing the environment properties) are given in an explicit form. Cross relaxation and cross correlation are taken properly into account there. The important case of spin 1 is discussed in more detail. Some useful expressions and relations among the relaxation rates are given in the Appendixes.

Scattering of a Ps atom off a He target has been investigated in the framework of the close-coupling approximation using two basis sets: (a) $\mathrm{Ps}\mathrm{}\left(1s\right)+\mathrm{He}{(1s}^2{,1s2\mathrm{}}^1{s,1s2\mathrm{}}^{1}p)$ and (b) $\mathrm{Ps}\mathrm{}(1s,2p)+\mathrm{He}{(1s}^2{,1s2\mathrm{}}^1{s,1s2\mathrm{}}^{1}p).\mathrm{}$ Target inelastic channels reduce the elastic cross sections appreciably near zero energy. The present results are in good agreement with the theoretical prediction of Drachman and Houston and the measured data of Canter, McNutt, and Roellig and Coleman et al. and are also in good agreement with the measured data of the UCL group from 15–20 eV.

The cumulative reaction probability (CRP) is a gross characteristic of rearrangement collision processes defining the reaction rate constant. This paper presents a complete development of the approach to the theory of CRP that we have recently proposed [Phys. Rev. Lett. 80, 41 (1998)]. In the core of this approach lies an alternative expression for CRP in terms of the outgoing wave Green’s function which is formally equivalent to the Miller’s definition of this quantity in terms of the scattering matrix [J. Chem. Phys. 62, 1899 (1975)] and to the Miller-Schwartz-Tromp formula [J. Chem. Phys. 79, 4889 (1983)], but is direct, in contrast to the former, and more suitable for practical calculations than the latter. Furthermore, our approach rests on solid grounds of time-independent quantum scattering theory and provides an appealing competitive alternative to the absorbing potential formulation given by Seideman and Miller [J. Chem. Phys. 96, 4412 (1992); 97, 2499 (1992)]. Ideologically, it is close to the approach considered earlier for a one-dimensional model by Manolopoulos and Light [Chem. Phys. Lett. 216, 18 (1993)], but is formulated from scratch for realistic systems with many degrees of freedom. The strongest point of our approach is that its final working formulas are expressed in terms of the Wigner-Eisenbud $\mathcal{R}$ matrix, so they can be easily implemented on the basis of many existing quantum scattering codes. All these features are discussed and illustrated by calculations of the CRP and reaction eigenprobabilities for two prototypical light atom transfer reactions in heavy-light-heavy triatomic systems in three dimensions for zero total angular momentum.

Equilibrium geometric structures, stability, ionization potentials, electron affinities, hardness, and static dipole polarizabilities of aluminum-doped sodium clusters $({\mathrm{Na}}_n\mathrm{Al},$ $n<~10)$ are studied with the linear combination of atomic-orbitals scheme within density-functional theory, using both the local and nonlocal approximations for exchange-correlation effects. GGA is found to extend bond lengths, and to widen the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), compared to LSDA. The evolution of the HOMO-LUMO gap, ionization potential, electron affinity, hardness, and polarizability with size of cluster shows ${\mathrm{Na}}_5\mathrm{Al}$ and ${\mathrm{Na}}_7\mathrm{Al}$ to be the most stable of those studied. The enhanced stability of these two clusters is due to shell closure. Aluminum exhibits a trivalent nature in these systems in contrast to its monovalent nature in small, pure aluminum clusters.

We consider the collective mode spectrum of a normal Fermi gas in a spherical harmonic trap. Using a self-consistent random-phase approximation, we systematically examine the effects of the two-body interactions on modes of various symmetries. For weak coupling, where the spectrum is shifted very little away from the ideal gas case, a sum-rule approach is shown to work well. For stronger coupling, the interplay between the single particle and collective excitations causes effects such as mode splitting and Landau damping. A finite low-frequency response present at stronger coupling is predicted for the quadrupole mode. Finally, we briefly discuss the effect of a finite temperature on the spectrum, and the excitation of higher collective modes.

Ground-state energies and superfluid gaps are calculated for degenerate Fermi systems interacting via long attractive scattering lengths such as cold atomic gases, neutron, and nuclear matter. In the intermediate region of densities, where the interparticle spacing $\left(\sim {1/k}_F\right)$ is longer than the range of the interaction but shorter than the scattering length, the superfluid gaps and the energy per particle are found to be proportional to the Fermi energy and thus differ from the dilute and high-density limits. The attractive potential increase linearly with the spin-isospin or hyperspin statistical factor such that, e.g., symmetric nuclear matter undergoes spinodal decomposition and collapses whereas neutron matter and Fermionic atomic gases with two hyperspin states are mechanically stable in the intermediate density region. The regions of spinodal instabilities in the resulting phase diagram are reduced and do not prevent a superfluid transition.