The equation-of-motion method based on Heisenberg’s matrix mechanics, utilized in this paper, was originally developed within the context of the nuclear many-body problem. The method was later applied successfully to anharmonic oscillators and other problems in quantum mechanics with polynomial potentials in one and two dimensions. Here we apply the method to the one-dimensional quantum system with the nonpolynomial potential $\lambda {\sinh }^{2}x,$ as an illustration of its applicability to a wider class of problems than has been previously considered. We examine some of the structural and numerical aspects of this one-dimensional quantum system, and show that it is essential to work with $\sinh x$ instead of x as the dynamical variable for this nonpolynomial potential problem. This choice is suggested by a preliminary study of the exactly solvable Poschl-Teller potential, $-\lambda /{\cosh }^{2}x,$ where our methods provide an exact algebraic solution. For the potential $\lambda {\sinh }^{2}x,$ the same methods yield equations that can be studied numerically by a controlled sequence of nonperturbative approximations.

The inclusion of the continuum in the study of weakly bound systems is discussed. A transformed harmonic-oscillator basis is introduced to provide an appropriate discrete and finite basis for treating the continuum part of the spectrum. As examples of application of the method the one-dimensional Poeschl-Teller and Morse potentials are worked out. The strength functions corresponding to different operators that couple the ground state to the continuum are investigated. It is found that the energy moments of those distributions are accurately reproduced with a small basis set.

We present different schemes for preparing and maintaining the quantum state of multilevel systems. This is achieved via a suitable combination of coherent trapping and the Zeno effect which serves to protect the prepared state against undesired jumps to other states.

We present a method to entangle qubits or qutrits (where He quantum information is stored in spin 1 systems), belonging to N distant users. All the operations (unitary transformations and measurements) needed to achieve our goal are performed in a center of distribution C. This procedure supplies the N users with a powerful resource (multiparticle entanglement) without requiring any effort on their side. We show that entangled qutrits generated with this scheme can be used for secret sharing between N users. Qutrit secret sharing is argued to be optimal.

A continuous key-distribution scheme is proposed that relies on a pair of conjugate quantum variables. It allows two remote parties to share a secret Gaussian key by encoding it into one of the two quadrature components of a single-mode electromagnetic field. The resulting quantum cryptographic information versus disturbance trade-off is investigated for an individual attack based on the optimal continuous cloning machine. It is shown that the information gained by the eavesdropper then simply equals the information lost by the receiver.

The Deutsch-Jozsa algorithm to implement an f-controlled-NOT transformation on a quantum computer was generalized to create arbitrary phases. This phase-creation algorithm was applied to solve an extended Deutsch problem for a function that maps $\{0,1{\}}^n$ to $\{0,1{\}}^m.$ Implementation of the algorithm on a NMR quantum computer is discussed.

We show that for any Hilbert-space dimension, the optimal $\overrightarrow{1}2$ universal quantum cloner can be constructed from essentially the same quantum circuit, i.e., we find a universal design for universal cloners. In the case of infinite dimensions (which includes continuous variable quantum systems) the universal cloner reduces to an essentially classical device. More generally, we construct a universal quantum circuit for distributing qudits in any dimension which acts covariantly under generalized displacements and momentum kicks. The behavior of this covariant distributor is controlled by its initial state. We show that suitable choices for this initial state yield both universal cloners and optimized cloners for limited alphabets of states related by generalized phase-space displacements.

The phenomenon of directed motion of electrons and ions in gases under the action of ionizing radiation pressure is investigated. It is shown that for photon energies from the thresholds of atomic photoionization to several keV the photoionization process is the main mechanism for the transfer of electromagnetic radiation momentum to an atom. Expressions for the drag currents that appear under the action of ionizing radiation in atomic gases and their mixtures are obtained. The connection between the drag currents and one of the nondipole asymmetry parameters is established. Experimental investigation of the drag currents for use in precision measurement of the asymmetry parameters is discussed, particularly for small photoelectron energies where it is difficult to apply the traditional experimental schemes to measure the differential cross sections for photoionization. Nondipole parameters for the Ne $2s,$ Ne $2p,$ and Ar $1s$ subshell photoionization are calculated and compared with measurements and other calculations. Partial drag currents for the Ne $2s,$ Ne $2p,$ and Ar $1s$ subshells are also presented.

Doubly excited atoms with an outer large-$l$ electron are expected to exhibit moderate series interaction. However, accidental or systematic degeneracies may lead to strong configuration mixing. To describe such phenomena, the present formalism uses a partial diagonalization of the dielectronic interaction plus a second-order correction based on Coulomb Green’s function. It makes it possible to determine the eigenfunction composition, level positions, and autoionization widths. While series interaction turns out to be weak for almost degenerate high members of the ${4d}_j\mathrm{ng}$ series in strontium, a significant configuration mixing is observed on ${6p}_j\mathrm{nl}$ series of barium. A generally fair agreement is observed with ${6p}_j\mathrm{ng}$ experimental data. The ${6p}_j\mathrm{nh}$ levels are accurately predicted, too, and new assignations are reported for some of them; however, the computed linewidths are about twice as small as the measured ones. The method also applies to helium and multiply charged ions, where the relevance of collective quantum numbers is analyzed. Some level positions and widths are detailed.

Line shapes of the $R_0\mathrm{}\left(0\right)\mathrm{}$ and $R_0\mathrm{}\left(1\right)\mathrm{}$ lines in the pure rotational band, and of the $R_1\mathrm{}\left(0\right)\mathrm{}$ and $R_1\mathrm{}\left(1\right)\mathrm{}$ lines in the fundamental band of HD are computed from first principles for HD molecules that interact collisionally with He atoms. Interference of the permanent dipole of the HD molecule and the interaction-induced dipole of HD–He supermolecular complex shapes these profiles. We use the close-coupling scheme for the scattering calculations which take into account the anisotropy of the HD–He interaction potential. Thus rotational level mixing is accounted for in a non-perturbative manner. The treatment is fully quantum mechanical and takes into account single binary collisions between HD and He. Spectral absorption profiles and line shape parameters of the R-lines are computed for comparison with existing measurements at 77 K. Agreement between theory and measurements is observed in the low-helium-density limit of the measured absorption as expected.

We present calculations of spin-relaxation rates of alkali-metal atoms due to the spin-axis interaction acting in binary collisions between the atoms. We show that for the high-temperature conditions of interest here, the spin-relaxation rates calculated with classical-path trajectories are nearly the same as those calculated with the distorted-wave Born approximation. We compare these calculations to recent experiments that used magnetic decoupling to isolate spin relaxation due to binary collisions from that due to the formation of triplet van der Waals molecules. The values of the spin-axis coupling coefficients deduced from measurements of binary collision rates are consistent with those deduced from molecular decoupling experiments, and follow a physically plausible scaling law for the spin-axis coupling coefficients.

The ratio of the total x-ray scattering from Ne to that from He has been determined for photon energies in the range 4–15 keV at scattering angles of 45 and 90 degrees (corresponding to momentum transfers ranging from 0.90 to 5.69 a.u.). An arrangement of two gas cells in series was employed, allowing simultaneous measurements on both gases at the same scattering angle, which eliminates possible errors due to fluctuating beam intensity. Pairs of measurements corresponding to the same momentum transfer (at momentum transfers of 1.67 and 3.08 a.u.) but to different energies, provide a direct test of the corrections to the (momentum-transfer-dependent) form-factor incoherent-scattering-factor theory. These corrections include the anomalous p⋅A contributions, which are found to be important. We also consider corrections to the usual approximations made within the inelastic $A^2$ theory (the incoherent-scattering factor, using closure approximation, and the impulse approximation, assuming free-particle kinematics with a given momentum distribution). In these cases an incoherent-scattering-factor treatment is generally adequate, while anomalous scattering factor corrections to form factors are needed for elastic scattering.

We discuss in detail properties of trapped atomic condensates with anisotropic dipole interactions. A practical procedure for constructing anisotropic low-energy pseudopotentials is proposed and justified by the agreement with results of numerical multichannel calculations. The time dependent variational method is adapted to reveal several interesting features observed in numerical solutions of condensate wave function. Collective low-energy shape oscillations and their stability inside electric fields are investigated. Our results shed new light into macroscopic coherence properties of interacting quantum degenerate atomic gases.

The decay rate and the classical radiation power of an excited molecule (atom) in the center of a dispersive and absorbing dielectric sphere, taken as a simple model of a cavity, are calculated adopting the Onsager model for the local field. The local-field correction factor to the external (radiation and absorption) power loss of the molecule is found to be $|3\varepsilon \left(\omega \right)/\left[3\varepsilon \right(\omega )+1\mathrm{}]{|}^2,$ with $\varepsilon \left(\omega \right)$ being the dielectric function of the sphere. However, local-field corrections to the total decay rate (power loss) of the molecule are found to be much more complex including those to the decay rate in the infinite cavity medium, as derived recently by Scheel et al. [Phys. Rev. A $60,$ 4094 (1999)], and similiar corrections to the cavity-induced decay rate. The results obtained can be cast into general forms that do not rely on the specific cavity shape and molecule position considered. This suggests the general results for the local-field corrections to the decay rate and to the external power loss of a molecule in an absorbing cavity that are valid for molecule positions away from the cavity walls.

We show that shifts in locations of two-photon coincidence spectral peaks, for a bichromatically driven two-level atom passing through a single-mode cavity, are due to competition between excitation pathways for a Jaynes-Cummings system. We also discuss an analogous shift of (single-photon) spectral peaks for a driven three-level V system, which demonstrates that competition between excitation pathways is also important in this simple system.

Parity nonconservation that originates from the weak interaction of atomic electrons with the nuclei in heliumlike gadolinium and europium is considered. An experiment with a polarized ion beam is discussed. The mixed hyperfine- and weak-quenching effect in ${\mathrm{Gd}}^{62+}$ and ${\mathrm{Eu}}^{61+}$ isotopes is shown to lead to an asymmetry of the photon emission relative to the ion beam polarization. With complete beam polarization, the magnitude of the asymmetry in photon counting rates reaches about $0.39\times {10}^{-3}$ in gadolinium and is about $0.11\times {10}^{-3}$ in europium.

We investigate the low-lying excitations of a weakly interacting, harmonically trapped Bose-Einstein condensed gas under rotation, in the limit where the angular mometum L of the system is much less than the number of the atoms N in the trap. We show that in the asymptotic limit $\overrightarrow{N}\infty$ the excitation energy, measured from the energy of the lowest state, is given by ${27N}_3{(N}_3-{1)v}_0/68,$ where $N_3$ is the number of octupole excitations, and $v_0$ is the unit of the interaction energy.

A recent work [Pegg et al., Phys. Rev. Lett. 81, 1604 (1998)] showed how to generate a running-wave superposition of zero- and one-photon field states, $C_0|0〉{+C}_1|1〉,$ by physical truncation of the photon number superposition making up a coherent state. Here we discuss the extension of this device to the case of N components: $C_0|0〉{+C}_1|1〉+\cdot \cdot \cdot {+C}_N|N〉.$

The angular distributions of the spin-orbit state resolved S $2p$ photoelectrons of ${\mathrm{SF}}_6$ have been measured in the vicinity of the shape resonances. Relative partial photoionization cross sections of ${\mathrm{SF}}_6$ into the (S ${2p}_{3/2}{)}^{-1}$ and (S ${2p}_{1/2}{)}^{-1}$ states, and the asymmetry parameters of the S ${2p}_{3/2}$ and S ${2p}_{1/2}$ photoelectrons are presented. Enhancement of the photoionization cross section into the (S ${2p}_{3/2}{)}^{-1}$ state at the (S ${2p}_{1/2}{)}^{-1}$ ${2t}_{2g}$ resonance has been observed. The excitation photon energy dependence of the asymmetry parameter shows a broad dip at about the photon energies of the resonances. Continuum multiple-scattering calculation of the asymmetry parameters for the (S ${2p}_{3/2}{)}^{-1}$ and (S ${2p}_{1/2}{)}^{-1}$ states of ${\mathrm{SF}}_6$ reproduces this behavior.

We consider the problem of the meaning of quantum unstable states including their dressing. According to both Dirac and Heitler this problem has not been solved in the usual formulation of quantum mechanics. A precise definition of excited states is still needed to describe quantum transitions. We use our formulation given in terms of density matrices outside the Hilbert space. We obtain a dressed unstable state for the Friedrichs model, which is the simplest model that incorporates both bare and dressed quantum states. The excited unstable state is derived from the stable states through analytic continuation. It is given by an irreducible density matrix with broken time symmetry. It can be expressed by a superposition of Gamow density operators. The main difference from previous studies is that excited states are not factorizable into wave functions. The dressed unstable state satisfies all the criteria that we can expect: it has a real average energy and a nonvanishing trace. The average energy differs from Green’s function energy by a small effect starting with fourth order in the coupling constant. Our state decays following a Markovian equation. There are no deviations from exponential decay neither for short nor for long times, as is the case for the bare state. The dressed state satisfies an uncertainty relation between energy and lifetime. We can also define dressed photon states and describe how the energy of the excited state is transmitted to the photons. There is another very important aspect: deviations from exponential decay would be in contradiction with indiscernibility as one could define, e.g., old mesons and young mesons according to their lifetime. This problem is solved by showing that quantum transitions are the result of two processes: a dressing process, discussed in a previous publication, and a decay process, which is much slower for electrodynamic systems. During the dressing process the unstable state is prepared. Then the dressed state decays in a purely exponential way. In the Hilbert space the two processes are not separated. Therefore it is not astonishing that we obtain for the unstable dressed state an irreducible density matrix outside the Liouville-Hilbert-space. This is a limit of Hilbert space states that are arbitrarily close to the decaying state. There are experiments that could verify our proposal. A typical one would be the study of the line shape, which is due to the superposition of the short-time process and the long-time process. The long-time process taken separately leads to a much sharper line shape, and avoids the divergence of the fluctuation predicted by the Lorentz line shape.