The long-time behavior of the survival probability for unstable multilevel systems that follows the power-decay law is studied based on the $N$-level Friedrichs model, and is shown to depend on the initial population in unstable states. A special initial state maximizing the asymptote of the survival probability at long times is found and examined by considering the spontaneous-emission process for the hydrogen atom interacting with the electromagnetic field.

It is proved that all states of three spin-$\frac{1}{2}$ particles exhibiting an “all versus nothing” contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli’s matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality.

A method is studied wherein two noninteracting quantum subsystems, that each interact with a third subsystem, are entangled via repeated projective measurements of the state of the third subsystem. A variety of condensed matter and quantum optical examples are presented. The method can be used to establish long range entanglement between distant parties in one parallel measurement step, thus obviating the need for entanglement swapping.

In Phys. Rev. A 58, 1833 (1998), Grassl et al. presented a family of polynomial invariants which separate the orbits of multiqubit density operators $\rho$ under the action of the local unitary group. We consider this family of invariants for the class of those $\rho$ that are the projection operators describing stabilizer codes and give a complete translation of these invariants into the binary framework in which stabilizer codes are usually described. Such an investigation of local invariants of quantum codes is of natural importance in quantum coding theory, since locally equivalent codes have the same error-correcting capabilities and local invariants are powerful tools to explore their structure. Moreover, the present result is relevant in the context of multipartite entanglement and the development of the measurement-based model of quantum computation known as the one-way quantum computer.

We demonstrate the implementation of a quantum algorithm on a liquid-state NMR quantum computer using almost pure states. This was achieved using a two-qubit device where the initial state is an almost pure singlet nuclear spin state of a pair of ${}^1\mathrm{H}$ nuclei arising from a chemical reaction involving parahydrogen. We have implemented Deutsch’s algorithm for distinguishing between constant and balanced functions with a single query.

We calculate the effect of polarization-dependent scattering by disorder on the degree of polarization entanglement of two beams of radiation. Multimode detection converts an initially pure state into a mixed state with respect to the polarization degrees of freedom. The degree of entanglement decays exponentially with the number of detected modes if the scattering mixes the polarization directions and algebraically if it does not.

Absolute, total, single- and multiple-electron-loss cross sections are measured for $1.4\text{−}\mathrm{MeV}∕\mathrm{u}{\mathrm{U}}^{4,6,10+}$ ions colliding with neon and argon atoms and nitrogen molecules. It is found that the cross sections all have the same dependence on the number of electrons lost and that multiplying the cross sections by the initial number of electrons in the $6s$, $6p$, and $5f$ shells yields good agreement between the different projectiles. By combining the present data with previous measurements made at the same velocity, it is shown that the scaled cross sections slowly decrease in magnitude for incoming charge states between 1 and 10, whereas the cross sections for higher-charge-state ions fall off much more rapidly.

We analyze a system of two colliding ultracold atoms under strong harmonic confinement from the viewpoint of quantum defect theory and formulate a generalized self-consistent method for determining the allowed energies. We also present two highly efficient computational methods for determining the bound state energies and eigenfunctions of such systems. The perturbed harmonic oscillator problem is characterized by a long asymptotic region beyond the effective range of the interatomic potential. The first method, which is based on quantum defect theory and is an adaptation of a technique developed by one of the authors (G.P.) for highly excited states in a modified Coulomb potential, is very efficient for integrating through this outer region. The second method is a direct numerical solution of the radial Schrödinger equation using a discrete variable representation of the kinetic energy operator and a scaled radial coordinate grid. The methods are applied to the case of trapped spin-polarized metastable helium atoms. The calculated eigenvalues agree very closely for the two methods, and with the eigenvalues computed using the generalized self-consistent method.

All possible conformations of a ${\mathrm{H}}_2$ molecule inside the cubic water octamer ${\left({\mathrm{H}}_2\mathrm{O}\right)}_8$ have been examined using ab initio molecular theory. Starting structures were based on the 14 geometries of the cubic water octamer. In all, optimizations were performed on 39 different ${\left({\mathrm{H}}_2\mathrm{O}\right)}_8·{\mathrm{H}}_2$ structures in order to determine which conformers could contain ${\mathrm{H}}_2$ and which ones would release it. Of the 39 optimizations performed, nine resulted in structures with the ${\mathrm{H}}_2$ contained within the molecular water box. Vibrational frequency analyses were used to determine that five of these nine were minima of the ${\left({\mathrm{H}}_2\mathrm{O}\right)}_8·{\mathrm{H}}_2$ potential-energy surface. An analysis of these structures from the perspective of relative and order of stability and hydrogen bonding was performed. From this analysis, we find a set of hydrogen-bonding topologies that contribute to stabilizing and destabilizing the ${\left({\mathrm{H}}_2\mathrm{O}\right)}_8·{\mathrm{H}}_2$ cage system.

We present oscillator strength spectra of the hydrogen atom in parallel magnetic and electric fields obtained via the pseudospectral method, a two-dimensional spatial discretization scheme. We have observed that for the field strength regimes of interest ($\gamma ⩽0.2\mathrm{a.u.}$ and $F⩽{10}^8\mathrm{V}∕\mathrm{m}$), a simple perturbation theory analysis accurately accounts for the electric-field effect on most transitions in the Balmer $\alpha$ series. Nearly constant oscillator strengths for some transitions at given field strengths observed by Fassbinder and Schweizer [Astron. Astrophys. 314, 700 (1996)] are explained theoretically. An effective strategy in using the pseudospectal method has also been suggested for handling the hydrogen atom in crossed magnetic and electric fields.

We present saturation and polarization laser spectroscopy experiments of indium vapor with a single color on the $410\mathrm{nm}$ transition and with two colors at 410 and $451\mathrm{nm}$. The spectra observed by polarization spectroscopy are discussed in terms of a quantitative model. The line shapes observed with two-color spectroscopy can phenomenologically be described taking into account hyperfine changing collisions, velocity changing collisions, and dark resonances. As an application, we actively stabilized a $410\mathrm{nm}$ diode laser on the resonances of saturation and polarization spectroscopy, and obtained long term frequency stabilities in the $100\mathrm{kHz}–1\mathrm{MHz}$ range.

The explicit formulation of the initial conditions of the definition of the wave-packet tunneling time is proposed. This formulation takes adequately into account the irreversibility of the wave-packet space-time spreading. Moreover, it explains the violations of the Hartman effect, leading to a strong decrease of the tunneling times up to negative values for wave packets with large momentum spreads due to strong wave-packet time spreading.

Intense laser-induced recombination of electrons and ions has been investigated with ultrashort few-cycle pulses. Our numerical simulations demonstrate that the absolute phase of a few-cycle laser field with respect to its pulse envelope plays a crucial role in the inverse above-threshold-ionization processes. By controlling the phase of a few-cycle pulse we can maximize the multiphoton recombination probability for electrons having certain energies.

We provide optimal measurement schemes for estimating relative parameters of the quantum state of a pair of spin systems. We prove that the optimal measurements are joint measurements on the pair of systems, meaning that they cannot be achieved by local operations and classical communication. We also demonstrate that in the limit where one of the spins becomes macroscopic, our results reproduce those that are obtained by treating that spin as a classical reference direction.

A semiclassical complex angular momentum theory, used to analyze atom-diatom reactive angular distributions, is applied to several well-known potential (one-particle) problems. Examples include resonance scattering, rainbow scattering, and the Eckart threshold model. Padé reconstruction of the corresponding matrix elements from the values at physical (integral) angular momenta and properties of the Padé approximants are discussed in detail.

When cold atoms approach a surface, they can be quantum reflected by quantal regions in the tail of the atom-surface potential. We study the phase of the reflection amplitude for Casimir–van der Waals potential tails, depending on the critical parameter $\rho =\rho (C_3,C_4)$, which describes the relative importance of the $-C_3∕r^3$ and $-C_4∕r^4$ parts of the potential. The phase is related to observable kinematic quantities, the space and time shifts, the reflected atom experiences. We study three different models for the shape of the potential between the asymptotic limits and observe that the phases are more sensitive to the potential shape than the quantum reflection probabilities. At threshold, there are always time delays in comparison to the free movement. This is in contrast to the classical movement, which shows time gains. Further above threshold, the quantum reflected atom experiences a time gain relative to free motion, but this time gain is generally smaller than that of the classical particle.

In the spirit of quantum nondemolition measurements, we show that by exploiting suitable vibronic couplings and repeatedly measuring the atomic population of a confined ion, it is possible to distill center-of-mass vibrational states with a well-defined square of angular momentum or, alternatively, angular momentum projection Schrödinger cat states.

The lowest-lying collective modes of a trapped Bose gas in an optical lattice are studied in the Bose-Hubbard model. An exact diagonalization of the Hamiltonian is performed in a one-dimensional five-particle system in order to find the lowest few eigenstates. The dipole and breathing character of the eigenstates is confirmed in the limit where the tunneling dominates the dynamics, but under Mott-like conditions the excitations do not correspond to oscillatory modes.

By stochastic modeling of the process of Raman photoassociation of Bose-Einstein condensates, we show that, the farther the initial quantum state is from a coherent state, the farther the one-dimensional predictions are from those of the commonly used zero-dimensional approach. We compare the dynamics of condensates, initially in different quantum states, finding that, even when the quantum prediction for an initial coherent state is relatively close to the Gross-Pitaevskii prediction, an initial Fock state gives qualitatively different predictions. We also show that this difference is not present in a single-mode type of model, but that the quantum statistics assume a more important role as the dimensionality of the model is increased. This contrasting behavior in different dimensions, well known with critical phenomena in statistical mechanics, makes itself plainly visible here in a mesoscopic system and is a strong demonstration of the need to consider physically realistic models of interacting condensates.

We propose an experimental scheme for one-step implementation of maximally entangled states of many three-level atoms in microwave cavity QED. In the scheme, many three-level atoms initially prepared in the same superposition states are simultaneously sent through one superconducting cavity, and maximally entangled states can be generated without requiring the measurement and individual addressing of the atoms.