A theoretical and experimental investigation is made of the spectrum of a near-resonant femtosecond laser pulse propagating through a two-level atomic system. Measurements made using a high-resolution Fabry-Perot microcavity show that at the transition frequency the spectrum of the transmitted pulse acquires a feature whose structure depends sensitively on the pulse area, the pulse detuning, and the absorption path length. Our observations are in excellent agreement with the predictions of the Maxwell-Bloch equations. In the thin-sample limit, these results show that from the shape of the spectral feature it is possible to infer the quantum state of the atomic system excited by the pulse.

Recoil-ion momentum spectroscopy and molecular fragment imaging techniques are combined to study dissociative electron capture from He by ${\mathrm{HeH}}^{+}$ at 0.20-a.u. collision velocity. Groups of final HeH states which dissociate to ground or excited H and He atoms are separated. For each group, the experiment provides two-dimensional H fragment distributions with respect to the collision plane and for fixed transverse momentum transfer. These patterns show that the capture probability is highest for ${\mathrm{HeH}}^{+}$ ions with their axis oriented normal to the scattering plane for two of the three groups populated.

Retention of orbital alignment during near-resonant energy transfer collisions of rare-gas projectiles with excited alkaline-earth-metal atoms is explored theoretically for scattering of Xe from Rydberg states of Ca. For such collisions, conventional interpretations of alignment phenomena, which are based on potential curves for a transient molecule thought to form during the collision, are not relevant. Theoretical partial magnetic sublevel cross sections for ${\mathrm{Ca}}^{**}(4s17d{}^1{D}_2\to 4s18p{}^1{P}_1)$ transitions confirm the existence of alignment effects, as demonstrated experimentally by Spain et al. [J. Chem. Phys. 102, 9532 (1995)], at a mean relative velocity of 914 m/s. Theory further predicts heretofore unobserved oscillatory structures in these cross sections as a function of relative velocity and that these oscillations depend strongly on the initial magnetic quantum number of the Rydberg electron.

A test of special relativity has been carried out using data of clock comparisons between hydrogen maser clocks on the ground and cesium and rubidium clocks on board 25 global positioning system (GPS) satellites. The clocks were compared via carrier phase measurements of the GPS signal using geodetic receivers at a number of stations of the International GPS Service for Geodynamics (IGS) spread worldwide. In special relativity, synchronization of distant clocks by slow clock transport and by Einstein synchrony (using the transmission of light signals) is equivalent in any inertial frame. A violation of this equivalence can be modeled using the parameter $\delta c/c,$ where $c$ is the round-trip speed of light ($c=299\mathrm{}792458\mathrm{m}/\mathrm{s}$ in vacuum) and $\delta c$ is the deviation from $c$ of the observed velocity of a light signal traveling one way along a particular spatial direction with the measuring clocks synchronized using slow clock transport. In special relativity $\delta c/c=0.\mathrm{}$ Experiments can set a limit on the value of $\delta c/c$ along a particular spatial direction (henceforth referred to as “direction of $\delta c$”). Within this model our experiment is sensitive to a possible violation of special relativity in any direction of $\delta c,$ and on a nonlaboratory scale (baselines $>~20000\mathrm{km}$). The results presented here set an upper limit on the value of $\delta c/c<\mathrm{}5\mathrm{}\times {10}^{-9}$ when considering all spatial directions of $\delta c$ and $\delta c/c<\mathrm{}2\mathrm{}\times {10}^{-9}$ for the component in the equatorial plane.

A variant of variational perturbation theory is developed for a calculation of the quantum-statistical density matrix in thermal equilibrium. For the diagonal elements, which represent the particle distribution, higher-order corrections are calculated, and show excellent agreement with numerical results from Schrödinger theory.

The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, $-1/ħ\int H\left(t\right)dt,$ given by the integrated expectation value of the Hamiltonian, and a geometric phase ${\Phi }_G\mathrm{}\left(C\right)\mathrm{}$ which depends only on the geometry of the curve traced in ray space. We have performed an interference experiment using polarized neutrons which clearly demarcates the separate contributions of the dynamical and geometric phases to the total. In the experiment, the two phases arise from two distinct physical operations, a translation and a rotation of a spin flipper within the interferometer, respectively. This work also constitutes the first direct observation of the Pauli anticommutation; a purely geometric phase shift of π radians appears after a reversal of the current in one of the spin flippers. The experiment was carried out at the 10 MW University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. A detailed description of the experiment and its interpretation is given in this paper.

We calculate the number of photons produced by the parametric resonance in a cavity with vibrating walls. We consider the case that the frequency of vibrating wall is $n{\omega }_1$ $(n=1,2,3,\dots ),$ which is a generalization of other works considering only $2{\omega }_1$, where ${\omega }_1$ is the fundamental-mode frequency of the electromagnetic field in the cavity. For the calculation of time evolution of quantum fields, we introduce a method that is borrowed from the time-dependent perturbation theory of the usual quantum mechanics. This perturbation method makes it possible to calculate the photon number for any $n$ and to observe clearly the effect of the parametric resonance.

A model for a quantum register dissipatively coupled with a bosonic thermal bath is studied. The register consists of $N$ quantum bits (qubits) the bath is described by $N_b$ bosonic modes. The register-bath coupling is chosen in such a way that the total number of excitations is conserved. The Hilbert space splits, allowing the study of the dynamics separately in each sector. Assuming that the coupling with the bath is the same for all qubits, the excitation sectors have a further decomposition according the irreducible representations of the su(2) spin algebra. The stability against environment-generated noise of the information encoded in a quantum state of the register depends on its SU(2) symmetry content. At zero temperature we find that states belonging to the vacuum symmetry sector have, for long time, vanishing fidelity, whereas each lowest spin vector is decoupled from the bath and therefore is decoherence free. Numerical results are shown in the one-excitation space in the case of qubit-dependent bath-system coupling.

We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this notion to describe the amount of entanglement between two quantum systems from a statistical point of view. Our measure is independent of the number of entangled systems and their dimensionality.

We present a mathematical physics analysis of entangled translucent eavesdropping in quantum cryptography, based on the recent work of Ekert, Huttner, Palma, and Peres [Phys. Rev. A 50, 1047 (1994)]. The key generation procedure involves the transmission, interception, and reception of two nonorthogonal photon polarization states. At the receiving end, a positive operator valued measure (POVM) is employed in the measurement process. The eavesdropping involves an information-maximizing von Neumann–type projective measurement. We propose a design for a receiver that is an all-optical realization of the POVM, using a Wollaston prism, a mirror, two beam splitters, a polarization rotator, and three photodetectors. We present a quantitative analysis of the receiver. We obtain closed-form algebraic expressions for the error rates and mutual information, expressed in terms of the POVM-receiver error rate and the angle between the carrier polarization states. We also prove a significant result, namely, that in the entangled translucent eavesdropping approach, the unsafe error rate based on standard mutual information comparisons is equivalent to the maximum allowable error rate based on perfect mutual information for the eavesdropper. In this case, the above unsafe error rate is in fact not overly conservative.

We construct generally applicable short-time perturbative expansions for some fidelities, such as the input-output fidelity, the entanglement fidelity, and the average fidelity. Successive terms of these expansions yield characteristic times for the damping of the fidelities involving successive powers of the Hamiltonian. The second-order results, which represent the damping rates of the fidelities, are extensively discussed. As an interesting application of these expansions, we use them to study spatially correlated dissipation of quantum bits. Spatial correlations in the dissipation are described by a correlation function. Explicit conditions are derived for independent decoherence and for collective decoherence.

Two hundred coefficients of the renormalized strong-coupling perturbation expansion for the ground and first excited states of the quartic anharmonic oscillator are calculated numerically. The large-order behavior of the perturbation coefficients is analyzed, a general and comparatively simple analytic formula describing their large-order behavior is proposed, and it is shown that this formula is consistent with known results from the divergent weak-coupling expansion. The accuracy of our numerically determined coefficients is checked by summation rules. In particular, if the summation rules are supplemented by the leading terms of our large-order formula, we obtain remarkably accurate results. This independently confirms the correctness of our large-order analysis. It is shown that the renormalized strong-coupling expansion converges—in contrast to other perturbation expansions—for all physically relevant coupling constants.

Collins’s conjecture [Z. Naturforsch. 48A, 68 (1993)] that the correlation energy of a system is proportional to the Jaynes entropy [in Papers on Probability, Statistics and Statistical Physics, edited by R. Rosencrantz (Reidel, Dordrecht, 1983)] is investigated for small molecular systems. Numerical evidence supporting the conjecture is obtained by computing entropies from highly correlated configuration-interaction wave functions at various correlation levels, using sequences of increasingly larger basis sets. Further evidence is also obtained by examination of results obtained from a variety of correlation methods utilizing a fixed basis set.

We consider the hyperfine structure, the atomic spectrum, and the decay channels of the bound ${\mu }^{+}{\mu }^{-}$ system (dimuonium). The annihilation lifetimes of low-lying atomic states of the system lie in the ${10}^{-12}$ s range. The decay rates could be measured by detection of the decay products (high-energy photons or electron-positron pairs). The hyperfine-structure splitting of the dimuonic system and its decay rate are influenced by electronic vacuum polarization effects in the far timelike asymptotic region. This constitutes a previously unexplored kinematic regime. We evaluate next-to-leading-order radiative corrections to the decay rate of low-lying atomic states. We also obtain order ${\alpha }^5{m}_{\mu }$ corrections to the hyperfine splitting of the $1S$ and $2S$ levels.

Using a single trial function, we perform an accurate calculation of the ground state $1{\sigma }_g$ of the hydrogenic molecular ion ${\mathrm{H}}_2^{+}$ in a constant uniform magnetic field ranging from 0 to ${10}^{13}$ G. We show that this trial function also makes it possible to study the negative parity ground state $1{\sigma }_u.$ We show that, over the whole range of magnetic fields studied the calculated binding energies are in most cases larger than binding energies obtained previously by other authors using different methods.

The experimental values of pressure broadening and shift parameters of the 326.1-nm Cd line perturbed by Xe are measured and compared with those calculated from the impact theory for different interaction potentials. The role of the correlations between collisional and Doppler broadening for the Cd-Xe system is discussed.

The vacuum-polarization corrections to the hyperfine structure intervals for the ${2s}_{1/2}$ state of ${}_{83}^{209}$Bi${}^{80+}$ ion and the ${2p}_{3/2}$ state of Li-like, B-like, and N-like ${}_{83}^{209}$Bi ions are calculated. The “dynamical” model of the hyperfine interaction is used, in which the electron is assumed to interact with the valence proton in ${}_{83}^{209}$Bi nucleus via exchange of a photon. In this model, the magnetic dipole moment and the electric quadrupole moment distributions inside the nucleus are automatically taken into account. The contributions of the vacuum polarization to the hyperfine structure intervals are evaluated in the Uehling approximation. To calculate the hyperfine splittings, the Dirac-Hartree-Fock wave functions for an extended nucleus are used.

The photoinduced $K\alpha$ and $K\beta$ x-ray spectra of argon and krypton were measured by means of high-resolution crystal diffractometry. Ar $K{\alpha }_{1,2}{L}^{\mathrm{}\left(1\right)\mathrm{}}$ and $K{\beta }_{1,3}{M}^{\mathrm{}(1,2)\mathrm{}}$ and Kr $K{\alpha }_1{L}^{\mathrm{}\left(1\right)\mathrm{}}$ and $K{\beta }_2{M}^{\mathrm{}(1,2)\mathrm{}}$ satellites were observed and resolved from the corresponding diagram lines. From the satellite to parent diagram line yield ratios, the probabilities for producing via shake processes $K^{\mathrm{}\left(1\right)\mathrm{}}{L}^{\mathrm{}\left(1\right)\mathrm{}}$ and $K^{\mathrm{}\left(1\right)\mathrm{}}{M}^{\mathrm{}\left(1\right)\mathrm{}}$ double-hole states were deduced. The results are compared to the few other existing experimental data and to theoretical sudden approximation predictions. The latter are found to underestimate somewhat the experimental values.

The relativistic coupled-cluster method in a large four-component Gaussian-spinor basis is applied to the ionization potentials and electron affinities of group-13 elements B, Al, Ga, In, and Tl. Many shells are correlated (up to 35 electrons for Tl) to account for core effects. Calculated ionization potentials are in excellent agreement (within 0.01–0.05 eV) with experiment. The electron affinities are 0.279 eV for B (experimental 0.277$\pm$0.010), 0.427 eV for Al (0.44094${}_{-0.00048}^{+0.000\mathrm{}66})$, 0.301 eV for Ga (0.30$\pm$0.15), 0.419 eV for In (0.30$\pm$0.20), and 0.40$\pm$0.05 eV for Tl (experimental 0.20$\pm$0.20). The first four are in close agreement with recent multiconfiguration Dirac-Fock (MCDF) values; it is shown that the smaller affinity predicted by MCDF for Tl (0.291 eV) is due to the neglect of dynamic correlation, in particular that of the $5d$ electrons, which has a substantial contribution in this case.

We study doubly excited ${}^{1,3}{S}^e$, ${}^{1,3}{P}^o,$ and ${}^{1,3}{D}^e$ resonances in He below the $n=2\mathrm{}$ ${\mathrm{He}}^{+}$ threshold by the saddle-point complex-rotation method with $B$-spline functions. We calculated 78 resonances. Recently, accurate measurements on the ${}^1{P}^o$ have been performed, which allow detailed comparisons with our ab initio theoretical results. For ${}^1{P}^o$, we calculate six members in the ${}_2{\mathrm{}(0,1)\mathrm{}}_n^{+}(2\mathrm{}<~n<~7)$ series, five members in the ${}_2{\mathrm{}(1,0)\mathrm{}}_n^{-}(3\mathrm{}<~n<~7)$ series, and four members in the ${}_2\left(-{1,0)}_n^0\right(3\mathrm{}<~n<~6)$ series. The resonance energies and widths are compared with accurate experimental and theoretical results. The agreement is good. For other symmetries, the energies and widths are also calculated up to $n\cong$7, and are also in good agreement with available experimental and theoretical results.