We develop an information-theoretic formalism to describe a quantum-cryptographically protected communication channel. We thereby establish the fundamental limits on the security of the channel. This formalism enables us to propose protocols that allow detection of an eavesdropper by examination of data that would normally be discarded.

We report unusual profiles in the resonance fluorescence spectrum of a two-level atom interacting with a resonant classical field of intermediate intensity and a squeezed vacuum. These have a dispersive profile, quite unlike any previously described, and are a distinctive feature of the interaction of atomic systems with nonclassical fields. An approximate analytic expression is obtained which explains these features, and it is shown that they arise from atomic correlations not probed in normal resonance fluorescence.

We have investigated Ba high-l 8snl double Rydberg states produced by multistep laser excitation in the presence of a temporarily applied electric field to probe the Coulomb interaction between the two excited electrons. The spectra for the 6s→8s excitation with n=13 (l=12 to 6) show a strong dependence on the orbital momentum of the external electron, due to multipole effects. To explain the 5fn’l’ resonances appearing in the n=13 and 14 l=6 spectra, terms higher than the dipole interaction have to be considered in the multipole expansion.

This paper intends to clarify some issues in the theory of quantum measurement by taking advantage of the self-consistent quantum formulation of nonlinear optics. A quantum-nondemolition measurement of the photon number of an optical pulse can be performed with a nonlinear Mach-Zehnder interferometer followed by a balanced detector. The full quantum-mechanical treatment shows that the shortcut in the description of the quantum-mechanical measurement, the so-called ‘‘collapse of the wave function,’’ is not needed for a self-consistent interpretation of the measurement process. Coherence in the density matrix of the signal to be measured is progressively reduced with increasing accuracy of the photon-number determination. The quantum-nondemolition measurement is incorporated in the double-slit experiment and the contrast ratio of the fringes is found to decrease systematically with increasing information on the photon number in one of the two paths. The ‘‘gain’’ in the measurement can be made arbitrarily large so that postprocessing of the information can proceed classically.

The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method, a requisite external field is obtained to track exactly a prescribed molecular objective expectation value as a function of time. Applications to diatomic and polyatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for position and energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.

The time evolution of a free particle confined to the half space x>0 and subject to a sequence of periodic δ-function linear kicks has been investigated. The quasienergies and quasistates of the system are determined exactly. It turns out that the quasiboundedness of the system makes the quasienergy spectrum discrete and leads to a recurrent behavior of the system.

We consider the Einstein-Podolsky-Rosen correlation between two spins with arbitrary j values using the phase-space description of the angular-momentum operators [G. S. Agarwal, Phys. Rev. A 24, 2889 (1981)]. The phase-space formulation provides insight into hidden-variable theories and enables us to understand why Bell’s inequalities are violated. We use the analogs of the Wigner function and the P function for the analysis of the correlations. We show that the Wigner function for the singlet state becomes positive in the limit j→∞. We also show the extent to which Bell’s inequalities can be violated for higher spins and present physical quantities, the correlations between which would violate Bell’s inequalities.

So far, the wave function has been interpreted as a probability amplitude, which is given physical meaning by ensemble averages of a large number of identical systems at a given time. We give an alternative interpretation of the wave function for a single system by means of a measurement which lasts a long time. This is a measurement on a single quantum system which determines the expectation values of (not necessarily commuting) observables while the wave function is protected from collapsing because it undergoes another suitably chosen interaction. This type of measurement enables the distinction between states which are not orthogonal, but are protected by a suitable interaction with the states of their environment, even for a single system. It therefore gives a different ontological meaning to the wave function. Several experiments in which such a measurement is realized, which can in principle be performed using electrons, neutrons, or atoms, are studied.

The validity domain, within quantum mechanics, of a full set of eight Bell inequalities for four observables is determined and represented geometrically. It turns out that the incorporation of all inequalities increases considerably the domain of invalidity. For special spin constellations, the validity regions become arbitrarily small. The results are compared with experiment and used to elucidate the status of the existing experimental evidence in favor of quantum theory and against hidden variables.

Atomic- and neutron-beam interferometry offer a sensible technique for tests of the space-time structure. One important ingredient of the space-time structure is given by the null cones, which are related to local Lorentz invariance. A possible deviation from this structure described as splitting of the null cones gives rise to non-Lorentz invariance effects. It is shown that in the nonrelativistic limit this typically amounts to a new type of spin-momentum coupling. Starting from a generalization of the Dirac equation, based on fundamental principles, reasons are given for this special kind of coupling. The outcome of this model theory is taken to propose experiments which use atomic-beam interferometry and give improved upper limits on possible non-Lorentz invariance parameters.

The extreme-eigenstate approach to the solution of dynamic group representation is formulated systematically based on the continuous representation of the group generators and their intrinsic counterparts by virtue of two complete sets of commuting operators of first and second kinds (CSCO I and CSCO II). The high-order partial differential equations for the general representation eigenstates in the conventional approach are replaced by a set of first-order partial differential equations for the extreme eigenstate in this approach. This set of first-order partial differential equations is tractable for analytical solutions. By applying the ladder operators, any representation eigenstates can be obtained by standard differential operation. In application, the Wigner SU(2) D function and the Elliott SU(3) irreducible representation basis are obtained by this approach as illustrations. The approach is proved to be simple, useful, and efficient for physicists.

The quantum dynamics of minimum uncertainty wave packets in a system described by the surface-state-electron Hamiltonian are studied herein. The quantum evolution is found to be strongly dependent upon the orbit structure in the classical phase space. A Gaussian wave packet, initially centered on the part of the phase space incased by Kolmogorov-Arnold-Moser tori remains localized, while the packets located in the chaotic region spread rapidly, filling the available phase space. To quantify the observed spreading quantum uncertainty is introduced as a dynamical variable, and its time development is determined by the ballistic growth of the position uncertainty and the erratic oscillations of the momentum uncertainty. The quantum evolution is analyzed within the framework of the Floquet formalism. The Floquet spectrum of the stable packet is shown to be dominated by a few quasienergy states with the corresponding Husimi distribution embedded in the classical stability island. Further, the classical concept of diffusion previously used in this context is shown to be inappropriate.

We present a unified treatment of a number of double-slit experiments which give ‘‘which-path’’ information. The loss of coherence is described by a random-average model over basis states of the path detector. While the precise physical mechanism depends on the choice of the detector basis, the random-average model shows that the loss of coherence may always be described in terms of a stochastic disturbance to the system due to coupling with the path detector. The possibility of quantum erasers is shown to arise naturally from an appropriate choice of detector basis.

The tunneling-time problem is shown to be analogous to the interpretation of the two-slit interference experiment. A measurement assuming an arbitrarily small interaction between a particle and a clock is shown to contradict the uncertainty principle and leads to complex times. A real non-negative traversal time is obtained in a measurement which selects Feynman paths that spend in the barrier a known amount of time; this, however, strongly perturbs the tunneling. The Larmor clock demonstrates both types of behavior.

The exchange energy for pairs of helium and neon atoms was calculated with recently proposed exchange-energy functionals for Hartree-Fock electron densities, and compared with the exact (Hartree-Fock) exchange energy. While all of the functionals calculate the total exchange energies to within 1%, most of the functionals give very poor results for Δ${\mathit{E}}_{\mathrm{exc}}$, the exchange-energy contribution to the interaction energy. At the positions of the energy minima for the atom pairs, most functionals give Δ${\mathit{E}}_{\mathrm{exc}}$ in error by over 100%. The reason for the difference in accuracy between the total exchange energy and Δ${\mathit{E}}_{\mathrm{exc}}$ is that the total exchange energy is dominated by the high density and small gradient regions near the nuclei, while Δ${\mathit{E}}_{\mathrm{exc}}$ is dominated by the low density and large gradient regions between the atoms. We propose an exchange functional which gives good results for both the total exchange energy and Δ${\mathit{E}}_{\mathrm{exc}}$. We also show that the Lieb-Oxford bound can only be applied globally, and not locally as some investigators have suggested.

We present a detailed theoretical analysis of experimental rates for ddμ molecular formation and dμ hyperfine transitions at temperatures 25.5–150 K, which were reported by Zmeskal et al. [Phys. Rev. A 42, 1165 (1990)]. Theoretical effective ddμ formation rates are fitted to the observed rates by adjusting the ddμ binding energy ${\mathrm{\varepsilon }}_{11}$, the effective dd fusion rate λ${\mathrm{̃}}_{\mathit{f}}$, and the nonresonant ddμ formation rate ${\lambda }_{\mathrm{nr}}$. The value of ${\mathrm{\varepsilon }}_{11}$=-1966.1±0.2 meV is determined with extreme accuracy and agrees with the theoretical prediction within 0.1 meV. Experimental findings for ${\lambda }_{\mathrm{nr}}$ are compatible with theory. Since the value of λ${\mathrm{̃}}_{\mathit{f}}$ extracted from observed formation rates depends on the calculated value of ddμ formation matrix elements ‖${\mathit{V}}_{\mathit{i}\mathit{f}\mathrm{\Vert }}$, we present the region of pairs (λ${\mathrm{̃}}_{\mathit{f}}$,‖${\mathit{V}}_{\mathit{i}\mathit{f}\mathrm{\Vert })}$ allowed by experiment. The theoretical values of λ${\mathrm{̃}}_{\mathit{f}}$ and ‖${\mathit{V}}_{\mathit{i}\mathit{f}\mathrm{\Vert }}$ lie outside this region. A significant discrepancy remains for the dμ hyperfine transitions, where the theoretical rates, which consist of scattering and back-decay contributions, exceed experimental rates by ∼40%. Fits of the experimental data indicate that mostly the scattering contribution is smaller than calculated. The extrapolation of our fit to higher temperatures is in good agreement with other experiments on ddμ formation.

The coupled-cluster method with single and double excitations is applied to the (1,2) sector of the Fock space, the sector of one valence hole and two valence particles added to a closed shell. The coupled-cluster equations in the (1,2) sector are linear and are solved directly. The systems investigated are the two isoelectronic sequences B, ${\mathrm{C}}^{+}$ , ${\mathrm{N}}^{2+}$ and Al, ${\mathrm{Si}}^{+}$, ${\mathrm{P}}^{2+}$. The primary interest is in the excitation spectra of these systems. In addition, due to the hierarchical nature of the Fock-space approach, other results are obtained gratuitously in the lower sectors. Excellent results are obtained, with most calculated energies differing from experimental values by less than 0.1 eV.

Doubly excited ridge states of atoms are states in which two electrons reach high and comparable excitations. Our goal is to calculate sequences for some of these states by using a wave function that treats the pair of electrons as a single entity in solving the two-electron Schrödinger equation in hyperspherical coordinates: R, α, ${\mathrm{\theta }}_{12}$. For double escape of slow electrons, the so-called Wannier theory predicts that the wave function will be concentrated in the region α=π/4, ${\mathrm{\theta }}_{12}$=π (that is, ${\mathbf{r}}_1$=-${\mathbf{r}}_2$) and we expect something similar for the ridge states. By expanding the Schrödinger equation around these points and retaining the first nontrivial quadratic dependences in α and ${\mathrm{\theta }}_{12}$, we seek a solution in which the form of the wave function in these two variables is analytically determined as in the Wannier theory. The R dependence of this wave function is then handled numerically and differs from the double-escape solution only in the exponential decay appropriate for bound states. For L=0 a polynomial in R is included, giving the proper number of nodes for the solution. Numerical eigenvalues for autoionizing ridge states are calculated and compared with available results.

We first evaluate the exact propagator for a δ-function potential moving with constant velocity by summing over the spectrum of eigenstates and by calculating the path integral directly. The ‘‘one-time Green’s functions’’ are then derived from the Fourier transform of the propagator obtained. We finally investigate the propagator through an asymptotic approximation.

The hyperfine structure of 5snd ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ states in ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$ was studied for principal quantum numbers 11≤n≤25 by Doppler-free two-photon excitation combined with thermionic detection. Based on the more accurate data, compared to previous results, the hyperfine structure was analyzed by second-order perturbation theory using multichannel quantum-defect theory wave functions. As a result we find that the surprisingly large B factors obtained by fitting the data with the Casimir formula do not reflect a quadrupolar interaction but rather consist predominantly of second-order magnetic dipole contributions. Further, inconsistencies in the King plot of odd-even isotope shifts were removed by this type of analysis. The result demonstrates the importance of higher-order effects in hyperfine splittings of excited states in atoms with two valence electrons, even when the fine-structure splitting is large compared to the hyperfine splitting.