Using Floquet spectroscopy, we have measured the scalar and tensor polarizabilities of a nominally hydrogenic state of a multielectron atom. We obtain ${\mathrm{\alpha }}_0$=426.1±16 MHz/(V/cm${)}^2$ and ${\mathrm{\alpha }}_2$=-66.3±22 MHz/(V/${\mathrm{cm}}^2$) for the Stark states linked to the 30${\mathit{d}}^2$D zero-field states of sodium, which we compare with the results of several theoretical treatments. We have also mapped the important transition from quadratic to linear behavior, thus measuring the hyperpolarizability as well. The measurements are discussed within the framework of a semiclassical model for the atomic response to the external field. © 1996 The American Physical Society.

Angular distributions of the intensity and the fourth-order correlation function are studied for light scattered by acoustic waves with thermal statistics. In the case when the beam diameter exceeds the coherence length of the acoustic wave, the fourth-order correlation function is found to contain an interference structure, whereas the intensity angular distribution has a one-peak shape. © 1996 The American Physical Society.

We show how maximally correlated states of N two-level particles can be used in spectroscopy to yield a frequency uncertainty equal to (NT${)}^{\mathrm{-}1}$, where T is the time of a single measurement. From the time-energy uncertainty relation we show that this is the best precision possible. We rephrase these results in the language of particle interferometry and obtain a state and detection operator which can be used to achieve a phase uncertainty exactly equal to the 1/N Heisenberg limit, where N is the number of particles used in the measurement.

We report on measurements of the saturated single frequency output of a GeXXIII x-ray laser on the J=0→1 transition at 19.6 nm from a refraction compensating double target driven by 150 J of energy from 75-ps Nd-glass laser pulses. The 19.6-nm line completely dominated the laser output. The output energy was measured to be 0.9 mJ in a beam of 6.6×30 ${\mathrm{mrad}}^2$ divergence, corresponding to a conversion efficiency of 6×${10}^{\mathrm{-}6}$. © 1996 The American Physical Society.

We investigate the Rabi Hamiltonian (or the Jaynes-Cummings model without the rotating-wave approximation), describing the coupling of a single mode of electromagnetic radiation to a two-level system, by means of the coupled cluster method. We find strong evidence for a second-order quantum phase transition. © 1996 The American Physical Society.

Over the last decade, Handy and Bessis have developed a moment-problem-based, multiscale quantization theory, the eigenvalue moment method (EMM), which has proven effective in solving singular, strongly coupled, multidimensional Schrödinger Hamiltonians. We extend the scope of EMM by demonstrating its essential role in the generation of wavelet transforms for one-dimensional quantum systems. Combining this with the function-wavelet reconstruction formulas currently available, we are able to recover the wave function systematically, from first principles, through a multiscale process proceeding from large spatial scales to smaller ones. This accomplishment also addresses another outstanding problem, that of reconstructing a function from its moments. For the class of problems considered, the combined EMM-wavelet analysis yields a definitive solution. © 1996 The American Physical Society.

In earlier work we proposed a family of nonlinear time-evolution equations for quantum mechanics associated with certain unitary group representations [Doebner and Goldin, Phys. Lett. A 162, 397 (1992); J. Phys. A 27, 1771 (1994)]. Such nonlinear Schrödinger equations are expected to describe irreversible and dissipative quantum systems. Here we introduce and justify physically the group of nonlinear gauge transformations necessary to interpret our equations. We determine the parameters that are actually gauge invariant and describe some of their properties. Our conclusions contradict, at least in part, the view that any nonlinearity in quantum mechanics leads to unphysical predictions. We also show how time-dependent nonlinear gauge transformations connect our equations to those proposed by Kostin [J. Chem. Phys. 57, 3589 (1972)] and by Bialynicki-Birula and Mycielski [Ann. Phys. 100, 62 (1976)]. We believe our approach to be a fundamental generalization of the usual notions about gauge transformations in quantum mechanics. © 1996 The American Physical Society.

By considering the simple binary symmetric random walk on a discrete lattice in 1+1 dimensions, we show that the discrete analog of Schrödinger’s equation describes a simple counting problem involving the sample paths on the lattice. Schrödinger’s equation is obtained in the continuum limit with the result that this equation is confirmed to have a classical as well as a quantum context. © 1996 The American Physical Society.

Applying a technique developed recently [L. H. Yu and C. P. Sun, Phys. Rev. A 49, 592 (1994); L. H. Yu, Phys. Lett. 202, 167 (1995)] for a harmonic oscillator coupled to a bath of harmonic oscillators, we present an exact solution for the tunneling problem in an Ohmic dissipative system with inverted harmonic potential. The result shows that while the dissipation tends to suppress the tunneling, the Brownian motion tends to enhance the tunneling. Whether the tunneling rate increases or not would then depend on the initial conditions. We give a specific formula to calculate the tunneling probability determined by various parameters and the initial conditions. © 1996 The American Physical Society.

Generalized quantum measurements can be used to separate deterministically two nonorthogonal quantum states. However, such measurements also lead to inconclusive results, where the initial state remains unknown. We introduce a particular type of generalized quantum measurement, which we term loss induced generalized (LIGe) quantum measurement, and present an experimental realization. This LIGe measurement achieves optimal deterministic separation of two nonorthogonally polarized single photons. © 1996 The American Physical Society.

The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe-Salpeter formalism as well as the most simple generalization of the nonrelativistic Schrödinger formalism towards incorporation of relativistic effects) with the Coulomb interaction potential (the static limit of the exchange of some massless bosons, as present in unbroken gauge theories). The nonlocal nature of the Hamiltonian encountered here, however, renders it extremely difficult to obtain rigorous analytic statements on the corresponding solutions. In view of this rather unsatisfactory state of affairs, we derive (sets of) analytic upper bounds on the involved energy eigenvalues. © 1996 The American Physical Society.

Usual quantum mechanics predicts probabilities for the outcomes of measurements carried out at definite moments of time. However, realistic measurements do not take place in an instant, but are extended over a period of time. The assumption of instantaneous alternatives in usual quantum mechanics is an approximation whose validity can be investigated in the generalized quantum mechanics of closed systems in which probabilities are predicted for spacetime alternatives that extend over time. In this paper we investigate how alternatives extended over time reduce to the usual instantaneous alternatives in the quantum mechanics of a nonrelativistic particle moving in one dimension. Specifically, we consider the coarse-grained alternatives of whether the particle remains to the left, remains to the right, or sometimes crosses the origin in a period of time. We show how the decoherence of this set of spacetime alternatives becomes automatic as the time over which they extend approaches zero and estimate how large this time can be before the interference between the alternatives becomes non-negligible. These results suggest that the time scale over which this kind of coarse graining of quantities such as the center of mass position of a massive body may be extended in time before producing significant interference is much longer than characteristic dynamical time scales. © 1996 The American Physical Society.

The direct method of integration of the operator Heisenberg equations of motion is extended to the solution of quantum tunneling when the central potential is a sum of inverse powers of the radial distance. By obtaining the equation of motion for the Weyl-ordered basis set {${\mathit{S}}_{\mathit{m},\mathit{n}}$(t)} formed from r(t) and ${\mathit{p}}_{\mathit{r}}$(t), one can express the time evolution of any member of the set as an infinite sum involving the operators {${\mathit{S}}_{\mathit{m},\mathit{n}}$(0)}. The direct integration enables one to find the expectation values of the radial position operator and its conjugate momentum and higher moments of these operators as functions of time. © 1996 The American Physical Society.

A simple inequality shows that any change in the expectation value of an observable quantity must be associated with some degree of uncertainty. This inequality is often more restrictive than the Heisenberg uncertainty principle. © 1996 The American Physical Society.

Sensitivity of the time evolution to small changes in the state is a characteristic feature of classical chaos. It has been believed that state sensitivity could not exist in quantum mechanics because of the unitary invariance of the Hilbert-space overlap of states. We argue that this Hilbert-space criterion is irrelevant and show that both quantum states and classical statistical states exhibit a similar kind of state sensitivity. This is demonstrated by the degree to which the initial state can be recovered in computational motion reversal: forward evolution for a time T, perturbation of the state, and backward time evolution. Some differences between classical and quantum state sensitivity remain, and these seem to be insensitive to decoherence. © 1996 The American Physical Society.

Detection of parity-violating asymmetries in 1${\mathit{s}}_{1/2}$2${\mathit{p}}_{1/2}$${\mathrm{}}^3$${\mathit{P}}_0$-1${\mathit{s}}^2$${\mathrm{}}^1$${\mathit{S}}_0$ two-photon transitions in high-Z He-like ions is discussed. The circular polarization asymmetry of one of the two photons emitted in the two-photon decay of the 2${\mathrm{}}^3$${\mathit{P}}_0$ level in He-like uranium is of order 3×${10}^{\mathrm{-}4}$. Parity-violating asymmetries in the laser-driven processes of singly stimulated two-photon emission and anti-Stokes Raman scattering are also discussed. Further experimental and theoretical research is needed to determine if parity experiments based on these processes are feasible. © 1996 The American Physical Society.

Entanglement purification protocols (EPPs) and quantum error-correcting codes (QECCs) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbitrary quantum state |ξ〉 can be transmitted at some rate Q through a noisy channel χ without degradation. We prove that an EPP involving one-way classical communication and acting on mixed state M^(χ) (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel χ) yields a QECC on χ with rate Q=D, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts ${\mathit{D}}_1$(M) and ${\mathit{D}}_2$(M) that can be locally distilled from it by EPPs using one- and two-way classical communication, respectively, and give an exact expression for E(M) when M is Bell diagonal. While EPPs require classical communication, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way communication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way communication is available. We exhibit a family of codes based on universal hashing able to achieve an asymptotic Q (or D) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single-error-correcting quantum block code. We prove that iff a QECC results in high fidelity for the case of no error then the QECC can be recast into a form where the encoder is the matrix inverse of the decoder. © 1996 The American Physical Society.

The K-LM and K-MM radiative Auger (RA) x-ray spectra of Kr and Xe were measured. The transitions were photoinduced by an x-ray tube and measured with a high-resolution transmission curved-crystal spectrometer. For Kr the K-LM and K-MM RA yields, relative to the K${\mathrm{\alpha }}_{1,2}$ and K${\mathrm{\beta }}_{1,3}$ lines, were found to be 0.15%±0.04% and 0.77%±0.2%, respectively. For Xe, only an upper limit of 0.008% relative to the K${\mathrm{\alpha }}_{1,2}$ line could be deduced for the K-LM RA yield, whereas the total relative intensity of the unresolved K-${\mathit{M}}_{4,5}$${\mathit{M}}_{4,5}$ and K-${\mathit{M}}_1$${\mathit{N}}_1$ RA transitions was found to be 0.06%±0.02% relative to the K${\mathrm{\beta }}_{1,3}$ line. In addition, the Xe K-${\mathit{M}}_{2,3}$${\mathit{N}}_1$, K-${\mathit{M}}_1$${\mathit{N}}_{4,5}$, and K-${\mathit{M}}_1$${\mathit{N}}_{2,3}$ RA transitions of Xe were also observed with a total relative intensity of 0.05%±0.02%. © 1996 The American Physical Society.

Lower bounds for the first-order gradient corrections to the kinetic- and exchange-energy functionals in atoms are derived using Benson’s inequality. They are formulated in terms of the expectation values and the momentum expectation value in a simple manner, namely, ${\mathit{T}}_2$[ρ]=1/72 ∫ |∇ρ(r)${\mathrm{|}}^2$/ρ(r) dr⩾${\mathit{n}}^2$/72 〈${\mathbf{r}}^{\mathit{n}\mathrm{-}3}$${\mathrm{〉}}^2$〈${\mathbf{r}}^{2\mathit{n}\mathrm{-}4}$${\mathrm{〉}}^{\mathrm{-}1}$ and |${\mathit{K}}_2$[ρ]|=β∫ |∇ρ(r)${\mathrm{|}}^2$/${\mathrm{\rho }}^{4/3}$(r) dr⩾0.051 05〈${\mathbf{r}}^{\mathrm{-}1}$${\mathrm{〉}}^2$〈p${\mathrm{〉}}^{\mathrm{-}1}$, where n is the natural number, 〈${\mathit{r}}^{\mathit{n}\mathrm{-}3}$〉 and 〈${\mathit{r}}^{2\mathit{n}\mathrm{-}4}$〉 are the expectation values, 〈p〉 is the momentum value, and ρ(r) is the electron density with the normalization condition of ∫ρ(r)dr=N, the number of electrons. The bounds derived in this work are tested for atoms Z=1–36. A comparison is also made with the previously derived lower bound estimates for ${\mathit{T}}_2$[ρ] and ${\mathit{K}}_2$[ρ]. The bounds presented are sharper than the previous ones given by Pathak and Gadre [Phys. Rev. A 25, 3426 (1982); 24, 2906 (1981)] (atomic units are used throughout the paper). © 1996 The American Physical Society.

An implicit Poisson equation is derived for the change in density Δn(r) from summed atomic or atomiclike densities within the Hohenberg-Kohn formulation of density-functional theory. Iterative and perturbation solutions are detailed. The first-order perturbation and first iterative solutions are equivalent, yielding Δn(r)=(4π${)}^{\mathrm{-}1}$${\mathrm{\nabla }}^2$[(δG/δn${)}_{\mathrm{system}}$-(δG/δn${)}_{\mathrm{atoms}}$], where the kinetic-exchange-correlation potential of the full system and the summed isolated atoms are (δG/δn${)}_{\mathrm{system}}$ and (δG/δn${)}_{\mathrm{atoms}}$, respectively. G is the integrand of the kinetic-exchange-correlation energy. The second-order perturbation solution leads to a Fredholm equation relating (1) the second functional derivative, (${\mathrm{\delta }}^2$G/δ${\mathit{n}}^2$${)}_{\mathrm{system}}$, with summed atomic densities; (2) the induced electrostatic energy; and, (3) the difference between (δG/δn${)}_{\mathrm{system}}$ and (δG/δn${)}_{\mathrm{atoms}}$. Numerical examples are shown for the Ni, O, and Na atoms embedded in jellium. © 1996 The American Physical Society.