Very weak laser resonances of unfavored transitions (n,l)→(n+1,l-1) have been observed in metastable p-|${\mathrm{Am}}^4$${\mathrm{He}}^{+}$ atoms by using a pulsed antiproton beam. The observed wavelengths (713.578±0.006 nm for l=34 and 726.095±0.004 nm for l=35), as well as those of the known favoured transitions, are to a few ppm accounted for by a recent variational calculation of Korobov [Phys. Rev. A 54, R1749 (1996); and (unpublished)] which includes the relativistic correction to the motion of the electron.

The triplet s-wave scattering length of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ is determined using two-photon photoassociative spectroscopy of the diatomic a${\mathrm{}}^3$${\mathrm{\Sigma }}_{\mathrm{u}}^{+}$ state of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_2^{}{}_{}{}^{}$. The measured binding energy of the highest-lying bound state, combined with knowledge of the potential, determines the s-wave scattering length to be (-2160±250)${\mathrm{a}}_0$, where ${\mathrm{a}}_0$ is the Bohr radius. This extraordinarily large scattering length signifies a near-threshold resonance. A complete table of singlet and triplet scattering lengths for collisions involving ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ determined from this and our previous spectroscopic investigations is given.

We investigate coherence in near-threshold photodetachment from ${\mathrm{O}}^{\mathrm{-}}$ in a magnetic field, using laser pulses much shorter than the cyclotron period of the electron. Illumination of the ions by one pulse creates a wave packet of uniformly spaced cyclotron orbits. A second, identical pulse creates a second wave packet that interferes with the first. The observed interference is similar to but not in complete agreement with a model in which the interference is modulated at the cyclotron frequency. This is an observation of Ramsey interference in a one-dimensional continuum.

Quantum evolution of a collective mode of a Bose-Einstein condensate containing a finite number N of particles can demonstrate the phenomena of collapses and revivals. The characteristic collapse time depends on the scattering length, the initial amplitude of the mode, and N. The corresponding time values have been derived analytically under certain approximations and numerically for the parabolic atomic trap. The revival of the mode amplitude at a time of several seconds, as direct evidence of the effect, can occur if the normal component is significantly suppressed.

We present a theoretical study of the index of refraction of argon for the propagation of sodium matter waves. The sensitivity of the index of refraction to the details of the molecular potential curve is analyzed. Our calculations reveal velocity-dependent oscillations in the index of refraction that may be detectable, particularly at low temperatures, in atom interferometry measurements. A procedure for refining molecular potential curves is outlined.

Interacting argon atoms are simulated with a recently developed quantum Langevin transport treatment that takes approximate account of the quantum fluctuations inherent in microscopic many-body descriptions based on wave packets. The mass distribution of the atomic clusters is affected significantly near the critical temperature and thus it may be important to take account of quantum fluctuations in molecular-dynamics simulations of cluster formation processes.

Using two laser pulses of femtosecond duration we excite a diatomic molecule (${\mathrm{I}}_2$) to a dissociative state where the wave function is localized around two internuclear separations. The structure of the wave function is controlled by the relative amplitude and the temporal separation of the exciting laser pulses. A delayed intense probe pulse measures the square of the wave function as a function of the internuclear separation |Ψ(R)${\mathrm{|}}^2$ by Coulomb exploding the molecule. We report a resolution of ∼2 Å in the internuclear range ∼6–15 Å. We discuss how intense femtosecond laser pulses provide a different approach to time-resolved photochemistry.

Photon-number fluctuations 1.3 dB below the semiclassical shot-noise limit are observed in the output of a semiconductor microcavity laser. Although the laser oscillates in a single longitudinal mode, photon-number squeezed light is realized through nonclassical correlations between two orthogonally polarized, transverse laser modes.

Quantum operations provide a general description of the state changes allowed by quantum mechanics. Simple necessary and sufficient conditions for an ideal quantum operation to be reversible by a unitary operation are derived in this paper. These results generalize recent work on reversible measurements by Mabuchi and Zoller [Phys. Rev. Lett. 76, 3108 (1996)]. Quantum teleportation can be understood as a special case of the problem of reversing quantum operations. We characterize completely teleportation schemes of the type proposed by Bennett et al. [Phys. Rev. Lett. 70, 1895 (1993)].

The nonrelativistic reduction of quasipotential equations in QED and Wick-Cutkosky models is considered. It is shown that if we retain an energy dependence of the potential (i.e., make the nonrelativistic reduction only partially), there may arise discrete levels in the continuum for some large critical values of the coupling constant. The fact that the discrete levels disappear in the exact nonrelativistic limit indicates a possible connection with the abnormal solutions of the Bethe-Salpeter equation. Thorough investigation (both analytical and numerical) of the von Neumann–Wigner type potentials is provided.

Multiport beam splitters are shown to be applicable in feasible optical realizations of higher-dimensional EPR correlations, and of tests of local realism involving measurements of nondichotomic variables. These multiports permit optical realizations of any unitary operator in Hilbert spaces of arbitrary finite dimension. Thus it is shown that one is by no means constrained to entangled spin systems, and to Stern-Gerlach apparatuses. In the analysis the concept of generalized Bell numbers is employed, which is more suitable than the standard set of spin eigenvalues. The results presented here move the discussion on entangled higher-than- spin systems from the realm of gedanken experiments to real experiments.

A quantum problem on an isospectral deformation of one-dimensional potentials (and of corresponding wave functions) is considered. The isospectral deformation defined in the form of a phase flow is shown to obey a system of coupled Liouville equations. In a simple case of an individual flow the well-known integrable Liouville equation arises; its solution provides known families of isospectral potentials. Operators performing this deformation are studied; their unitary property is proved. An evolution of spectral shift operators is determined using those unitary operators. An asymptotical behavior of both a potential and wave functions under this isospectral deformation is studied. It is shown, in particular, that the deformation of the Rosen-Morse potential and that of the harmonic oscillator's potential have common analytical properties. The approach used in the paper can be extended to the case of a deformation leading to a shift of one selected energy level. In the case of the simplest individual flow we get a generalization of the integrable Liouville equation.

A two-boson Hamiltonian is constructed whose induced unitary evolution implements in the corresponding Fock space the algorithm devised by Shor [Algorithms for Quantum Computation: Discrete Logarithms and Factoring, in Proceedings of the 35th Annual Symposium on Foundation of Computer Science, edited by S. Goldwasser (IEEE Computer Society Press, Los Alamitos, CA, 1994), p. 124] to factorize an integer into prime factors.

We show through a series of arguments that, given a total average photon number 〈N〉, the fundamental limit in the precision phase measurement is set by quantum mechanics to be the so-called Heisenberg limit, i.e., 1/〈N〉. Some specific types of phase measurement are considered in the discussion. However, the proof based on the general principle of complementarity of quantum mechanics applies to any scheme of phase measurement. From the general argument by the complementarity principle, we are able to find a necessary condition for those states that can achieve the Heisenberg limit if they are employed for precision phase measurement. A general guideline is given for the search of the measurement schemes in which the Heisenberg limit is achieved. We demonstrate the procedure by applying it to a few specific examples.

For a time-dependent system characterized by the potential V(x,t)=${\mathrm{a}}_2$(t)${\mathrm{x}}^2$+${\mathrm{a}}_1$/${\mathrm{x}}^2$, we first demonstrate the construction of classical and quantum invariants and then obtain an exact solution of the Schrödinger equation for this potential. The role of the invariant so constructed is further discussed in the context of studies of the coherent states.

A time-dependent perturbation theory is presented for constructing operator invariants iteratively when a Hamiltonian consists of a time-independent zeroth-order term plus a time-dependent perturbation. The procedure uses a single canonical transformation that involves an invariant operator that is canonically conjugate to the zeroth-order Hamiltonian. Such an invariant operator has recently been constructed for the case in which the zeroth-order Hamiltonian describes a harmonic oscillator.

With the aid of two linearly independent Whittaker functions, Loudon obtained the solutions with even and odd parity for the one-dimensional hydrogen atom. Applying the Schwarz inequality, Andrews made an objection to Loudon's ``ground state.'' Either solving the problem in the momentum representation or basing our work on the theory of singular integral equations, we have proved that these solutions with even parity do not exist. Due to its importance related to the nondegeneracy theorem and to the study of the exciton and Wigner crystal (by electron gas above the helium surface), we have reexamined this problem in the coordinate representation by means of the orthogonality criterion for singular states and the natural connection condition of the wave function's derivatives. We have proved again that all these eigenstates with even parity do not exist. This result is consistent with that of exact solutions in the momentum representation and in the integral equation method canceling divergence. This study not only emphasized the importance of the orthogonality criterion but also generalized its application, including the singular states with poles, essential singular points, phase angle uncertainty, and the logarithmic singularity of derivatives.

Higher-order WKB methods are used to investigate the border between the solvable and insolvable portions of the spectrum of quasiexactly solvable quantum-mechanical potentials. The analysis reveals scaling and factorization properties that are central to quasiexact solvability. These two properties define a new class of semiclassically quasiexactly solvable potentials.

Within density-functional theory a time-dependent perturbation theory is derived that yields exact orbital-dependent expressions for the time-dependent exchange-correlation potential in the form of a perturbation series. This leads to an exact time-dependent Kohn-Sham scheme based on perturbation theory. In first order an ``exchange-only'' Kohn-Sham procedure is obtained, that is a generalization of a recently presented time-dependent optimized potential method. The exact, in higher order, but quite complicated expressions for the exchange-correlation potential may serve as a starting point for the construction of approximate exchange-correlation potentials. An adiabatic connection or coupling constant path between a time-dependent physical system and its corresponding Kohn-Sham system is introduced.

The interpair and intrapair electron pair correlation energies of the low-energy ${}_{}{}^2{}_{}{}^{}$ ${\mathrm{A}}_1$ excited state of ${\mathrm{NaCl}}_2$ have been analyzed and compared with the corresponding energies of the ground ${}_{}{}^2{}_{}{}^{}$ ${\mathrm{B}}_2$ states. The total interpair electron correlation energy in the excited state dominates, just as in the ground state.