We develop a fully quantized model of a Bose-Einstein condensate driven by a far off-resonant pump laser and interacting with a single mode of an optical ring cavity. This geometry leads to the generation of two condensate side modes that grow exponentially and are strongly entangled with the cavity mode. By changing the initial state of the optical field one can vary the quantum-statistical properties of the atomic side modes between thermal and coherent limits, as well as vary the degree of quantum entanglement.

We analyze the connection between the path integral and operator approaches to the quantum measurement problem. In general, an act of measurement is shown to destroy interference between components of the wave function related to the particle’s histories. Classically, there exist a class of meters suitable for measuring the value of a given dynamical variable F. Quantally, different meters produce different results. The standard von Neumann measurement is one particular case. Rearranging Feynman paths according to the value of (time average of) F defines a different type of meter. The two methods disagree if the duration of the measurement is very short. Possible ways to measure the particle’s momentum are studied in detail. The semiclassical limit of a measurement is analyzed.

This paper compares the proposal made in previous papers for a quantum probability distribution of the time of arrival at a certain point with the corresponding proposal based on the probability current density. Quantitative differences between the two formulations are examined analytically and numerically with the aim of establishing conditions under which the proposals might be tested by experiment. It is found that quantum regime conditions produce the biggest differences between the formulations which are otherwise near indistinguishable. These results indicate that in order to discriminate conclusively among the different alternatives, the corresponding experimental test should be performed in the quantum regime and with sufficiently high resolution so as to resolve small quantum effects.

The dynamics of the electron wave function in a hydrogen atom is mapped onto that of a two-dimensional harmonic oscillator. Based on the harmonic-oscillator eigenstates, a coherent state wave function for the atomic electron is proposed.

We propose a scheme to create distant entangled atomic states. It is based on driving two (or more) atoms with a weak laser pulse, so that the probability that two atoms are excited is negligible. If the subsequent spontaneous emission is detected, the entangled state is created. We have developed a model to analyze the fidelity of the resulting state as a function of the dimensions and location of the detector, and the motional properties of the atoms.

The celebrated Wigner rotation $\mathbf{d}^\left(\beta \right)$ matrices can be given in terms of vector columns of the renormalized associated Legendre polynomials.

An optomechanical sensor suitable for the study of quantum effects has been developed and characterized. The sensor reads out the vibrations of a microfabricated miniature silicon mechanical oscillator which forms one end mirror of a high finesse Fabry-Pérot cavity. The mechanical quality factor is up to $Q=300\mathrm{}000$ at 300 K and rises up to $Q=4\mathrm{}\times {10}^6$ at 4 K. The thermal noise of the oscillator has been measured in the time and frequency domains at room temperature and at 4.5 K. The prospects for observing the standard quantum limit are discussed.

We propose a framework for temporal quantum theories for the purpose of describing states and observables associated with extended regions of space-time quantum mechanically. The proposal is motivated by Isham’s history theories. We discuss its relation to Isham’s history theories and to standard quantum mechanics. We generalize the Isham-Linden information entropy to the present context.

For the Dirac equation in one space dimension, we examine the possibility of harmonic oscillator (HO) potentials. A HO potential is such that it has only bound states and the energy levels are equally spaced. Regarding their Lorentz transformation properties, there are three types of potentials for the Dirac equation: vector, scalar, and pseudoscalar. HO potentials are possible for the scalar and pseudoscalar types, but not for the vector type. We show how HO potentials can be constructed by means of the “inverse scattering method.” We also examine the behavior of a wave packet in the HO potentials so constructed. The behavior is, in most of the cases, very similar to that of Schrödinger’s coherent wave packet of the nonrelativistic harmonic oscillator.

The dynamics of circular Rydberg wave packets for the hydrogen atom with particular emphasis on fractional and full revivals previously studied by Gaeta and Stroud [Phys. Rev. A 42, 6308 (1990)], is developed within the de Broglie-Bohm pilot-wave theory. The classical limit at high quantum numbers as described within the correspondence principle is compared with the classical limit of pilot-wave theory. By studying ensembles of particles it is found that pilot-wave theory is able to deliver a consistent picture of the particle dynamics even in the high-quantum-number limit, where classical and quantum features coexist.

We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles that also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.

We propose a scheme for enhancing the information capacity to more than 2 bits in dense coding quantum communication that involves transmitting a polarization entangled twin photon and a subsequent joint measurement with a Bell-state analyzer. Although direct modulation of the timing position and optical frequency of the photon play no role in dense coding quantum communication, we show that the frequency-dependent phase correlation of polarization entangled twin photons can be used for this enhancement if photon twins are generated through optical parametric down-conversion. With our proposed Bell-state analyzer containing a nonlinear optical gate, the capacity can be enhanced from the reported 2 bits to 3 bits by the local operation of a frequency-dependent phase shift on the transmitted photon.

In most current quantum computers simple electromagnetic pulses implement computations using a minimal set of universal gates. We propose an approach in which quantum control techniques combined with flexible electromagnetic pulse shaping are used to replace several universal gates with a single instruction. We show that this complex instruction set approach can significantly reduce the time required to perform quantum computations.

A simple effective energy operator is constructed for doubly excited two-electron atoms. This operator generalizes the “molecular” Hamiltonian of the supermultiplet model based in approximate $O\left(4\right)\mathrm{}$ symmetry. The Hamiltonian is compared to spectra of two-electron systems with both electrons in the $n=2\mathrm{}$ shell. Nonlinear least-squares fits show systematic trends related to shielding, independent particle, and correlation effects. Operators for atoms with three or more outer electrons are briefly considered.

To apply the methods of dimensional scaling to higher-angular-momentum states, a formalism needs to be developed which factors the $D$-dimensional rotational degrees of freedom from the internal degrees of freedom. The rotational degrees of freedom multiply with increasing dimensionality, while the internal degrees of freedom remain finite in number. A suitable expansion which achieves this has been presented by the authors recently and is an $N$-electron $D$-dimensional generalization of the Schwartz expansion. A derivation of the coupled differential equations in the internal variables that result from the application of the Hamiltonian to this wave-function expansion for the atomic two-electron system has been presented by the authors in another recent paper. The coupled differential equations admit continuation in $D$ and clearly show the complete spectrum of exact interdimensional degeneracies of the two-electron system. However, to apply the methods of dimensional scaling to the two-electron system, the system of coupled differential equations have to be solved for large $D.\mathrm{}$ This paper concerns itself with this issue.

Theoretical binding energies have been obtained for the metastable ${\mathrm{np}}^3{}^4{S}^o$ states in the alkaline-earth sequence using a B-spline configuration-interaction approach. The results agree with available experimental and theoretical data within 5 meV for ${\mathrm{Be}}^{-}$ and within 10 meV for ${\mathrm{Mg}}^{-}.$ The binding energies of the $p^3{}^4{S}^o$ state in ${\mathrm{Mg}}^{-},$ ${\mathrm{Ca}}^{-},$ and ${\mathrm{Sr}}^{-}$ are larger than the one in ${\mathrm{Be}}^{-}$ by roughly 250 meV due to the stronger interactions with the $d^{2}p$ configurations. For ${\mathrm{Ca}}^{-},$ the ${}^4{S}^o$ binding energy is determined to be 555.5 meV, including a contribution of $-70$ meV due to dielectronic core polarization. For ${\mathrm{Sr}}^{-}$ the ${}^4{S}^o$ binding energy is 557.9 meV, including a decrease of only 6 meV due to dielectronic core polarization. This behavior for the ${}^4{S}^o$ states in ${\mathrm{Ca}}^{-}$ and ${\mathrm{Sr}}^{-}$ is ascribed to the different neutral-atom states to which the ${}^4{S}^o$ states are bound.

Starting from known identities in density-functional theory, it is shown that for finite electronic systems the density functionals $E_c^{\lambda }\left[\rho \right]$ and $T_c^{\lambda }\left[\rho \right]$ can be expanded in terms of powers of the classical moments $〈x^q{y}^r{z}^s\rho 〉$ of the electron density, with the expansion coefficients of the two series related in a simple way. For neutral atoms and coupling constant $\lambda =1,$ two-term universal linear expansions are demonstrated to be reasonably accurate: $E_c\left[\rho \right]=-0.1659〈\rho 〉\ln Z+0.000\mathrm{}40〈r\rho 〉Z$ and $T_c\left[\rho \right]=0.1659\mathrm{}〈\rho 〉\ln Z-0.00080〈r\rho 〉Z,$ where Z is the atomic number. The factors $\ln Z$ and Z in these formulas are rationalized.

An algorithm is formulated for the construction of hyperspherical functions with an arbitrary permutational symmetry. As proposed by Novoselsky and Katriel [Phys. Rev. A $49,$ 833 (1994)], we use a recursive procedure, introducing hyperspherical coefficients of fractional parentage (hscfps). These coefficients are the eigenvectors of the transposition class sum of the symmetric group in an appropriate basis. Utilizing a reversed-order set of the Jacobi coordinates we obtain a set of symmetrized basis functions well suited for few-body calculations as the evaluation of matrix elements of two-body and three-body forces involves the hscfps but no further rotation of the Jacobi coordinates. The results are applicable to the study of atomic, molecular and nuclear few-body problems. Numerical results for nuclear soft-core model potential are presented for 3, 4, and 5 body systems.

A theory of radiative and nonradiative x-ray Raman scattering based on nuclear wave-packet dynamics is presented. The theory is evaluated with special emphasis on the cases when the intermediate and/or final state potentials are dissociative. Different “one-step” and “two-step” time-dependent wave-packet formalisms are proposed and evaluated, giving different interpretational content and computational efficiency. An interference between the molecular background and the narrow atomiclike contributions is predicted and evaluated. Due to this interference the atomiclike spectral feature manifests itself as a peak or as a spectral hole depending on the circumstances in terms of excitation energy, spectral width of incident radiation, and the form of the interatomic potentials. The counterintuitive situation may even arise that a narrow peak is formed by increasing the spectral photon width. The duration of the resonant x-ray Raman scattering influences in a qualitatively different manner the space distributions of the wave packets in the molecular and the dissociative domains, something that is crucial for the formation of the cross section profile. It is shown that the scattering cross section is proportional to the square of the core excited wave packet and inversely proportional to the derivative of the difference between core excited and final state potentials. The atomiclike profile is shown to consist of a Lorentzian inner part and red or blue wings which give direct information about the long-range regions of the potentials; red wings for diverging potentials, and blue for converging. A technique of mapping of the space distribution of the squared core excited wave packet and the interatomic potentials is suggested. The various features are demonstrated by an ab initio computational study of the resonant Auger spectra of the HCl molecule close to the Cl $L_{\mathrm{I}\mathrm{I},\mathrm{I}\mathrm{I}\mathrm{I}}$ edge.

Cross sections for capture of the antiproton $\left(\overline{p}\right)$ and negative muon $\left({\mu }^{-}\right)$ by the ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ molecules are calculated using fermion molecular dynamics (FMD). All the cross sections are significantly larger than those for capture by the corresponding atom, also evaluated by the FMD method. The largest molecular cross sections are obtained when the negative projectile mass best matches the nuclear mass in the molecular target, thus for $\overline{p}+{\mathrm{H}}_2.$ The vibrational degree of freedom is shown to be most important in distinguishing the four reactions, but the effects of rotations, two-center electronic charge distribution, and nonadiabaticity are also significant. The predicted initial capture fractions (i.e., not taking subsequent transfer into account) in a ${\mathrm{H}}_2+{\mathrm{D}}_2$ mixture are $P_{\mathrm{capt}}^{\mathrm{}\left(p\right)\mathrm{}}{/P}_{\mathrm{capt}}^{\mathrm{}\left(d\right)\mathrm{}}{=qc}_p{/c}_d,$ where $q=1.585\mathrm{}$ for $\overline{p}$ and $q=1.186\mathrm{}$ for ${\mu }^{-}$ independent of $c_p$ and $c_d.$ The energy-dependent quantum-number distributions of the exotic atoms formed, the angular distributions of antiprotonic atoms, and the initial kinetic energies of muonic atoms are also presented.