We investigate the process of intracavity photoassociation of Bose-Einstein-condensed atoms to form a molecular condensate. As shown previously, this process can only be successfully described by a quantum treatment of all the interacting fields. We extend our previous work by representing the full quantum aspects of the problem using an extension of the positive P representation to model non-Wiener noises. This allows the mapping of a generalized Fokker-Planck equation with third-order derivatives onto a set of coupled stochastic difference equations. We also investigate parameter regimes not covered previously, as well as the effects of spontaneous dissociation of the condensed molecules.

We construct the optimal strategy for the estimation of an unknown unitary transformation $U\in \mathrm{SU}\mathrm{}\left(d\right).$ This includes, in addition to a convenient measurement on a probe system, finding which is the best initial state on which U is to act. When $U\in \mathrm{SU}\mathrm{}\left(2\right),$ such an optimal strategy can be applied to simultaneously estimate both the direction and the strength of a magnetic field, and shows how to use a spin 1/2 particle to transmit information about a whole coordinate system instead of only a direction in space.

Recently, Levy has shown that quantum computation may be performed using an $\mathrm{ABAB}\dots$ chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions. Levy notes that all necessary elementary computational “gates” may be achieved purely by manipulating the spin-spin interaction: he proposes using “spin-resonance” techniques involving modulating the interaction strength at high frequency. Here, we establish an alternative: it is possible to perform the elementary gates via simple, nonoscillatory switching of the interaction strength. This approach removes a time “bottle neck” in Levy’s scheme, so that all elementary operations may now be performed within a time scale of order $ħ{/(E}_A-E_B).\mathrm{}$

Some results for equal-energy-sharing constant-${\Theta }_{12}$ geometry electron-hydrogen-atom ionization collisions, calculated in a hyperspherical partial wave-approach, including coupling effects, at 30 eV energy, are reported here. Inclusion of the coupling effects reduces the cross-section values dramatically to the desired level. The results are comparable with those of two most recent respectable calculations, the convergent close-coupling and the ECS calculations.

In this paper we investigate the averaged dynamics of quantum systems under the influence of classical stochastic fields. This influence is modeled using a stochastic Hamiltonian evolution for the system-density matrix. From the averaged dynamics, a general characterization of the short-time decoherence behavior is obtained. General applicable short-time perturbation expansions for the input-output fidelity and its generalizations for mixed states are developed. The master equations of the systems that can be worked out without a perturbative expansion, i.e., any system subject to dispersive noise and the quantum harmonic oscillator subject to amplitude noise, are extensively analyzed. In both cases all non-Markovian features are worked out in an exact way. We apply these cases to the study of heating of trapped ions.

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (“qubits”). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices that are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.

We present numerical values for the self-energy shifts predicted by QED for hydrogenlike ions (nuclear charge number $60<~Z<~110)$ with an electron in an $n=3,$ 4, or 5 level with high angular momentum $(5/2\mathrm{}<~j<~9/2).$ Its applications include precise predictions of transition energies and studies of the outer-shell structure of atoms and ions.

Few-body problems involving Coulomb or gravitational interactions between pairs of particles, whether in classical or quantum physics, are generally handled through a standard multipole expansion of the two-body potentials. We develop an alternative based on an old, but hitherto forgotten, expression for the inverse distance between two points that builds on azimuthal symmetry. This alternative should have wide applicability throughout physics and astronomy, both for computation and for the insights it provides through its emphasis on different symmetries and structures than are familiar from the standard treatment. We compare and contrast the two methods, develop addition theorems for Legendre functions of the second kind and a number of useful analytical expressions for these functions. Two-electron “direct” and “exchange” integrals in many-electron quantum systems are evaluated to illustrate the procedure, which is more compact than the standard one using Wigner coefficients and Slater integrals.

The second-order nonlinear optical susceptibility, in the electric dipole approximation, is only nonvanishing for materials that are noncentrosymmetric. Should the medium be isotropic, then only a chiral system, such as an optically active liquid, satisfies this symmetry requirement. We derive the quantum-mechanical form of the isotropic component of the sum- and difference-frequency susceptibility and discuss its unusual spectral properties. We show that any coherent second-order nonlinear optical process in a system of randomly oriented molecules requires the medium to be chiral, and the incident frequencies to be different and nonzero. Furthermore, a minimum of two nondegenerate excited molecular states are needed for the isotropic part of the susceptibility to be nonvanishing. The rotationally invariant susceptibility is zero in the static field limit and shows exceptionally sensitive resonance and dephasing effects that are particular to chiral centers.

A simple scheme for conditional generation of nonclassical light with sub-Poissonian photon-number statistics is proposed. The method utilizes entanglement of signal and idler modes in a two-mode squeezed vacuum state generated in an optical parametric amplifier. A quadrature component of the idler mode is measured in the balanced homodyne detector and the signal mode is accepted only if the absolute value of the measured idler quadrature lies inside a certain chosen interval of quadratures. It is shown that the conditionally generated state of the signal mode can exhibit reduction of photon-number fluctuations below the coherent-state level.

Given N quantum systems prepared according to the same density operator $\rho ,$ we propose a measurement on the N-fold system that approximately yields the spectrum of $\rho .$ The projections of the proposed observable decompose the Hilbert space according to the irreducible representations of the permutations on N points, and are labeled by Young frames, whose relative row lengths estimate the eigenvalues of $\rho$ in decreasing order. We show convergence of these estimates in the limit $\overrightarrow{N}\infty ,$ and that the probability for errors decreases exponentially with a rate we compute explicitly.

The multiconfiguration Dirac-Fock (MCDF) and Hartree-Fock (MCHF) models are employed to compute the electric field gradients in the ground states of the bromine and iodine atoms. Combined with experimental electric quadrupole hyperfine interaction constants B, they yield the nuclear quadrupole moments ${Q(}_{35}^{79}\mathrm{Br})$ of 313(3) millibarn (1 ${\mathrm{m}\mathrm{b}=10\mathrm{}}^{\mathrm{-}31}$ ${\mathrm{m}}^2),$ ${Q(}_{35}^{81}\mathrm{Br})$ of 261.5(2.5) mb, and ${Q(}_{\hspace{0.5em}53}^{127}\mathrm{I})$ of $-710\left(10\right)\mathrm{}$ mb. “Molecular” Q values at Douglas-Kroll coupled cluster singles and doubles with perturbative triples [CCSD(T)] level using data on HBr and HI fully support these “atomic” Q values after a “picture-change” correction is applied. In conjunction with several other recent determinations, these results indicate that the previous standard Q values of 331, 276, and $-789$ mb for ${}^{79}\mathrm{Br},$ ${}^{81}\mathrm{Br},$ and ${}^{127}\mathrm{I},$ respectively, should be revised. Q values are also reported for ${}^{129}\mathrm{I}$ and for the Mössbauer states of ${}^{127,129}\mathrm{I}.$

We present the results of a joint experimental and theoretical study on the absolute photoabsorption cross sections from the ground state leading to resonance structures between the ${\mathrm{Mg}}^{+}\hspace{0.5em}3p{}^{2}P$ and ${\mathrm{Mg}}^{+}\hspace{0.5em}4s{}^{2}S$ thresholds. The absolute cross sections are determined by measuring the light attenuation through a heatpipe using the synchrotron radiation. The observed spectra are compared and analyzed with the help of a B-spline based multichannel K-matrix calculation. A hidden $3d4p{}^{1}P$ resonance missing from the observed spectrum is examined in detail. In addition, a nearly degenerate overlap between $3d5f$ and $4s8p{}^{1}P$ resonances near 77.6 nm is carefully analyzed.

We discuss the relaxation of a spin-polarized alkali-metal vapor due to the electric-quadrupole interaction in ${}^1{\Sigma }_g^{+}$ dimers, and present a model that accurately describes the measured relaxation rates under a wide variety of conditions. We use the model along with experimental results to deduce the quadrupole interaction strength, atom-dimer chemical-exchange reaction rate, and the rate of reorientation of singlet dimers due to collisions with the buffer gas.

Vacuum ultraviolet fluorescence decay spectra of Ar atom resonance lines excited by pulsed vacuum ultraviolet light in a synchrotron single bunch operation were obtained under a static electric field. When an atom under the static electric field was excited simultaneously to both the magnetic sublevels $M=0\mathrm{}$ and $|M|=1\mathrm{}$ by polarized light and the observation area was asymmetric, Stark beats were observed in the fluorescent decay spectra. All observed beat frequencies varied proportionally to the square of the external electric field. The results for $8d$ and $9d$ doublet lines were compared with those obtained by the usual second order perturbation theory, assuming mixing ratios between three $\mathrm{jl}$ coupling scheme d-type states. The beat frequencies were also measured for other resonance lines.

A light-induced frequency shift is observed in single-photon photoassociative spectra of magnetically trapped, quantum degenerate ${}^7\mathrm{Li}.$ The shift is a manifestation of the coupling between the threshold continuum scattering states and discrete bound levels in the excited-state molecular potential induced by the photoassociation laser. The frequency shift is observed to be linear in the laser intensity with a measured proportionality constant that is in good agreement with theoretical predictions. This phenomenon has important implications for a scheme to alter the interactions between atoms in a Bose-Einstein condensate using photoassociation resonances.

The definition of entanglement in identical-particle system is introduced. The separability criterion in two-identical-particle system is given. The physical meaning of the definition is analyzed. Applications to two-boson and two-fermion systems are made. It is found that some different entanglement and correlation phenomena in identical-boson systems exist, and they may have applications in the field of quantum information.

We have derived a closed form analytic expression for the asymptotic motion of a pair of identical ions in a high-precision Penning trap. The analytic solution includes the effects of special relativity and the Coulomb interaction between the ions. The existence and physical relevance of such a final state is supported by a confluence of theoretical, experimental, and numerical evidence.

We derive scaling laws for the number of atoms, collision rate, and phase-space density as a function of trap depth for evaporative cooling in an adiabadically lowered optical trap. The results are in excellent agreement with a Boltzmann equation model and show that very large increases in phase-space density can be obtained without excessive slowing of the evaporation rate. Predictions are in reasonable agreement with a recent experiment that achieves Bose-Einstein condensation by evaporation in an optical trap. We also discuss evaporation of fermionic mixtures and explain why Pauli blocking does not strongly inhibit cooling.

We present a theoretical calculation on the tuning of Casimir forces using superlattices. The Casimir force is calculated for a system made of two parallel heterogeneous slabs, each one made of alternate layers of materials with different dielectric properties. The calculations are based on the quantization of the electromagnetic field in absorbing media and a transfer matrix formalism. Our results show that the attractive force can be modified by structural (dielectric properties) and geometrical (ordering and size) properties of the slabs. In particular, the combination of metallic and dielectric layers allows a modification of the Casimir force by changing the ordering and relative width of the materials used to construct the superlattices.