We address the decomposition of a multimode pure Gaussian state with respect to a bipartite division of the modes. For any such division the state can always be expressed as a product state involving entangled two-mode squeezed states and single-mode local states at each side. The character of entanglement of the state can therefore be understood modewise; that is, a given mode on one side is entangled with only one corresponding mode of the other, and therefore the total bipartite entanglement is the sum of the modewise entanglement. This decomposition is generally not applicable to all mixed Gaussian states. However, the result can be extended to a special family of “isotropic” states, characterized by a phase space covariance matrix with a completely degenerate symplectic spectrum.

We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation theory for time-dependent Hamiltonians. It is strictly unitary upon truncation at an arbitrary order and not restricted to periodic or quasiperiodic Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the Kolmogorov-Arnold-Moser transformations involved in the iterative procedure. The technique is illustrated on a two-level model perturbed by a pulsed interaction for which we obtain convergence all the way from the sudden regime to the opposite adiabatic regime.

The one-loop nuclear structure corrections of order $(Z\alpha {)}^5$ to the Lamb shift and hyperfine splitting of deuterium are calculated. The contribution of the deuteron structure effects to the isotope shifts $\mathrm{}\left(\mathrm{ep}\right)\mathrm{}-\mathrm{}\left(\mathrm{ed}\right)\mathrm{}$ and $\left(\mu p\right)-\left(\mu d\right)$ in the interval $1S–2S$ is obtained on the basis of modern experimental data on the deuteron electromagnetic form factors. Comparison with similar contributions to the Lamb shift for electronic and muonic hydrogen shows that the relative contribution due to the nuclear structure increases on passing from hydrogen to deuterium.

Energies of ${(3s}^2{3p}^6{3d}^9{4l4l}^{\prime }),$ ${(3s}^2{3p}^5{3d}^{10}{4l4l}^{\prime }),$ and ${(3s3p}^6{3d}^{10}{4l4l}^{\prime })$ states for Cu-like ions with $Z=30\mathrm{}–100$ are evaluated to second order in relativistic many-body perturbation theory (RMBPT) starting from a Ni-like Dirac-Fock potential. Second-order Coulomb and Breit-Coulomb interactions are included. Correction for the frequency dependence of the Breit interaction is taken into account in lowest order. The Lamb shift correction to energies is also included in lowest order. Intrinsic particle-particle-hole contributions to energies are found to be 20–30 % of the sum of one- and two-body contributions. Transition rates and line strengths are calculated for the $3l-{4l}^{\prime }$ electric-dipole $\mathrm{}\left(E1\mathrm{}\right)\mathrm{}$ transitions in Cu-like ions with nuclear charge $Z=30\mathrm{}–100.$ RMBPT including the Breit interaction is used to evaluate retarded $E1\mathrm{}$ matrix elements in length and velocity forms. First-order RMBPT is used to obtain intermediate coupling coefficients, and second-order RMBPT is used to calculate transition matrix elements. A detailed discussion of the various contributions to the dipole- matrix elements and energy levels is given for copperlike tungsten $\mathrm{}(Z=74\mathrm{}).$ The transition energies used in the calculation of oscillator strengths and transition rates are from second-order RMBPT. Trends of the transition rates as functions of Z are illustrated graphically for selected transitions. Comparisons are made with available experimental data. These atomic data are important in the modeling of M-shell radiation spectra of heavy ions generated in electron-beam ion trap experiments and in M-shell diagnostics of plasmas.

Transferability of norm-conserving pseudopotentials to low-energy electron-molecule scattering processes has been very successful [Bettega et al., Phys. Rev. A 47, 1111 (1993)]. In this paper we discuss the possibility of using effective potentials in calculations of valence electrons photoionization cross sections. Through atomic targets, we illustrate that pseudopotentials can be optimized to give cross sections in good agreement with all-electron calculations. The present work represents a first step towards more elaborate computer programs for photoionization of molecular targets containing heavy atoms.

We solve the two-component Dirac equation in the presence of a spatially one-dimensional symmetric cusp potential. We compute the scattering and bound state solutions and we derive the conditions for transmission resonances as well as for supercriticality.

Doubly differential cross sections for single and multiple ionization of Ar have been measured for 500, 750, and 1000 eV electron impact. The cross sections were measured as a function of projectile energy loss and scattering angle. The energy loss range was 0–85 % of the initial projectile energy and scattering angles were between $\pm 22°.$ The data were put on an absolute scale by normalizing to total ionization cross sections available in the literature and found to be in good agreement with the absolute electron impact cross sections from DuBois and Rudd. For 750 eV impact, a comparison was made between the present electron impact data and positron impact data obtained using the same experimental conditions. The same energy dependence and yields for single ionization were found for both electron and positron impact. On the other hand, the double- and triple-ionization yields are smaller for positron impact as compared to electron impact. Comparisons with photoionization data showed that for outer shell ionization the fractions of double and triple ionization of argon by photon impact are in quite good agreement with the present electron impact data.

Direct K-shell ionization probabilities were measured in coincidence with elastically scattered particles in 30-MeV/u $\mathrm{Ne}+\mathrm{Sn},$ Tb, Pb, Th and 8.3-MeV/u $\mathrm{C}+\mathrm{Zr},$ Ag, Sn, Sm, Au, Pb, Th reactions. Experimental data were compared with calculations in the semiclassical approximation. The transitional behavior at the reduced velocity ${\xi }_K\approx 1,$ where the projectile velocity approaches the velocity of the K-shell electrons, is discussed.

We study the limit of large on-site repulsion of the one-dimensional Bose-Hubbard model at low densities, and derive a strong-coupling effective Hamiltonian. By taking the lattice parameter to zero, the Hamiltonian becomes a continuum model of fermions with attractive interactions. The leading corrections to the internal energy of a hard-core-boson (Tonks) gas as well as the (finite temperature) pair correlations of a strongly interacting Bose gas are calculated. We explore the possibility of realizing, in an optical lattice, a Luttinger liquid with stronger density correlations than the Tonks gas. A quantum phase transition to a charge-density-wave Mott insulator is also discussed.

We have studied the interaction between the low-lying transverse collective oscillations and the thermal excitations of an elongated Bose-Einstein condensate by means of perturbation theory. We consider a cylindrical trapped condensate and calculate the transverse elementary excitations at zero temperature by solving the linearized Gross-Pitaevskii equations in two dimensions (2D). We use them to calculate the matrix elements between the thermal excited states and the quasi-2D collective modes. The Landau damping of transverse collective modes is studied as a function of temperature. At low temperatures, the corresponding damping rate is in agreement with the experimental data for the decay of the transverse quadrupole mode, but it is too small to explain the observed slow decay of the transverse breathing mode. The reason for this discrepancy is discussed.

We study a quantum phase transition in phase-separated mixtures of Bose-Einstein condensates. In this transition, the distribution of the two components changes from a symmetric to an asymmetric shape. We discuss the nature of the phase transition, the role of interface tension, and the phase diagram. The symmetric to asymmetric transition is the simplest quantum phase transition that one can imagine. Careful study of this problem should provide us insight into this burgeoning field of discovery.

We study the effect of a one-dimensional periodic potential on the dynamic structure factor of an interacting Bose-Einstein condensate at zero temperature. We show that, due to phononic correlations, the excitation strength toward the first band develops a typical oscillating behavior as a function of the momentum transfer, and vanishes at even multiples of the Bragg momentum. The effects of interactions on the static structure factor are found to be significantly amplified by the presence of the optical potential. Our predictions can be tested in stimulated photon scattering experiments.

We discuss the dynamics of a Bose-Einstein condensate initially loaded into every third site of an optical lattice using a description based upon the discrete nonlinear Schrödinger equation. An analytic solution is developed for the case of a periodic initial condition and is compared with numerical simulations for more general initial configurations. We show that mean field effects in this system can cause macroscopic quantum self-trapping, a phenomenon already predicted for double-well systems. In the presence of a uniform external potential, the atoms exhibit generalized Bloch oscillations which can be interpreted in terms of the interference of three different Bloch states. We also discuss how the momentum distribution of the system can be used as an experimental signature of the macroscopic self-trapping effect.

We compare the dynamics of a Bose-Einstein condensate in two coupled potential wells with atoms diffracting from a standing light wave. The corresponding Hamiltonians have an identical appearance, but with a different set of commutation rules. Well-known diffraction phenomena as Pendellösung oscillations between opposite momenta in the case of Bragg diffraction, and adiabatic transitions between momentum states are shown to have analogies in the two-well case. They represent the collective exchange of a fixed number of atoms between the wells.

We present an effective potential and the corresponding modified Gross-Pitaevskii equation, which account for the energy dependence of the two-body scattering amplitude through an effective-range expansion. For the ground-state energy of a trapped condensate, the theory leads to what we call a shape-dependent confinement correction that improves agreements with diffusion Monte Carlo calculations. The theory illustrates, for relatively strong confinement and/or high density, how the shape dependence on atom-atom interaction can come into play in a many-atom quantum system.

The quantum theory of the mazer in the nonresonant case (a detuning between the cavity mode and the atomic transition frequencies is present) is described. The generalization from the resonant case is far from being direct. Interesting effects of the mazer physics are pointed out. In particular, it is shown that the cavity may slow down or speed up the atoms according to the sign of the detuning and that the induced emission process may be completely blocked by use of a positive detuning. It is also shown that the detuning adds a potential step effect not present at resonance and that the use of positive detunings defines a well-controlled cooling mechanism. In the special case of a mesa cavity mode function, generalized expressions for the reflection and transmission coefficients have been obtained. The general properties of the induced emission probability are finally discussed in the hot, intermediate, and cold atom regimes. Comparison with the resonant case is given.

We develop a versatile theoretical framework for the study of fluorescence resonant energy transfer (FRET, or Förster transfer) in complex environments, under arbitrary illumination, including optical near fields. By combining the field-susceptibility formalism with the optical Bloch equations method, we derive general equations for the computation of the energy transfer between pairs of donor-acceptor molecules excited by optical near fields and placed in a complex geometry. This approach allows accounting for both the variations of the molecular population rates and the influence of the environment. Several examples illustrate the ability of the technique to analyze recent FRET experiments performed in the optical near field.

The dynamical response of a laser to a frequency-shifted optical feedback (heterodyne optical feedback) is investigated both theoretically and experimentally. Compared to a conventional heterodyne method, the intensity modulation induced by the coherent interaction between the laser electric field and the frequency-shifted reinjected electric field can be several orders of magnitude higher. This method permits high sensitive interferometry and hence imaging. We call this laser detection technique: Laser optical feedback imaging (LOFI). By adding to the heterodyne feedback a small amount of homodyne optical feedback (i.e., feedback with the same optical frequency as the laser optical frequency), the laser can reach a Hopf instability domain. By working close to this instability, we are able to amplify still further the LOFI modulation induced by the heterodyne optical feedback.

We have demonstrated the phase coherence of stored light in Rb vapor with a completely optical technique. Combining this technique with polarization measurements provides strong evidence that arbitrary polarizations can be stored. The fidelity obtained exceeds 95% for all polarizations. We view the capability to store polarizations as a first step towards building a quantum memory in such a system.

In this paper we investigate the squeezing of a finite-bandwidth optical field which may be thought of as originating from Einstein-Podolsky-Rosen- (EPR-) like quantum correlations between the upper and lower sidebands. Ordinarily, when EPR pairs are created from such a resource, the bandwidth is preserved, and the signal-to-noise ratio of the quadrature correlations is reduced. Here we show that by using frequency-dependent beam splitters we may create N EPR pairs from a single finite-bandwidth squeezed beam with no reduction in the correlations’s signal-to-noise ratio. However, the bandwidth is reduced by a factor of N relative to the original squeezed beam. Because this transformation is linear it may be inverted to retrieve the single squeezed beam from the corresponding N EPR pairs.