Using the exact renormalization group we calculate the momentum-dependent self-energy $\Sigma \left(k\right)$ at zero frequency of weakly interacting bosons at the critical temperature $T_c$ of Bose-Einstein condensation in dimensions $3⩽D<4$. We obtain the complete crossover function interpolating between the critical regime $k⪡k_c$, where $\Sigma \left(k\right)\propto k^{2-\eta }$, and the short-wavelength regime $k⪢k_c$, where $\Sigma \left(k\right)\propto k^{2(D-3)}$ in $D>3$ and $\Sigma \left(k\right)\propto \ln (k∕k_c)$ in $D=3$. Our approach yields the crossover scale $k_c$ on the same footing with a reasonable estimate for the critical exponent $\eta$ in $D=3$. From our $\Sigma \left(k\right)$ we find for the interaction-induced shift of $T_c$ in three dimensions $\Delta T_c∕T_c\approx 1.23a{n}^{1∕3}$, where $a$ is the $s$-wave scattering length and $n$ is the density.

We report observations of novel dynamic behavior in resonantly enhanced stimulated Raman scattering in Rb vapor. In particular, we demonstrate a dynamic hysteresis of the Raman scattered optical field in response to changes of the drive laser field intensity and/or frequency. This effect may be described as a dynamic form of optical bistability resulting from the formation and decay of atomic coherence. We have applied this phenomenon to the realization of an all-optical switch.

Using an electronic-state close-coupling method, we treated the electron capture and excitation processes of ${\mathrm{O}}^{+}$ ions both in ground state ${\mathrm{O}}^{+}\left({}^{4}S\right)$ and metastable states ${\mathrm{O}}^{+*}\left({}^{2}D\right)$ and ${\mathrm{O}}^{+*}\left({}^{2}P\right)$ in collisions with the ${\mathrm{H}}_2$ molecule. In the ground-state projectile energy region considered (from $50\text{eV}∕\text{amu}$ to $10\text{keV}∕\text{amu}$), the experimental data vary by orders of magnitude: our results smoothly connect to the data by Flesch and Ng [J. Chem. Phys. 94, 2372 (1991)] and Xu et al. [J. Phys. B 23, 1235 (1990)] at low energy and agree with Phaneuf et al. [Phys. Rev. A 17, 534 (1978)] in the high-energy region. The present values differ from Sieglaff et al. [Phys. Rev. A 59, 3538 (1999)] and Nutt et al. [J. Phys. B 12, L157 (1979)], especially in the energy region below $1\text{keV}∕\text{amu}$. We provide the first calculated state-resolved cross sections of electron capture and target-projectile electronic excitations for the ${\mathrm{O}}^{+}({}^{4}S,{}^{2}D,{}^{2}P)\text{−}{\mathrm{H}}_2$ collision system.

We study the superfluid state of atomic Fermi gases using a BCS-Bose-Einstein-condensation crossover theory. Our approach emphasizes noncondensed fermion pairs which strongly hybridize with their (Feshbach-induced) molecular boson counterparts. These pairs lead to pseudogap effects above $T_c$ and non-BCS characteristics below. We discuss how these effects influence the experimental signatures of superfluidity.

We analyze operation of a cold-atom accelerometer, an interferometric device which measures linear accelerations. We develop an analytic model that predicts a decrease in the visibility of the interference fringes and also their shift caused by the acceleration of the device. This effect places an upper limit on the maximum value of acceleration that can be measured for given parameters of the confining potential and the measurement cycle time.

The relative energy- and angle- dependent cross sections for emission of electrons from ${\mathrm{SF}}_6$ molecule by impact of $16\mathrm{keV}$ electrons have been measured. The angular distributions of ejected electrons are shown to exhibit an oscillatory structure which is suggested to arise due to an interference effect. The condition for interference effect for the present collision system has been examined and it is shown that the appearance of interference pattern takes place above a threshold energy of $65\mathrm{eV}$ for the ejected electrons. The ejected electrons producing an interference structure are suggested to originate from two atomic centers of a transiently formed doubly ionized parent molecule, namely, ${\mathrm{SF}}_6^{2+}$. This extremely unstable ion suffers a Coulomb explosion and gives rise to many singly charged stable radical and atomic ions. The time of flight mass spectrometric results of our earlier work [Phys. Rev. A 67, 022704 (2003)] on partial ionization of ${\mathrm{SF}}_6$ molecule by impact of $16\mathrm{keV}$ electrons are found to support the existence of these stable ions.

In this paper we establish a deep connection between the 3-qubit one-to-two phase-covariant quantum cloning network of Fuchs et al. [Phys. Rev. A 56, 1163 (1997)], and its low-cost two-qubit counterpart due to Niu and Griffiths [Phys. Rev. A 60, 2764 (1999)]. A general, necessary, and sufficient criterion is derived in order to characterize the reducibility of 3-qubit one-to-two cloners to two-qubit one-to-two cloners. When this criterion is fulfilled, low-cost cloning is possible. We show that the optimal isotropic or universal 3-qubit one-to-two cloning machine is not reducible to a 2-qubit one-to-two cloner.

The potential-energy surface corresponding to the complex resonance energy of the ${}^{2}B_1$ Feshbach resonance state of the water anion is constructed in its full dimensionality. Complex Kohn variational scattering calculations are used to compute the resonance width, while large-scale configuration interaction calculations are used to compute the resonance energy. Near the equilibrium geometry, an accompanying ground-state potential surface is constructed from configuration interaction calculations that treat correlation at a level similar to that used in the calculations on the anion.

Calculations of cross sections for dissociative attachment to water through the ${}^{2}B_1$ resonance state are presented using the ab initio surfaces calculated previously for the energy $E_R$ and width $\Gamma$ of this resonance state as a function of nuclear geometry. The dynamics of the dissociative attachment process are treated in full dimensionality using the local complex potential model. For the ${\mathrm{H}}^{-}+\mathrm{OH}$ channel, the calculations presented here are in substantial agreement with experiment with regard to total cross section and vibrational excitation of the $\mathrm{OH}$ fragment. Cross sections for dissociative attachment to excited initial ro-vibrational states are presented and isotope effects are also examined.

Within the framework of the coplanar binary geometry where it is justified to use plane wave solutions for the study of the $(e,2e)$ reaction and in the presence of a circularly polarized laser field, we introduce as a first step the Dirac-Volkov plane wave Born approximation 1 where we take into account only the relativistic dressing of the incident and scattered electrons. Then, we introduce the Dirac-Volkov plane wave Born approximation 2 where we take totally into account the relativistic dressing of the incident, scattered, and ejected electrons. We then compare the corresponding triple differential cross sections for laser-assisted ionization of atomic hydrogen by electron impact both for the nonrelativistic and the relativistic regime.

Classical exact $\left(\mathrm{CE}\right)$ wave functions are certain integral representations of energy eigenfunctions that are parameterized in terms of the motion of the corresponding classical system in a semiclassically relevant way. When applied to systems for which they are not exact, such expressions serve as semiclassical approximations. Previous work identified $\mathrm{CE}$ wave functions for a number of specific systems and established their semiclassical usefulness. This paper explores the degree to which such representations can be found for more general systems. It is shown that $\mathrm{CE}$ wave functions exist, in principle, for bound states of an arbitrary integrable system that are confined to a single classically allowed region. Evidence is presented that $\mathrm{CE}$ representations also exist for more general states of such a system that are unbound, or that extend over more than one allowed region. The $\mathrm{CE}$ expressions are not unique: an innumerable variety exists for each such system. The existence proof provides a formal method for constructing $\mathrm{CE}$ expressions by Fourier transforming certain superpositions of energy eigenstates. The parameterization in terms of the classical motion is achieved by identifying certain quantities in these superpositions as classical action and angle variables. The semiclassical relevance of this identification is ensured by imposing some mild conditions on the coefficients in the superposition. This procedure for parameterizing exact wave functions in terms of classical variables indicates a basic relationship between the quantum and classical descriptions of states. The method of constructing $\mathrm{CE}$ wave functions introduced in the proof is shown to be consistent with a number of previously obtained $\mathrm{CE}$ formulas and is used to derive two new, closed-form, $\mathrm{CE}$ expressions. A simple numerical example is presented to illustrate the semiclassical application of one of these expressions and to further verify the physical significance of the classical parameterization.

In order to reduce errors, error correction codes need to be implemented fast. They can correct the errors corresponding to the first few orders in the Taylor expansion of the time evolution operator corresponding to the Hamiltonian of the interaction with the environment. If implemented fast enough, the zeroth order error predominates and the dominant effect is of error prevention by measurement (Zeno effect) rather than correction. In this “Zeno regime,” codes with less redundancy are sufficient for protection. We describe such a simple scheme, which uses two “noiseless” qubits to protect a large number, $n$, of information qubits from noise from the environment. The “noisless qubits” can be realized by treating them as logical qubits to be encoded by one of the previously introduced encoding schemes.

We have computed cross sections and asymmetry parameters for the outer- and inner-valence photoionization of ethane using the Schwinger variational method with Padé corrections. The calculated total cross section is found to be in rather good agreement with the available electron-impact and photoabsorption measurements. One-electron resonant processes in the ${\left(1e_g\right)}^{-1}$, ${\left(3a_{1g}\right)}^{-1}$, and ${\left(2a_{1g}\right)}^{-1}$ ionization channels were examined comparing resonant states predicted from the virtual orbitals of a minimum basis set self-consistent-field (MBS-SCF) calculations with scattering resonances found using a local model potential for the electron-molecule interaction. The analysis of the interaction potential in terms of adiabatic radial components provides a description of the mechanism of the resonant trapping.

The effect of target polarization fields on the bond-angle distribution following the foil-induced Coulomb explosion of $\mathrm{CH}_2{}^{+}$ has been measured. Incorporating a detailed model description of the polarization effects and other target effects into a Monte Carlo simulation of the experiment, a good description of the various observables is obtained. In particular, the bond-angle distribution is found to agree with existing ab initio calculations.

We study the problem of multiphoton processes for intense, long-wavelength irradiation of atomic and molecular electrons. An exact, nonperturbative approach is applied to the standard vector potential coupling Hamiltonian for a three-dimensional hydrogenlike atom in a microwave field treated semiclassically. Multiphoton probability exchange is calculated in both the velocity and the length gauges, by applying the Goeppert-Mayer gauge transformation. The expansion of the time-dependent solution in terms of Floquet states delineates the mechanism of multiphoton transitions. A detailed analysis of the Floquet states and quasienergies as functions of the field parameters allows us to describe the relation between avoided quasienergy crossings and multiphoton probability exchange. We formulate analytical expressions for the variation of quasienergies and Floquet states with respect to the field parameters, and demonstrate that avoided quasienergy crossings are accompanied by dramatic changes in the Floquet states. Analysis of the Floquet states, for small values of the field strength, yields selection rules for the avoided quasienergy crossings. In the case of strong fields, the simultaneous choice of frequency and strength of the field producing an avoided crossing results in improved ionization probability.

A simple theoretical solution to the design of a control field that generates complete population transfer from an initial state, via $N$ nondegenerate intermediate states, to one arbitrary member of $M(M⩽N)$ degenerate states is constructed. The full control field exploits an $(M+N-1)$-node null adiabatic state, created by designing the relative phases and amplitudes of the component fields that together make up the full field. The solution found is universal in the sense that it does not depend on the exact number of the unwanted degenerate states or their properties. The results obtained suggest that a class of multilevel quantum systems with degenerate states can be completely controllable, even under extremely strong constraints, e.g., never populating a Hilbert subspace that is only a few dimensions smaller than the whole Hilbert space.

We propose a method for finding analytical solutions of the Bogoliubov–de Gennes (BdG) equations for the low-lying collective excitations in a harmonically trapped Bose-Einstein condensate beyond the Thomas-Fermi limit. We first use a simple variational wave function for ground state to eliminate the divergence at the boundary layer of the condensate, which appears in the Thomas-Fermi approximation. We then solve the BdG equations analytically and obtain explicit and divergence-free expressions for the eigenvalues and eigenfunctions of the excitations for the traps with spherical and cylindrical symmetries. The solutions of the zero-energy mode of the BdG equations are also presented.

In this paper we systematically study the double-layer vortex lattice model, which is proposed to illustrate the interplay between the physics of a fast rotating Bose-Einstein condensate and the macroscopic quantum tunneling. The phase diagram of the system is obtained. We find that under certain conditions the system will exhibit a phase transition which is a consequence of the competition between interlayer coherent hopping and the interlayer density-density interaction. In one phase the vortices in one layer coincide with those in the other layer. In another phase two sets of vortex lattices are staggered, and as a result the quantum tunneling between two layers is suppressed. To obtain the phase diagram we use the quantum Hall mean field and Thomas-Fermi mean field theories. Two different criteria for the transition taking place are obtained, which reveals some fundamental differences between these two mean-field states. The sliding mode excitation is also discussed.

We investigate quantum scattering of a single photon packet from a $\Lambda$-type three-level atom confined in an optical cavity. The evolution of the coupled system is analyzed by projecting the quantum state onto “dark” and “bright” states. In the asymptotic long time limit, quantum interference between these states is determined by a frequency-dependent phase angle. We present an analytic expression of such a scattering phase factor, and indicate how it leads to a family of transformations between polarization states of the photon and atom. Specific examples include quantum state swapping and the generation of maximally entangled states.

The breakup dynamics of ${\mathrm{D}}_2{\mathrm{H}}^{+}$ and ${\mathrm{H}}_2{\mathrm{D}}^{+}$following dissociative recombination with low energetic electrons has been studied combining two-dimensional imaging and storage ring techniques. The kinematical correlation between the hydrogen and deuterium atoms produced in the three-body channel was measured. We found that the three particles tend to dissociate with a geometry close to linear, and that the deuterium atom has a large probability to be at the center. The data also show that the remaining average internal excitation energy stored in the rotation of the ${\mathrm{D}}_2{\mathrm{H}}^{+}$ and ${\mathrm{H}}_2{\mathrm{D}}^{+}$ molecules corresponds to a temperature of less than $70\mathrm{meV}$, much less than observed for the $\mathrm{H}_3{}^{+}$ and $\mathrm{D}_3{}^{+}$ species previously examined.