We precisely measured the binding energy $\left({\epsilon }_{\mathrm{bind}}\right)$ of a molecular state near the Feshbach resonance in a ${}^{85}\mathrm{Rb}$ Bose-Einstein condensate (BEC). Rapid magnetic-field pulses induced coherent atom-molecule oscillations in the BEC. We measured the oscillation frequency as a function of B field and fit the data to a coupled-channel model. Our analysis constrained the Feshbach resonance position [155.041(18) G], width [10.71(2) G], and background scattering length $\left[-{443\left(3\right)a}_0\right]$ and yielded new values for the Rb interaction parameters. These results improved our estimate for the stability condition of an attractive BEC. We also found evidence for a mean-field shift to ${\epsilon }_{\mathrm{bind}}.$

The nondipole parameters that characterize the angular distribution of the photoelectrons from the $3d$ subshell of Cs are found to be altered significantly by the inclusion of correlation in the form of interchannel coupling between the ${3d}_{3/2}$ and ${3d}_{5/2}$ photoionization channels. A prominent characteristic maximum is predicted only in the parameters for ${3d}_{5/2}$ photoionization, while the effect for ${3d}_{3/2}$ is rather weak. The results are obtained within the framework of the generalized random-phase approximation with exchange (GRPAE), which in addition to the RPAE effects takes into account the rearrangement of all atomic electrons due to the creation of a $3d$ vacancy.

First-principles density-functional-theory investigations of small ${\mathrm{Mn}}_n$ $(n=2\mathrm{}–7,13)$ clusters reveal a competition between ferromagnetic and antiferromagnetic ordering of atomic magnetic moments. For smaller sizes $(n<~6),$ this competition results in a near degeneracy between the two types of orderings, whereas AF arrangements are clearly favored for larger clusters. The calculations thus predict a size-dependent transition in the magnetic ordering of Mn clusters.

Transformations from pure to mixed states are usually associated with information loss and irreversibility. Here, a protocol is demonstrated allowing one to make these transformations reversible. The pure states are diluted with a random noise source. Using this protocol one can study optimal transformations between states, and from this derive the unique measure of information. This is compared with irreversible transformations where one does not have access to noise. The ideas presented here shed some light on attempts to understand entanglement manipulations and the inevitable irreversibility encountered there where one finds that mixed states can contain “bound entanglement.”

It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin-$\frac{1}{2}$ particles. In the nonrelativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper, we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components, which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wave function is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie–Bohm ones, such as crossing of the axis of symmetry.

A method of quantum-state tomography for quantum-information processing is described. The method is based on the use of the Fourier-transform technique and involves detection of all the diagonal elements of the density matrix in a one-dimensional experiment and all the off-diagonal elements by a two-dimensional experiment. The method is efficient for a large number of qubits $(>~5).$ The proposed method is outlined using a two-qubit system and demonstrated using simulations by tomographing arbitrary complex density matrices of two- and four-qubit systems.

The Kohn variational method is used with a configuration-interaction (CI)-type wave function to determine the phase shifts and $Z_{\mathrm{eff}}$ for positron-copper scattering. The method is first tested for positron-hydrogen scattering and it is found to give phase shifts and $Z_{\mathrm{eff}}$ within 1–2% of the best previous calculations. Although the phase shift for Cu converged more slowly with $L_{\max }$ (the maximum angular momentum of the electron and positron orbitals included in the short-range basis), it was still possible to get reliable estimates of the phase shifts by including orbitals with $\mathcal{l}<~18$ and the use of an extrapolation technique. Calculation of $Z_{\mathrm{eff}}$ was more problematic since the convergence of $Z_{\mathrm{eff}}$ with respect to $L_{\max }$ was very slow. Despite the uncertainties, it was clear that the p-wave phase shift was showing signs of forming a shape resonance at about 0.5 eV incident energy. This resulted in a p-wave contribution to $Z_{\mathrm{eff}}$ that was larger than that of the s wave for $k>~{0.1a}_0^{-1}.$ Speculative calculations based upon a model potential suggest that a p-wave shape resonance centered at thermal energies, e.g., about 0.025 eV, could result in a thermally averaged $Z_{\mathrm{eff}}$ exceeding 10 000.

The Bose-Hubbard Hamiltonian of spin-2 cold bosons with repulsive interaction in an optical lattice is proposed. After neglecting the hopping term, the site-independent Hamiltonian and its energy eigenvalues and eigenstates are obtained. We consider the hopping term as a perturbation to do the calculations in second order and draw the phase diagrams for different cases. The phase diagrams show that there is a phase transition from Mott insulator with integer number bosons to superfluid when the ratio $c_0/t$ ${(c}_0$ is the spin-independent on-site interaction and t is the hopping matrix element between adjacent lattice sites) is decreased to a critical value and that there is a different phase boundary between superfluid and Mott-insulator phase for different Zeeman level component in some ground states. We find that the position of phase boundary for different Zeeman level component is related to its average population in the Mott ground state.

We systematically study the properties of lattice solitons in Bose-Einstein condensates with either attractive or repulsive atom interactions. This is done, by exactly solving the mean-field Gross-Pitaevskii equation in the presence of a periodic potential. We find new families of lattice soliton solutions that are characterized by the position of the energy eigenvalue within the associated band structure. These include lattice solitons in condensates with either attractive or repulsive atom interactions that exist in finite or semi-infinite gaps, as well as nonlinear modes that exhibit atomic population cutoffs.

We analyze the relation between the classical part of quantum observables and the distributions representing quantum states and observables on the classical phase space. We determine in which conditions such a relation can be established, and the proper phase-space distribution required for this purpose.

We have probed the interaction of intense laser fields with Xe clusters by measuring the energy and charge state distributions of emitted ions and electrons using ultrafast 20-fs pulses. This work demonstrates that the energetic particle emissions from laser-cluster interactions can be optimized by manipulating the character of ultrafast laser pulses, i.e., pulse duration and sign of chirp. The mean and maximum ion energies as high as 0.1 and 2 MeV, respectively, are achieved when Xe clusters are irradiated by 500-fs pulses with negative chirp as an optimal condition under a laser peak intensity of $2\times {10}^{17}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ The mean ion energy obtained from 500-fs pulses with negative chirp is found to be about 1.6 times larger than that with positive chirp.

We calculate the self-energy and the vertex radiative corrections to the effect of parity nonconservation in heavy atoms. The sum of the corrections is of the form $\mathcal{A}\ln \left({\lambda }_C{/r}_0\right)+\mathcal{B},$ where $\mathcal{A}$ and $\mathcal{B}$ are functions of $Z\alpha ,$ and ${\lambda }_C$ and $r_0$ are the Compton wavelength and the nuclear radius, respectively. The function $\mathcal{A}$ is calculated exactly in $Z\alpha$ and the function $\mathcal{B}$ is calculated in the leading order. In the leading order $\mathcal{A}\propto \alpha (Z\alpha {)}^2$ and $\mathcal{B}\propto \alpha \left(Z\alpha \right).\mathrm{}$ The sum of the corrections is $-0.85\%$ for Cs and $-1.48\%$ for Tl. Using these results, we have performed an analysis of the experimental data on atomic parity nonconservation. The values obtained for the nuclear weak charge, $Q_W=-{72.81\left(28\right)\mathrm{}}_{\mathrm{expt}}{\mathrm{}\left(36\right)\mathrm{}}_{\mathrm{theor}}$ for Cs and $Q_W=-{116.8\left(1.2\right)\mathrm{}}_{\mathrm{expt}}{\mathrm{}\left(3.4\right)\mathrm{}}_{\mathrm{theor}}$ for Tl, agree with the predictions of the standard model within $0.6\sigma .$ As an application of our approach we have also calculated the dependence of the Lamb shift on the finite nuclear size.

Noiseless subsystems offer a general and efficient method for protecting quantum information in the presence of noise that has symmetry properties. A paradigmatic class of error models displaying nontrivial symmetries emerges under collective noise behavior, which implies a permutationally invariant interaction between the system and the environment. We expand our previous investigation of the noiseless subsystem idea [L. Viola et al., Science 293, 2059 (2001)] by reporting and analyzing NMR experiments that demonstrate the preservation of a qubit encoded in a three-qubit noiseless subsystem for general collective noise. A complete set of input states is used to determine the superoperator for the implemented one-qubit process and to confirm that the fidelity of entanglement is improved for a large, noncommutative set of engineered errors. To date, this is the largest set of error operators that has been successfully corrected for by any quantum code.

The muon-transfer probabilities between muonic hydrogen and an oxygen atom are calculated in a constrained geometry one-dimensional model for collision energies between ${10}^{-6}$ and ${10}^3\mathrm{eV}.$ For relative translational energies below ${10}^{-1}\mathrm{eV},$ for which the de Broglie wavelength $(>\mathrm{}1\mathrm{}\mathrm{\AA })$ is much larger than the characteristic distance of the potential interaction $\left(\sim 0.1\mathrm{\AA }\right),$ the problem corresponds to an ultracold collision. The close-coupling time-independent quantum equations are written in terms of hyperspherical coordinates and a diabatic-by-sectors basis set. The muon-transfer probabilities are qualitatively interpreted in terms of a model involving two Landau-Zener crossings together with the threshold energy dependence. Based on this analysis, a simple procedure to estimate the energy dependence of the muon-transfer rate in three dimensions is proposed. These estimated rates are discussed in the light of previous model calculations and available experimental data for this process. It is concluded that the high transfer rates at epithermal energies inferred from experiments are unlikely to be correct.

The energies and the widths of berylliumlike ${2s}^2{2p}^2{}^{3}P$ and ${2s2p}^3{}^{5}S$ resonances for Z from 3 to 10 are calculated using the saddle-point complex-rotation method. The Auger decay branching ratios of these states are explained using the spin-alignment-dependent theory.

The absolute generalized oscillator strengths (GOSs) for 5s, ${5s}^{\prime },$ $5p$ $[5/2{]}_{3,2},$ $5p$ $[3/2{]}_{1,2},$ and $5p$ $[1/2{]}_0$ transitions of krypton have been determined in a large $K^2$ region at a high electron-impact energy of 2500 eV. The positions of the minima and maxima of these GOSs have been determined. The present results show that the angular resolution and pressure effect have great influence on the position and the amplitude of the minimum for the GOS of ${5s+5s}^{\prime }$ transitions. When these effects are considered, the measured minimum position for the GOS of ${5s+5s}^{\prime }$ transitions is in excellent agreement with the calculation of Chen and Msezane [J. Phys. B 33, 5397 (2000)].

We introduce density-functional theory for inhomogeneous Bose-Fermi mixtures, derive the associated Kohn-Sham equations, and determine the exchange-correlation energy in local-density approximation. We solve numerically the Kohn-Sham system, and determine the boson and fermion density distributions and the ground-state energy of a trapped, dilute mixture beyond mean-field approximation. The importance of the corrections due to exchange correlation is discussed by a comparison with current experiments; in particular, we investigate the effect of the repulsive potential-energy contribution due to exchange correlation on the stability of the mixture against collapse.

We study phase-conjugate degenerate four-wave mixing in an optically pumped, two-level atomic system (the ${3s}^2{S}_{1/2},$ $F=2,$ $m_{\mathrm{F}}=\overrightarrow{2}{3p}^2{P}_{3/2},$ $F=3,$ $m_{\mathrm{F}}=3\mathrm{}$ transition in a diffuse, collision-free, thermal beam of sodium). In this investigation, we study the detailed line shape and strength of the four-wave mixing signal as a function of the intensity of the cw pump waves, and of the velocity of the atoms. Our technique allows us to examine the four-wave mixing interaction under conditions in which the Doppler shift, the natural linewidth of the transition, and the Rabi frequency for the interaction are each comparable with one another. From our experimental measurements and computational results, we show that the line shapes are very complex in this regime, and that they depend sensitively upon the atomic velocity, especially in the case when the intensity of the forward and backward pump beams exceeds the saturation intensity for the transition.

In self-induced transparency (SIT), as described by the McCall-Hahn area theorem, the area of an optical pulse is modified as it propagates through a resonant absorbing medium, and in the limit of high optical thickness evolves to certain discrete (quantized) output values. We investigate the area evolution experienced by an optical pulse when interacting with an absorbing medium contained within a cavity. In the system studied, the intracavity medium is weakly attenuating on a single-pass basis, but the atom-cavity system’s effective optical thickness as viewed from input to output port is generally quite large. Interestingly, at the low end of effective optical thickness we find that the cavity system generates pulse-area evolution closely mirroring that seen in the SIT system, i.e., output pulse areas evolve toward stable values as the effective optical thickness increases. However, when the effective optical thickness increases to certain triggering levels, the output pulse area is seen to drop abruptly toward zero. Our theoretical predictions are experimentally probed using cavity-contained cryogenically coherence-stabilized ${\mathrm{Tm}}^{3+}$ ions.

Coherent population trapping is studied in ${}^{87}\mathrm{Rb}$ in a buffer gas. Experimental results are reported on the contrast of the field independent hyperfine resonance line and on its linewidth. A physical model, which includes an optical pumping process that traps atoms in a Zeeman sublevel of the ground state, is developed. The model explains the general behavior of the experimental observations.