We investigate the separability, nonlocality, and squeezing of the continuous-variable analog of the Werner state: a mixture of a pure two-mode squeezed vacuum state with local thermal radiations. Utilizing this Werner state, coherent-state teleportation in the Braunstein-Kimble setup is discussed.

We propose a simple scheme for implementing quantum logic gates with a string of two-level trapped cold ions outside the Lamb-Dicke limit. Two internal states of each ion are used as one computational qubit (CQ) and the collective vibration of ions acts as the information bus, i.e., the bus qubit (BQ). Using the quantum dynamics for the laser-ion interaction as described by a generalized Jaynes-Cummings model, we show that quantum entanglement between any one CQ and the BQ can be coherently manipulated by applying classical laser beams. As a result, universal quantum gates, i.e., the one-qubit rotation and two-qubit controlled gates, can be implemented exactly. The required experimental parameters for the implementation, including the Lamb-Dicke (LD) parameter and the durations of the applied laser pulses, are derived. Neither the LD approximation for the laser-ion interaction nor the auxiliary atomic level is needed in the present scheme.

We discuss the effects of imperfect photon detectors suffering from loss and noise on the reliability of linear optical quantum computers. We show that for a given detector efficiency there is a maximum achievable success probability, and that increasing the number of ancillary photons and detectors used for one controlled sign flip gate beyond a critical point will decrease the probability that the computer will function correctly. We have also performed simulations of some small logic gates and estimate the efficiency and noise levels required for the linear optical quantum computer to function properly. We find that the construction of a $99\%$ reliable controlled sign flip gate would require photon detectors with an efficiency greater than 0.999987.

A version of the Monty Hall problem is presented where the players are permitted to select quantum strategies. If the initial state involves no entanglement the Nash equilibrium in the quantum game offers the players nothing more than that obtained with a classical mixed strategy. However, if the initial state involves entanglement of the qutrits of the two players, it is advantageous for one player to have access to a quantum strategy while the other does not. Where both players have access to quantum strategies there is no Nash equilibrium in pure strategies, however, there is a Nash equilibrium in quantum mixed strategies that gives the same average payoff as the classical game.

Angular distribution of L x rays of Au and Pb following photoionization by synchrotron radiation has been measured at the incident photon energies corresponding to the energy between $L_3$ and $L_2,$ between $L_2$ and $L_1,$ and above $L_1$ absorption edges. No evidence of L x-ray anisotropy was observed within the experimental errors for all incident photon energies, but in the case of $L_l$ x rays an anisotropy of a few percent might be possible. The experimental results are in good agreement with the theoretical prediction.

The quasiparticle excitations and dynamical stability of an atomic Bose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms at zero temperature is studied. The Fermi gas is assumed to be either in the normal state or to have undergone a phase transition to a superfluid state by forming Cooper pairs. The quasiparticle excitations of the Bose-Einstein condensate exhibit a dynamical instability due to a resonant exchange of energy and momentum with quasiparticle excitations of the Fermi gas. The stability regime for the bosons depends on whether the Fermi gas is in the normal state or in the superfluid state. We show that the energy gap in the quasiparticle spectrum for the superfluid state stabilizes the low-energy excitations of the condensate. In the stable regime, we calculate the boson quasiparticle spectrum, which is modified by the fluctuations in the density of the Fermi gas.

We examine the effect of the trapping potential on the critical temperature $T_C$ for the BCS transition to a superfluid state in trapped atomic gases of fermions. $T_C$ for an arbitrary power-law trap is calculated in the Thomas-Fermi approximation. For anharmonic traps, $T_C$ can be increased by several orders of magnitude in comparison to a harmonic trap. Our theoretical results indicate that, in practice, one could manipulate the critical temperature for the BCS phase transition by shaping the traps confining the atomic Fermi gases.

The evaporative cooling of a two-component mixture of trapped atomic fermions into quantum degeneracy is investigated using the semiclassical Boltzmann equation for fermions. The influence of Fermi blocking for temperatures well below the Fermi temperature is discussed. Comparison between collisional and relaxation rates for a Fermi degenerate gas are made, and the similarities and differences between the cooling kinetics of the Fermi gas mixture and a mixture of classical gases is investigated, and discussed using a simple model. The latter also serves to clarify the processes which terminate the cooling in the quantum degenerate regime. Finally, a brief discussion of mean-field effects is given.

The K-shell photodetachment of the metastable ${1s2s2p}^4{P}^o$ ${\mathrm{He}}^{-}$ state is calculated ab initio with a complex scaled configuration interaction method in the photon energy region between the $\mathrm{He}\hspace{0.5em}2s2p{}^3{P}^o$ threshold and the second double ionization threshold ${\mathrm{He}}^{+}$ $\mathrm{}(n=2\mathrm{}).$ Within this photon energy range triply excited states of ${\mathrm{He}}^{-}$ are reached and they autoionize through electron detachment plus target excitation. The only two related calculations reported so far from J. Xi and C. Froese-Fischer [Phys. Rev. A 59, 307 (1999)] and H.L. Zhou et al. [Phys. Rev. A 64, 012714 (2001)], showed a strong discrepancy. Our calculation supports the latter of these results and also compares rather well with a very recent experiment by N. Berrah et al. [Phys. Rev. Lett. 88, 093001 (2002)]. Contrary to the previous interpretation, we find that the prominent structures appearing in the photodetachment spectrum above 43 eV are true triply excited state resonances.

Endohedral fullerenes $\mathrm{N}@{\mathrm{C}}_{60}$ and $\mathrm{N}@{\mathrm{C}}_{70}$ were dissolved in a liquid crystal and investigated by electron paramagnetic resonance. Sharp, liquid solution like spectra are observed. However, contrary to the usual solution spectra, the lines are split, indicating that the electron shell of the enclosed nitrogen atom is deformed and that an alignment with respect to the magnetic-field axis is achieved. The present results are of practical interest for controlling the interaction of endohedral fullerenes in a quantum computer.

This paper demonstrates that how well a state performs as an input to Grover’s search algorithm depends critically upon the entanglement present in that state; the more the entanglement, the less well the algorithm performs. More precisely, suppose we take a pure state input, and prior to running the algorithm apply local unitary operations to each qubit in order to maximize the probability $P_{\max }$ that the search algorithm succeeds. We prove that, for pure states, $P_{\max }$ is an entanglement monotone, in the sense that $P_{\max }$ can never be decreased by local operations and classical communication.

The configuration-interaction (CI) method is applied to the study of positronic magnesium ${(e}^{+}\mathrm{Mg}),$ positronic calcium ${(e}^{+}\mathrm{Ca}),$ and positronic strontium ${(e}^{+}\mathrm{Sr}).\mathrm{}$ The CI expansion was seen to converge slowly with respect to $L_{\max },$ the maximum angular momentum of any orbital used to construct the CI basis. Despite doing explicit calculations with $L_{\max }=10,$ extrapolation corrections to the binding energies for the $L_{\max }\to \infty$ limit were substantial in the case of $e^{+}\mathrm{Ca}$ (25%) and $e^{+}\mathrm{Sr}$ (50%). The extrapolated binding energies were 0.0162 hartree for $e^{+}\mathrm{M}\mathrm{g},$ 0.0165 hartree for $e^{+}\mathrm{Ca},$ and 0.0101 hartree for $e^{+}\mathrm{Sr}.$ The static-dipole polarizabilities for the neutral parent atoms were computed as a by-product, giving ${71.7a}_0^3,$ ${162a}_0^3,$ and ${204a}_0^3$ for Mg, Ca, and Sr, respectively.

The configuration-interaction method is applied to the study of positronic zinc ${(e}^{+}\mathrm{Zn})$ and positronic cadmium ${(e}^{+}\mathrm{Cd}).\mathrm{}$ The estimated binding energies and annihilation rates were 0.003 73 hartree and $0.42\times {10}^9\hspace{0.5em}{\sec }^{-1}$ for $e^{+}\mathrm{Zn}$ and 0.006 10 hartree and $0.56\times {10}^9\hspace{0.5em}{\sec }^{-1}$ for $e^{+}\mathrm{Cd}.$ The low-energy elastic cross section and $Z_{\mathrm{eff}}$ were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive ${(14.5a}_0$ for Zn and ${11.6a}_0$ for Cd) the differential cross sections are larger at backward angles than at forward angles just above threshold. The possibilities of measuring differential cross sections to confirm positron binding to these atoms is discussed.

There has been considerable recent interest in low-temperature interrogation of quantum helium nanodroplets. We consider the interaction of helium ground and metastable states, employing the best known molecular dimer potentials. Radiative transitions between different metastable rovibrational levels are compared with the discharge emission transition lines and good agreement is found. Collisional interactions between helium ground and metastable atoms are studied and elastic scattering, metastability excitation transfer and diffusion cross sections and rate coefficients are calculated at ultralow energies. The integral elastic cross section at ultralow energies is about $5000\hspace{0.5em}{\mathrm{\AA }}^2.$ Effect of shape resonances that form in the potential barriers, on the cross sections is investigated. We find that some shape resonances live for longer than 100 s. Long-range potential wells could support “shelf” levels. We discuss their collisional and spectroscopic properties.

A single ${}^{137}{\mathrm{Ba}}^{+}$ ion has been laser cooled to the first few vibrational states of an $80-\mu \mathrm{m}$ radius rf quadrupole trap. Initial measurements showed no anomalous heating of the vibrational phonon for observation times up to 1 ms, corresponding to a heating rate less than 3.3 phonons/ms at a 95% confidence level. Subsequently we observed the growth of large and unstable bias voltages that were correlated with exposure to the atomic beam. After loading over 250 ions over a period of 720 days the trap became unstable, with ion lifetimes $<1\mathrm{}\hspace{0.5em}\min .$ A possible connection between this trap instability and anomalous heating observed in quantum computation experiments is discussed. An isotopically selectively laser cooling method was used to refine ${}^{137}\mathrm{Ba}$ ions out of a naturally abundant cloud.

Using an optimal control scheme, based on genetic algorithms, to tailor a laser pulse, we find that molecular orientation can be achieved during and after the radiative interaction. The mechanism, which appears to be one of the possible ways leading to orientation, is based upon a kick imparted to the molecule by a sudden (with respect to molecular rotational motion), asymmetric laser pulse. We show how such pulses resulting from optimization can actually be produced experimentally and how the laser control of orientation could further be improved.

We report experimental results on the properties of Bose-Einstein condensates in one-dimensional optical lattices. By accelerating the lattice, we observed Bloch oscillations of the condensate in the lowest band, as well as Landau-Zener (LZ) tunneling into higher bands when the lattice depth was reduced and/or the acceleration of the lattice was increased. The dependence of the LZ tunneling rate on the condensate density was then related to mean-field effects modifying the effective potential acting on the condensate, yielding good agreement with recent theoretical work. We also present several methods for measuring the lattice depth and discuss the effects of the micromotion in the time-orbiting-potential trap on our experimental results.

The Bose-Einstein condensation of correlated atoms in a trap is studied by examining the effect of interparticle correlations to one-body properties of atomic systems at zero temperature using a simplified formula for the correlated two-body density distribution. Analytical expressions for the density distribution and rms radius of the atomic systems are derived using four different expressions of the Jastrow-type correlation function. In one case, in addition, the one-body density matrix, momentum distribution and kinetic energy are calculated analytically, while the natural orbitals and natural occupation numbers are also predicted in this case. Simple approximate expressions for the mean-square radius and kinetic energy are also given.

We investigate the spatial patterns of the ground state of two interacting Bose-Einstein condensates. We consider the general case of two different atomic species (with different mass and in different hyperfine states) trapped in a magnetic potential whose eigenaxes can be tilted with respect to the vertical direction, giving rise to a nontrivial gravitational sag. Despite the complicated geometry, we show that within the Thomas-Fermi approximations and upon appropriate coordinate transformations, the equations for the density distributions can be put into a very simple form. Starting from these expressions we give explicit rules to classify the different spatial topologies that can be produced, and we discuss how the behavior of the system is influenced by the interatomic scattering length. We also compare explicit examples with the full numeric Gross-Pitaevskii calculation.

We consider a Yb-doped double-clad fiber laser in a unidirectional ring cavity containing a polarizer placed between two half-wave plates. Depending on the orientation of the phase plates, the laser operates in continuous, Q-switch, mode-lock, or unstable self-pulsing regime. An experimental study of the stability of the mode-locking regime is realized versus the orientation of the half-wave plates. A model for the stability of self-mode-locking and cw operation is developed starting from two-coupled nonlinear Schrödinger equations in a gain medium. The model is reduced to a master equation in which the coefficients are explicitly dependent on the orientation angles of the phase plates. Analytical solutions are given together with their stability versus the angles.