We consider entanglement in a system with a fixed number of identical particles. Since any operation should be symmetrized over all the identical particles and there is the precondition that the spatial wave functions overlap, the meaning of identical-particle entanglement is fundamentally different from that of distinguishable particles. The identical-particle counterpart of the Schmidt basis is shown to be the single-particle basis in which the one-particle reduced density matrix is diagonal. But it does not play a special role in the issue of entanglement, which depends on the single-particle basis chosen. The nonfactorization due to (anti)symmetrization is naturally excluded by using the (anti)symmetrized basis or, equivalently, the particle number representation. The natural degrees of freedom in quantifying the identical-particle entanglement in a chosen single-particle basis are occupation numbers of different single-particle basis states. The entanglement between effectively distinguishable spins is shown to be a special case of the occupation-number entanglement.

A formula, which is a useful improvement over existing ones, has been obtained to calculate the generalized oscillator strengths (GOS’s) for the discrete transitions of both open-shell and closed-shell atoms. We illustrate our formula by calculating the GOS for the oxygen ${2p}^4{(}^3{P)-2p}^3{(}^4{S\left)3s\right(}^{3}S)$ transition and obtain overall good agreement with the experimental data. Our calculated GOS reveals a minimum at around the momentum transfer, $K=1.26\mathrm{}\mathrm{a}.\mathrm{u}.$ We recommend a careful experimental search for the position of the minimum around the predicted value for confirmation.

A single-component Fermi gas of polarized dipolar particles in a harmonic trap can undergo a mechanical collapse due to the attractive part of the dipole-dipole interaction. This phenomenon can be conveniently manipulated by the shape of the external trapping potential. We investigate the signatures of the instability by studying the spectrum of low-lying collective excitations of the system in the hydrodynamic regime. To this end, we employ a time-dependent variational method as well as exact numerical solutions of the hydrodynamic equations of the system.

Current methods of preparing maximally entangled states in the laboratory need an extremely accurate control of interaction times, requiring sophisticated experimental techniques. Here, we show that such precise control is not necessary when one utilizes short or weak interactions followed by measurements. We present a scheme for the probabilistic generation of Bell states in a pair of cavities, after each has interacted briefly with an atom. The advantage of the scheme, as compared to present schemes, is its low sensitivity to the exact values of experimental parameters such as atomic velocity and coupling strength, in fact, for a large range of parameters, the fidelity of the Bell states generated remains close to unity.

We study the amount of communication needed for two parties to transform some given joint pure state into another one, either exactly or with some fidelity. Specifically, we present a method to lower bound this communication cost even when the amount of entanglement does not increase. Moreover, the bound applies even if the initial state is supplemented with unlimited entanglement in the form of EPR (Einstein-Podolsky-Rosen) pairs and the communication is allowed to be quantum mechanical. We then apply the method to the determination of the communication cost of asymptotic entanglement concentration and dilution. While concentration is known to require no communication whatsoever, the best known protocol for dilution, discovered by H.-K. Lo and S. Popescu [Phys. Rev. Lett. 83, 1459 (1999)], requires exchange of a number of bits that is of the order of the square root of the number of EPR pairs. Here we prove a matching lower bound of the same asymptotic order, demonstrating the optimality of the Lo-Popescu protocol up to a constant factor and establishing the existence of a fundamental asymmetry between the concentration and dilution tasks. We also discuss states for which the minimal communication cost is proportional to their entanglement, such as the states recently introduced in the context of “embezzling entanglement” (W. van Dam and P. Hayden, e-print quant-ph/0201041).

Let $H^{\left[N\right]}{=H}^{\left[d_1\right]}\otimes \cdots \otimes H^{\left[d_n\right]}$ be a tensor product of Hilbert spaces and let ${\tau }_0$ be the closest separable state in the Hilbert-Schmidt norm to an entangled state ${\rho }_0.$ Let ${\tilde{\tau }}_0$ denote the closest separable state to ${\rho }_0$ along the line segment from $I/N$ to ${\rho }_0$ where I is the identity matrix. Following A. O. Pittenger and M. H. Rubin [Linear Algebr. Appl. 346, 75 (2002)] a witness $W_0$ detecting the entanglement of ${\rho }_0$ can be constructed in terms of I, ${\tau }_0,$ and ${\tilde{\tau }}_0.$ If representations of ${\tau }_0$ and ${\tilde{\tau }}_0$ as convex combinations of separable projections are known, then the entanglement of ${\rho }_0$ can be detected by local measurements. Gühne et al. [Phys. Rev. A 66, 062305 (2002)] obtain the minimum number of measurement settings required for a class of two-qubit states. We use our geometric approach to generalize their result to the corresponding two-qudit case when d is prime and obtain the minimum number of measurement settings. In those particular bipartite cases, ${\tau }_0={\tilde{\tau }}_0.$ We illustrate our general approach with a two-parameter family of three-qubit bound entangled states for which ${\tau }_0\ne {\tilde{\tau }}_0$ and we show that our approach works for n qubits. We elaborated earlier [A. O. Pittenger, Linear Algebr. App. 359, 235 (2003)] on the role of a “far face” of the separable states relative to a bound entangled state ${\rho }_0$ constructed from an orthogonal unextendible product base. In this paper the geometric approach leads to an entanglement witness expressible in terms of a constant times I and a separable density ${\mu }_0$ on the far face from ${\rho }_0.$ Up to a normalization this coincides with the witness obtained by Gühne et al. for the particular example analyzed there.

The angular distribution of the Xe $5s$ photoelectrons was measured in the 90–225 eV photon energy range using linearly polarized synchrotron radiation. The experimentally determined angular distribution parameters were compared with theoretical values obtained from calculations based on the random-phase approximation and the time-dependent density-functional theory. Experiment shows that the dipole (β) and nondipole (γ) parameters vary strongly as a function of the photon energy, in accordance with calculations that account for the interchannel coupling. Nondipole effects observed clearly in experiment confirm the role of multielectron correlation in describing the $5s$ photoionization of Xe far from the ionization threshold.

We analyze classically the scattering of sulfur ions by carbon using the classical-trajectory Monte Carlo method. It is assumed that the scatterer and scattered nuclei are coupled to each other as well as to all electrons, but there is no coupling between electrons themselves. To initialize the state of both atoms, quasiexact energies are used that are obtained from the Dirac-Fock method. Effective charges are used to partially take into account the intra-atomic interactions between electrons. We concentrate on the cross sections for production of vacancies in the K and L shells and capture of electrons to K, L, and M shells of the sulfur ions. The dependence of these cross sections on the energy of the projectile sulfur ions and on the initial charge states of these ions is analyzed. Our results will be helpful in the interpretation of x-ray spectra from highly ionized fast sulfur projectiles passing through a carbon foil.

Mixed clusters of B and N have been produced by sputtering BN with Cs or Rb. The atom ordering in assumed linear species has been deduced from measurements of the mass distribution of both the positive and negative products from the fragmentation of the anionic clusters in a gas target. The existence of the anions BBN, BNN, BBBN, BBBBN, BBNN, and BBBNN has been demonstrated. The structural isomer with the largest electron affinity is usually the dominant species produced in the sputter source.

Sympathetic laser cooling of ions stored within a linear-geometry, radio frequency, electric-quadrupole trap has been investigated using computational and theoretical techniques. The simulation, which allows five sample ions to interact with 35 laser-cooled atomic ions, revealed an instability heating mechanism, which can prevent ions below a certain critical mass from being sympathetically cooled. This critical mass can, however, be varied by changing the trapping field parameters, thus allowing ions with a very large range of masses to be sympathetically cooled using a single ion species. A theoretical explanation of this instability heating mechanism is presented which predicts that the cooling-heating boundary in trapping parameter space is a line of constant $q_u$ (ion trap stability coefficient), a result supported by the computational results. The threshold value of $q_u$ depends on the masses of the interacting ions. A functional form of this dependence is given.

We study the dynamics of a wave packet in a potential formed by the sum of a periodic lattice and a parabolic potential. The dynamics of the wave packet is essentially a superposition of oscillations with frequencies proportional to the local slope of the parabolic potential. The amplitude and the phase of the Fourier transform of a signal characterizing this dynamics then contain information about the amplitude and the phase of the wave packet at a given lattice site. Hence, complete reconstruction of the wave packet in real space can be performed from a study of the dynamics of the system.

The dissipative dynamics of a Josephson junction in Bose gases is considered within the framework of the model of a tunneling Hamiltonian. The effective action that describes the dynamics of the phase difference across the junction is derived using the functional integration method. The dynamic equation obtained for the phase difference across the junction is analyzed for the finite temperatures in the low-frequency limit involving the radiation terms. The asymmetric case of the Bose gases with the different order parameters is calculated as well.

We present a quantum description of the interaction between a Bose-Einstein condensate and a single-mode quantized radiation field in the presence of a strong far-off-resonant pump laser. In the linear regime, the atomic medium is described approximately by two momentum states coupled to the radiation mode. We calculate the evolution of the operators in the Heisenberg picture and their expectation values, such as average and variance of the occupation numbers, atom-atom and atom-field correlations, and two-mode squeezing parameters. Then, we disentangle the evolution operator and obtain the exact evolution of the state vector in the linear regime. This allows us to demostrate that the system can be atom-atom or atom-field thermally entangled. We define the quasiclassical and the quantum recoil limits, for which explicit expressions of the average population numbers are obtained.

A quantum well with a single exciton mode in a microcavity driven by squeezed vacuum is studied in the low exciton density regime. By solving the quantum Langevin equations, we study the intensity, spectrum, and intensity correlation function for the fluorescent light. An expression for the Q function of the field inside the cavity is derived from the solutions of the quantum Langevin equations. Using the Q function, the intracavity photon number distribution and the quadrature fluctuations for both the cavity and fluorescent fields are studied. Several interesting and new effects due to squeezed vacuum are found.

We suggest, using the dynamical Zeno effect, the isolation of a qubit in a quantum memory unit against a decoherence caused by a coupling with the reservoir at zero temperature. The proposed method is based on an analog of a zero-ground screening method in an electronic circuit and it utilizes an auxiliary casing system that mediates the qubit-reservoir interaction and that is frequently erased to the ground state. The applications of the screening procedure to the storage at the atomic and photonic qubit states in the cavity QED experiments are discussed.

In a recent paper, Whitehead, McCann, and Shimamura [Phys. Rev. A 64, 023401 (2001)] presented classical-trajectory Monte Carlo (CTMC) calculations of the effects of laser fields on the cross section for antihydrogen formation in collisions of antiprotons with positronium. They also use the same method to calculate the photoionization rate of isolated positronium in a strong field. The purpose of this Comment is to point out (i) the criteria for validity of the quasiclassical approximation are not satisfied for all the conditions used; (ii) some of their numerical results do not agree with the values obtained with a corroborated code; (iii) the ambiguity of a cross section when the target can ionize even before the projectile arrives; and (iv) the essential effect of quantum-mechanical tunneling on the strong-field ionization rate. A recently published method allowing tunneling in a CTMC calculation [J. S. Cohen, Phys. Rev. A 64, 043412 (2001)] is used for (iv). It is concluded that the laser effect on formation of antihydrogen may be much greater than that found by Whitehead et al., but the pulse must be better characterized for quantitative predictions.

In this paper, we propose a sequence of tests which give a definitive test for checking $2\times M$ separability. The test is definitive in the sense that each test corresponds to checking membership in a cone, and that the closure of the union of all these cones consists exactly of all $2\times M$ separable states. Membership in each single cone may be checked via semidefinite programming, and is thus a tractable problem. This sequential test comes about by considering the dual problem, the characterization of all positive maps acting $C^{2\times 2}\to C^{M\times M}.$ The latter in turn is solved by characterizing all positive quadratic matrix polynomials in a complex variable.

The lifetime of the metastable ${}^3{P}_2$ state of neon has been determined as $14.73\left(14\right)\mathrm{}\mathrm{s}$ [decay rate $0.06790\left(64\right)\mathrm{}{\mathrm{s}}^{-1}]$ by measuring the decay in fluorescence of an ensemble of ${}^{20}\mathrm{Ne}$ atoms trapped in a magneto-optical trap (MOT). Due to low background gas pressure $(p<\mathrm{}5\mathrm{}\times {10}^{-11}\mathrm{mbar})$ and low relative excitation to the ${}^3{D}_3$ state (0.5 % excitation probability) only small corrections have to be included in the lifetime extrapolation. Together with a careful analysis of residual loss mechanisms in the MOT a lifetime determination to high precision is achieved.

Measurements of electron velocity distributions emitted at $0°$ for collisions of 10- and 20-keV ${\mathrm{H}}^{+}$ incident ions on ${\mathrm{H}}_2$ and He show that the electron capture to the continuum cusp formation, which is still possible at these low impact energies, is shifted to lower momenta than its standard position (centered on the projectile velocity), as recently predicted. Classical trajectory Monte Carlo calculations reproduce the observations remarkably well, and indicate that a long-range residual interaction of the electron with the target ion after ionization is responsible for the shifts, which is a general effect that is enhanced at low nuclear velocities.

The geometric phase of an atomic system has been observed in $V$-type three-level barium atoms using photon echoes. The geometric phase results from a cyclic evolution of a two-level subsystem driven by a laser pulse. The phase change is observed on the echo field produced on a different subsystem that is coupled via the ground state to the driven subsystem. The measured geometric phase was half of the solid angle subtended by the Bloch vector along the driven evolution circuit. This evolution has the potential to form universal operations of quantum bits.