We evaluate the low-lying oscillation modes and the ballistic expansion properties of a harmonically trapped gas of fermionic ${}^{40}\mathrm{K}$ atoms containing thermal ${}^{87}\mathrm{Rb}$ impurities as functions of the anisotropy of the trap. Numerical results are obtained by solving the Vlasov-Landau equations for the one-body phase-space distribution functions and are used to test simple scaling Ansätzes. Starting from the gas in a weak impurity-scattering regime inside a spherical trap, the time scales associated to motions in the axial and azimuthal directions enter into competition as the trap is deformed to an elongated cigarlike shape. This competition gives rise to coexistence of collisionless and hydrodynamic behaviors in the low-lying surface modes of the gas as well as to a dependence of the aspect ratio of the expanding cloud on the collision time.

Using the axially symmetric time-dependent Gross-Pitaevskii equation we study the Josephson oscillation of an attractive Bose-Einstein condensate (BEC) in a one-dimensional periodic optical-lattice potential. We find that the Josephson frequency is virtually independent of the number of atoms in the BEC and of the interatomic interaction (attractive or repulsive). We study the dependence of the Josephson frequency on the laser wave length and the strength of the optical-lattice potential. For a fixed laser wave length (795 nm), the Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti et al. [Science 293, 843 (2001)]. For a fixed strength, the Josephson frequency remains essentially unchanged for a reasonable variation of laser wave length around 800 nm. However, the Josephson oscillation is disrupted with the increase of laser wave length beyond 2000 nm leading to a collapse of a sufficiently attractive BEC. These features of a Josephson oscillation can be tested experimentally with present setups.

The solutions of the time-independent Schrödinger equation for non-Hermitian (NH) Hamiltonians have been extensively studied and calculated in many different fields of physics by using $L^2$ methods that originally have been developed for the calculations of bound states. The existing non-Hermitian formalism breaks down when dealing with wave packets (WPs). An open question is how time-dependent expectation values can be calculated when the Hamiltonian is NH? Using the $F$-product formalism that was recently proposed by Moiseyev and Lein [J. Phys. Chem. 107, 7181 (2003)] we calculate the time-dependent expectation values of different observable quantities for a simple well-known study test case model Hamiltonian. We carry out a comparison between these results and those obtained from conventional (i.e., Hermitian) quantum mechanics (QM) calculations. The remarkable agreement between these results emphasizes the fact that in NH QM, unlike standard QM, there is no need to split the entire space into two regions, i.e., the interaction region and its surrounding. Our results open a door for a type of WP propagation calculations within the NH QM formalism that until now were impossible. In particular our work is relevant to the many different fields in physics and chemistry where complex absorbing potentials are introduced in order to reduce the propagation calculations to a restricted region in space where the artificial reflections from the edge of the numerical grid or box are avoided.

We derive an analytic approximation for the concurrence of weakly mixed bipartite quantum states—typical objects in state of the art experiments. This approximation is shown to be a lower bound of the concurrence of arbitrary states.

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call “comb”. For qubits (or spin $1∕2$) the combs are automatically invariant under $\mathrm{SL}(2,\mathbb{C})$. This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulas for the concurrence and the three-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-qubit entanglement.

Hypervirial theorems provide relationships exact electronic wave functions must satisfy, and the extent to which this is the case is a measure (additional to the energy) of wave function quality. The hypervirial relation known as the Vinti equation has been proposed for this purpose, but its application has been hampered by the absence of analytical formulas for the singular integrals occurring therein. The authors’ methods for singular integrals arising in atomic computations [J. Chem. Phys. 121, 6323 (2004)] resolve this bottleneck; quality assessments based on the Vinti equation are provided here for a number of wave functions of varying complexity describing the He isoelectronic series (from ${\mathrm{H}}^{-}$ through ${\mathrm{Ne}}^{8+}$).

We introduce a quantum component, the quantum high- and low-pass filter, and analyze its output characteristic. It is shown that a quantum bandpass filter can be achieved by using passive linear optics and projection measurements. Furthermore, we show that the sub-Poissonian state can be generated by using a cascaded quantum low-pass filter and high-pass filter.

The constrained molecular dynamics model, previously introduced for nuclear dynamics, has been extended to the atomic structure and collision calculations. Quantum effects, corresponding to the Pauli and Heisenberg principles, are enforced by constraints, following the idea of the Lagrange multiplier method. Our calculations for a small atomic system, H, He, Li, Be, and F reproduce the ground-state binding energies reasonably, compared with the experimental data. We discuss also the shell splitting due to $e\text{−}e$ correlation.

We develop a mathematically consistent approach for treating the quantum systems based on moving classical reference frames. The classical and quantum exact solutions show excellently classical-quantum correspondence, in which the quantum chaotic coherent states correspond to the classically chaotic motions. Applying the approach to the periodically driven linear and nonlinear oscillators, the regular and chaotic quantum states and quantum levels, and the quantum chaotic regions are evidenced. The results indicate that chaos may cause the collapse of matter wave packets and suppress the quantum effect of energy.

We study the pairwise concurrences, a measure of entanglement, of the ground states for the frustrated Heisenberg ring to explore the relation between entanglement and quantum phase transition associated with the momentum jump. The ground-state concurrences between any two sites are obtained analytically and numerically. It shows that the summation of all possible pairwise concurrences is an appropriate candidate to depict the phase transition. We also investigate the role that the momentum takes in the jump of concurrence at the critical points. We find that an abrupt momentum change results in the maximal concurrence difference of two degenerate ground states.

We calculate the amount of polarization-entanglement induced by two-photon interference at a lossless beam splitter. Entanglement and its witness are quantified, respectively, by concurrence and the Bell–Clauser-Horne-Shimony-Holt (CHSH) parameter. In the presence of a Mandel dip, the interplay of two kinds of which-path information—temporal and polarization—gives rise to the existence of entangled polarization states that cannot violate the Bell–CHSH inequality.

We examine the entanglement of thermal states of $n$ spins interacting through different types of $XY$ couplings in the presence of a uniform magnetic field, by evaluating the negativities of all possible bipartite partitions of the whole system and of subsystems. We consider both the case where every qubit interacts with all others and where just nearest neighbors interact in a one-dimensional chain. Limit temperatures for nonzero negativities are also evaluated and compared with the mean field critical temperature. It is shown that limit temperatures of global negativities are strictly independent of the magnetic field in all $XXZ$ models, in spite of the quantum transitions that these models may exhibit at zero temperature, while in anisotropic models they always increase for sufficiently large fields. Results also show that these temperatures are higher than those limiting pairwise entanglement.

We reexamine the charge transfer cross sections for ${\mathrm{C}}^{6+}+\mathrm{H}$ collisions for energies below $1\mathrm{keV}∕\mathrm{amu}$ using a fully quantum mechanical approach, based on the hyperspherical close-coupling method. Whereas most previous theoretical and experimental data agree well for the dominant charge transfer to the ${\mathrm{C}}^{5+}(n=4)$ states, there is significant disagreement among the theories for the transition to the weaker $n=5$ states. Using the present quantum mechanical calculations we analyze the origin of the discrepancy among these previous calculations. We further extend the calculations to collision energies down to about 1 eV and show that electron capture to the $n=5$ states begins to dominate over the $n=4$ states.

Multicharged xenon and krypton ions with charge states up to ${\mathrm{Xe}}^{11+}$ and ${\mathrm{Kr}}^{11+}$ have been observed in laser ionization of a pulsed xenon or krypton beam by a $25\mathrm{ns}$ Nd-YAG laser with laser intensity of ${10}^{10}–{10}^{11}\mathrm{W}{\mathrm{cm}}^{-2}$ at $532\mathrm{nm}$. There is strong evidence to support that those multicharged ions come from cluster-assisted electron recolliding ionizations inside the cluster after multiphoton ionization of atoms in the cluster, the electron can gain its kinetic energy by inverse bremsstrahlung absorption from a laser field quickly.

A microscopic theory of a nondissipative drag in a two-component superfluid Bose gas is developed. The expression for the drag current in the system with the components of different atomic masses, densities, and scattering lengths is derived. It is shown that the drag current is proportional to the square root of the gas parameter. The temperature dependence of the drag current is studied and it is shown that at temperature of order or smaller than the interaction energy the temperature reduction of the drag current is rather small. A possible way of measuring the drag factor is proposed. A toroidal system with the drag component confined in two half-ring wells separated by two Josephson barriers is considered. Under certain condition such a system can be treated as a Bose-Einstein counterpart of the Josephson charge qubit in an external magnetic field. It is shown that the measurement of the difference of number of atoms in two wells under a controlled evolution of the state of the qubit allows one to determine the drag factor.

This paper reports on the modeling of the Ni-like silver transient x-ray laser at the wavelength of 13.9 nm. Time-dependent populations and gain are calculated consistently with the output intensity. Two-dimensional refraction, i.e., in the direction of the driving laser and parallel to the slab target surface, is modeled by a ray trace code which is a postprocessor of a hydrodynamic code. Temperatures and electron-density variations are given by the hydrocode. Our calculations show that interaction of the x-ray laser field with the amplifying medium, and refraction, affect the output intensity and reduce the gain values by a large factor: from many hundreds per cm, as predicted by collisional-radiative models ignoring the above interaction, to one hundred per cm, at most.

We calculate the second-order roughness correction to the Casimir energy for two parallel metallic mirrors. Our results may also be applied to the plane-sphere geometry used in most experiments. The metallic mirrors are described by the plasma model, with arbitrary values for the plasma wavelength, the mirror separation, and the roughness correlation length, with the roughness amplitude remaining the smallest length scale for perturbation theory to hold. From the analysis of the intracavity field fluctuations, we obtain the Casimir energy correction in terms of generalized reflection operators, which account for diffraction and polarization coupling in the scattering by the rough surfaces. We present simple analytical expressions for several limiting cases, as well as numerical results that allow for a reliable calculation of the roughness correction in real experiments. The correction is larger than the result of the proximity force approximation, which is obtained from our theory as a limiting case (very smooth surfaces).

We present a technique for proving the security of quantum-key-distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the Bennett-Brassard 1984, the six-state, and the Bennett 1992 protocols with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel.

A configuration-average distorted-wave method is developed to calculate electron-impact excitation and ionization cross sections for diatomic molecules and their ions. The method is based on the construction of bound and continuum orbitals on a two-dimensional numerical lattice in $(r,\theta )$ center-of-mass polar coordinates. Our first applications are the calculation of $1s\sigma \to 2p\sigma$ and $1s\sigma \to 2p\pi$ excitation cross sections and $1s\sigma \to ϵl\lambda$ ionization cross sections for $\mathrm{H}_2{}^{+}$. Comparisons are made with plane-wave Born, distorted-wave, and $R$-matrix calculations, as well as experimental measurements.