Using the method of the local transmission matrix, we generalize the well-known WKB formula for barrier penetrability to multichannel systems. We compare the WKB penetrability with a solution of the coupled-channels equations, and show that the WKB formula works well at energies well below the lowest adiabatic barrier. We also discuss the eigenchannel approach to a multichannel tunneling, which may improve the performance of the WKB formula near and above the barrier.

The von Neumann entropy at the output of a bosonic channel with thermal noise is analyzed. Coherent-state inputs are conjectured to minimize this output entropy. Physical and mathematical evidence in support of the conjecture is provided. A stronger conjecture—that output states resulting from coherent-state inputs majorize the output states from other inputs—is also discussed.

We propose a method for the experimental generation of two different families of bound entangled states of three qubits. Our method is based on the explicit construction of a quantum network that produces a purification of the desired state. We also suggest a route for the experimental detection of bound entanglement, by employing a witness operator plus a test of the positivity of the partial transposes.

We analyze the nonlinear optical response of a four-level atomic system driven into a tripod configuration. The large cross-Kerr nonlinearities that occur in such a system are shown to produce nonlinear phase shifts of order $\pi$. Such a substantial shift may be observed in a cold atomic gas in a magneto-optical trap where it could be feasibly exploited towards the realization of a polarization quantum phase gate. The experimental feasibility of such a gate is here examined in detail.

The euv resonance lines $4s_{1∕2}\text{−}4p_{3∕2}$ of the $\mathrm{Cu}$- and $\mathrm{Zn}$-like ions of $\mathrm{Os}$, $\mathrm{Bi}$, $\mathrm{Th}$, and $\mathrm{U}$ $\left(\mathrm{Z}=76–92\right)$ have been observed in an electron beam ion trap, and their wavelengths measured using a high-resolution flat-field spectrometer. Our experiments achieve a spectral resolution three to six times better than earlier measurements and remove potential systematic errors from line blends encountered in earlier work. Our results for $\mathrm{Cu}$-like ions are in good agreement only with recent ab initio calculations that include quantum electrodynamical effects. Our experimental results for $\mathrm{Zn}$-like ions have a similarly high accuracy. However, theoretical predictions for $\mathrm{Zn}$-like ions of a quality comparable to those available for $\mathrm{Cu}$-like ions are lacking.

A method for structure determination of polyatomic molecules with equivalent atoms is suggested. The method is based on an interference pattern in the resonant Auger scattering process. This pattern is caused by interference of resonant Auger channels corresponding to a core hole localized on different equivalent atoms. The predicted effect can be observed in angular resolved electron-ion coincidence measurements or, alternatively, using the ordinary Auger technique on surface-oriented molecules.

A density-functional theory is developed for fermions in one dimension, interacting via a $\delta$ function. Such systems provide a natural testing ground for questions of principle, as the local-density approximation should be highly accurate since for this interaction type the exchange contribution to the local-density approximation is intrinsically self-interaction-free. The exact-exchange contribution to the total energy is a local functional of the density. A local-density approximation for correlation is obtained using perturbation theory and Bethe ansatz results for the one-dimensional contact-interacting uniform Fermi gas. The ground-state energies are calculated for two finite systems, the analogs of helium and of Hooke’s atom. The local-density approximation is shown to be excellent as expected.

We have experimentally demonstrated the enhancement of coherent Raman scattering in $\mathrm{Rb}$ atomic vapor by exciting maximal atomic coherence with fractional stimulated Raman adiabatic passage. Experimental results are in good agreement with numerical simulations. The results support the possibility of increasing the sensitivity of coherent anti-Stokes Raman spectroscopy by preparing maximal atomic or molecular coherence using short pulses.

We calculate the four-wave mixing (FWM) in a Bose-Einstein condensate system having multiple spin wave packets that are initially overlapping in physical space, but have nonvanishing relative momentum that causes them to recede from one another. Three receding condensate atom wave packets can result in production of a fourth wave packet by the process of FWM due to atom-atom interactions. We consider cases where the four final wave packets are composed of one, two, three, and four different internal spin components. FWM with one or two-spin state wave packets is much stronger than three- or four-spin state FWM, wherein two of the coherent moving Bose-Einstein condensate wave packets form a spin-polarization grating that rotates the spin projection of the third wave into that of the fourth diffracted wave (as opposed to the one- or two-spin state case where a regular density grating is responsible for the diffraction). Calculations of FWM for ${}^{87}\mathrm{Rb}$ and ${}^{23}\mathrm{Na}$ condensate systems are presented.

It is shown that simultaneously changing the scattering length of an elongated, harmonically trapped Bose-Einstein condensate from positive to negative and inverting the axial portion of the trap, so that it becomes expulsive, results in a train of self-coherent solitonic pulses. Each pulse is itself a nondispersive attractive Bose-Einstein condensate that rapidly self-cools. The axial trap functions as a waveguide. The solitons can be made robustly stable with the right choice of trap geometry, number of atoms, and interaction strength. Theoretical and numerical evidence suggests that such a pulsed atomic soliton laser can be made in present experiments.

Observation of $pp\mu *$, muonic proton-proton metastable ionic molecules, has been reported in recently published papers. They are produced in interactions of $\mu p\left(2s\right)$ atoms with protons. These ionic molecules play an important role in the muon-catalyzed fusion cycle. The structure of $pp\mu *$ is studied here using the variational method and by a related suitable wave function. Through this approach, the energies and nuclear size in the resonance states for $pp\mu *$ are calculated. To assess the reliability of the given wave function, the formation rate is also calculated. The obtained results are close to those previously reported and give strong indications that the related wave function is good enough for determining the resonance states of this mentioned ionic molecule.

We observe transformation of the electromagnetically induced transparency (EIT) resonance into an absorption resonance in a $\Lambda$ interaction configuration in a cell filled with ${}^{87}\mathrm{Rb}$ and a buffer gas. This transformation occurs as one-photon detuning of the coupling fields is varied from the atomic transition. No such absorption resonance is found in the absence of a buffer gas. The width of the absorption resonance is several times smaller than the width of the EIT resonance, and the changes of absorption near these resonances are about the same. Similar absorption resonances are detected in the Hanle configuration in a buffered cell.

Safronova et al. [Phys. Rev. A 65, 022507 (2002)] presented a “theoretical benchmark,” relativistic many-body perturbation theory (MBPT) calculation of energies of the $n=3$ states of Al-like ions with $Z=14–100$ and claimed excellent agreement with available experimental data. In this comment, we negate the claim by demonstrating, using $\mathrm{Ar}\mathrm{VI}$, $\mathrm{Ti}\mathrm{X}$, $\mathrm{Fe}\mathrm{XIV}$, and $\mathrm{Ni}\mathrm{XVI}$ as examples, disagreements between the Safronova et al. data on the one hand and experimental data and other theoretical calculations on the other, noting that the calculations of Safronova et al. clearly misidentify the ordering of the ${}^{2}D^o{}_{3∕2,5∕2}$ levels of the $3p^3$ and $3s3p\left({}^{3}P^o\right)3d$ configurations. There are other levels also which are interchanged by the MBPT calculation with respect to measurements. We conclude that the data for Al-like ions should be used with caution, including those for Mg-like ions [Phys. Rev. A 61, 052503 (2000)].

Quantum protocols for coin flipping can be composed in series in such a way that a cheating party gains no extra advantage from using entanglement between different rounds. This composition principle applies to coin-flipping protocols with cheat sensitivity as well, and is used to derive two results: There are no quantum strong coin-flipping protocols with cheat sensitivity that is linear in the bias (or bit-commitment protocols with linear cheat detection) because these can be composed to produce strong coin flipping with arbitrarily small bias. On the other hand, it appears that quadratic cheat detection cannot be composed in series to obtain even weak coin flipping with arbitrarily small bias.

Simple physical interactions between spin-$1∕2$ particles may result in quantum states that exhibit exotic correlations that are difficult to find if one simply explores state spaces of multipartite systems. In particular, we present a detailed investigation of the well-known Ising model of a chain (ring) of spin-$1∕2$ particles (qubits) in a transverse magnetic field. We present explicit expressions for eigenstates of the model Hamiltonian for arbitrary number of spin-$1∕2$ particles in the chain in the standard (computer) basis, and we investigate quantum entanglement between individual qubits. We analyze bipartite as well as multipartite entanglement in the ground state of the model. In particular, we show that bipartite entanglement between pairs of qubits of the Ising chain (measured in terms of a concurrence) as a function of the parameter $\lambda$ has a maximum around the point $\lambda =1$, and it monotonically decreases for large values of $\lambda$. We prove that in the limit $\lambda \to \infty$ this state is locally unitary equivalent to an $N$-partite Greenberger-Horn-Zeilinger state. We also analyze a very specific eigenstate of the Ising Hamiltonian with a zero eigenenergy (we denote this eigenstate as the $X$-state). This $X$-state exhibits the “extreme” entanglement in a sense that an arbitrary subset $A$ of $k⩽n$ qubits in the Ising chain composed of $N=2n+1$ qubits is maximally entangled with the remaining qubits (set $B$) in the chain. In addition, we prove that by performing a local operation just on the subset $B$, one can transform the $X$-state into a direct product of $k$ singlets shared by the parties $A$ and $B$. This property of the $X$-state can be utilized for new secure multipartite communication protocols.

It has recently been shown that one can perform quantum computation in a Heisenberg chain in which the interactions are always on, provided that one can abruptly tune the Zeeman energies of the individual (pseudo)spins. Here we provide a more complete analysis of this scheme, including several generalizations. We generalize the interaction to an anisotropic form (incorporating the $XY$ interaction as a limit), providing a proof that a chain coupled in this fashion tends to an effective Ising chain in the limit of far off-resonant spins. We derive the primitive two-qubit gate that results from exploiting abrupt Zeeman tuning with such an interaction. We also demonstrate, via numerical simulation, that the same basic scheme functions in the case of smoothly shifted Zeeman energies. We conclude with some remarks regarding generalizations to two- and three-dimensional arrays.

The nonlinear magneto-optical rotation in a medium consisting of $J=1\to J=0$ atoms placed in a static magnetic field is studied. The density matrix approach and irreducible atomic basis are used to describe the state of the atomic system. The stationary propagation equations for two collinear laser beams with perpendicular circular polarizations are derived and analyzed in the case of the magnetic field perpendicular to the light propagation direction. The effect of the linear polarization rotation toward the direction parallel or perpendicular to the magnetic field vector and lossless propagation of the resulting light are predicted. The conversion of the circularly polarized beam into linearly polarized one is shown. The propagation of the leading edges of switched on cw-laser beams and their stationary propagation are analyzed numerically. The dependence of the considered effects on the light detuning and on the additional magnetic field component parallel to the light propagation direction is discussed. The destructive role of the collisional relaxation is demonstrated.

We present the results of numerical calculations of the ground states of weakly interacting Bose-Einstein condensates containing large numbers of vortices. Our calculations show that these ground states appear to be close to uniform triangular vortex lattices. However, slight deviations from a uniform triangular lattice have dramatic consequences on the overall particle distribution. In particular, we demonstrate that the overall particle distribution averaged on a length scale large compared to the vortex lattice constant is well approximated by a Thomas-Fermi profile.

We construct three-dimensional structures of topological defects hosted in trapped wave fields, in the form of vortex stars, vortex cages, parallel vortex lines, perpendicular vortex rings, and parallel vortex rings, and we show that the latter exist as robust stationary, collective states of nonrotating Bose-Einstein condensates. We discuss the stability properties of excited states containing several parallel vortex rings hosted by the condensate, including their dynamical and structural stability.

Pulsed coherent excitation of a two-level atom strongly coupled to a resonant cavity mode will create a superposition of two coherent states of opposite amplitudes in the field. By choosing proper parameters of interaction time and pulse shape the field after the pulse will be almost disentangled from the atom and can be efficiently outcoupled through cavity decay. The fidelity of the generation approaches unity if the atom-field coupling strength is much larger than the atomic and cavity decay rates. This implies a strong difference between even and odd output photon number counts. Alternatively, the coherence of the two generated field components can be proven by phase-dependent annihilation of the generated nonclassical superposition state by a second pulse.