Bose-Einstein condensates of ${10}^4{}^{85}\mathrm{Rb}$ atoms in a cylindrical trap are studied using a recently proposed approach based on a local-density approximation. Since the existence of a Feshbach resonance allows for widely tuning the scattering length of the atoms, values of the peak gas parameter $x_{\mathrm{pk}}$ of the order of ${10}^{-2}$ may be attained and the standard analysis based on Gross-Pitaevskii and/or Thomas-Fermi equations may result in being questionable. Energy functionals derived from the correlated basis functions theory and the low-density expansion for a homogeneous hard-spheres gas are used to estimate corrections to the Gross-Pitaevskii equation. The two functionals give similar results, both showing large differences with respect to the Thomas-Fermi and Gross-Pitaevskii ones. The column densities at $z=0\mathrm{}$ may differ by as much as $\sim 30\%$ and the half maximum radius by $\sim 20\%.$ The scattering lengths estimated by fitting the half maximum radius may differ by $\sim 40\%$ from those given by a Thomas-Fermi-based analysis of the experimental data.

We study the system of coupled atomic and molecular condensates within the two-mode model and beyond mean-field theory. Large-amplitude atom-molecule coherent oscillations are shown to be damped by the rapid growth of fluctuations near the dynamically unstable molecular mode. This result contradicts earlier predictions about the recovery of atom-molecule oscillations in the two-mode limit. The frequency of the damped oscillation is also shown to scale as $\sqrt{N}/\ln N$ with the total number of atoms N, rather than the expected pure $\sqrt{N}$ scaling. Using a linearized model, we obtain analytical expressions for the initial depletion of the molecular condensate in the vicinity of the instability, and show that the important effect neglected by mean-field theory is an initially nonexponential “spontaneous” dissociation into the atomic vacuum. Starting with a small population in the atomic mode, the initial dissociation rate is sensitive to the exact atomic amplitudes, with the fastest (superexponential) rate observed for the entangled state formed by spontaneous dissociation.

An asymptotic theory of atom scattering by large amplitude periodic potentials is developed in the Raman-Nath approximation. The atom grating profile resulting from the scattering is evaluated in the Fresnel zone for triangular, sinusoidal, magneto-optical, and bichromatic field potentials. Analytic asymptotic expressions are obtained for the Fourier components of the atomic wave function following scattering. It is shown that, owing to the scattering into two groups of momentum states rather than two distinct momentum components, the corresponding spatial density profiles differ significantly from pure sinusoids.

Unit-efficiency homodyne detection of the resonance fluorescence of a two-level atom collapses the quantum state of the atom to a stochastically moving point on the Bloch sphere. Recently, Hofmann, Mahler, and Hess [Phys. Rev. A 57, 4877 (1998)] showed that by making part of the coherent driving proportional to the homodyne photocurrent one can stabilize the state to any point on the bottom-half of the sphere. Here we reanalyze their proposal using the technique of stochastic master equations, allowing their results to be generalized in two ways. First, we show that any point on the upper- or lower-half, but not the equator, of the sphere may be stabilized. Second, we consider nonunit-efficiency detection, and quantify the effectiveness of the feedback by calculating the maximal purity obtainable in any particular direction in Bloch space.

The influence of losses in the interferometric generation and the transmission of continuous-variable entangled light is studied, with special emphasis on Gaussian states. Based on the theory of quantum-state transformation at absorbing dielectric devices, the amount of entanglement is quantified by means of the relative-entropy measure. Upper bounds of entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure, the bounds can substantially overestimate the entanglement. In particular, they do not show the drastic decrease of entanglement with increasing mean photon number, as does the distance measure.

The use of third-harmonic generation of visible pulses in a magnesium-fluoride wedge has been proposed in order to obtain ultrashort pulses with photon energy in the vacuum ultraviolet range. Starting from a 200 fs blue pulse with 18 μJ of energy (which is the second harmonic of the IR pulses produced by a regenerative Ti-Sapphire laser system), ${10}^3$ photons were obtained at 9.4 eV, with ${10}^{-9}$ conversion efficiency. From the measurements it was inferred that ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}(-3\omega ;\omega ,\omega ,\omega )\approx 0.45\times {10}^{-22}{\mathrm{m}}^2/{\mathrm{V}}^2$ for the third-order susceptibility of magnesium fluoride. The simplicity of the arrangement makes this approach ideal for the generation of the ultraviolet probe required by time and angle-resolved photoemission spectroscopy.

This work treats degenerate four-wave mixing (DFWM) in noncentrosymmetric materials, taking into full account the fact that the DFWM signal arises from third-order nonlinear optical effects as well as from two distinct combinations of second-order effects: second-harmonic generation plus difference frequency generation and optical rectification plus Pockels effect. Because of these second order “cascaded” contributions, the DFWM signal becomes dependent on details of the experimental setup that do not normally matter for centrosymmetric materials, such as the wave vectors of the interacting beams and the pulse duration. The origin, consequences, and possible applications of these effects are discussed for both the “forward” and the “phase-conjugation” DFWM configurations. All second-order contributions are described quantitatively by introducing effective third-order susceptibilities, and their value is discussed using the example of two materials: ferroelectric ${\mathrm{KNbO}}_3$ and the organic salt $4-N,N-\mathrm{dimethylamino}-4^{\prime }-N^{\prime }-\mathrm{methyl}-\mathrm{stilbazolium}\mathrm{}\mathrm{tosylate}.$

When a quantum-optical Fredkin gate is embedded into a Mach-Zehnder interferometer, state reduction techniques permit the generation of maximally entangled states of the radiation field when Fock states are input to the device. These states exactly reach the Heisenberg limit of phase sensitivity. We investigate the consequences of injecting more general states, and particularly coherent states, into the apparatus. Applications to interferometry and photolithography are discussed.

We examine the passage of ultracold two-level atoms through the potential produced by the vacuum of the cavity field. We find that the phase time may be considered as the appropriate measure of the time required for the atom to traverse the cavity. The phase tunneling time for ultracold atoms exhibits both super- and sub-classical time and we show how this behavior may be understood in terms of the momentum dependence of the phase of transmission amplitude. The passage of the atom through the cavity is unique, as it involves a coherent addition of the transition amplitudes corresponding to both barrier and well.

The superfluidity of Bose-Einstein condensates (BECs) in optical lattices is investigated. Apart from the usual Landau instability, which occurs when a BEC flows faster than the speed of sound, the BEC can also suffer a dynamical instability, resulting in period doubling and other sorts of symmetry breaking of the system. Such an instability plays a crucial role in the dissipative motion of a trapped BEC in an optical lattice recently observed [Burger et al., Phys. Rev. Lett. 86, 4447 (2001)].

We discuss the interaction between two resonant states in a quantum double-well structure. The behavior of the resonant states depends on the coupling between the wells, i.e., the height and width of the barrier that separates them. We distinguish a region with resonant tunneling and a region where the two resonances repel each other. The transition between the two regions is marked by a double pole of the S matrix.

In this paper we consider a generalization of the three-level stimulated Raman adiabatic-passage process (STIRAP). In our scheme, there are $N-1$ ground levels and one excited level. The ground levels are coupled with laser pulses through the excited level at multiphoton resonance. The ultimate aim of this scheme is to create coherent-superposition states on the ground levels. In a previous paper [J. Mod. Opt. (to be published), special issue on quantum interference] we have considered this problem from the optimal-control point of view. Here we apply a different approach: We reconsider the adiabatic approximation, which is commonly utilized to describing the STIRAP process. It is shown that in our case, in the adiabatic limit, the dark and bright subspaces of the Hamiltonian are decoupled; however, the nonadiabatic corrections influence significantly the dynamics in the dark subspace. An analytic solution is presented for the case of a five-level system. Moreover, we consider some special examples for the pulse sequences that effect prescribed final superposition states. The robustness of the scheme is studied, and the extension of our scheme is also considered.

We present an operator-algebraic approach to derive the low-lying quasidegenerate spectrum of weakly interacting trapped N bosons with total angular momentum $ħL$ for the case of $L/N\ll 1.$ We demonstrate that the lowest-lying excitation spectrum is given by ${27gn}_3{(n}_3-1)/34,$ where g is the strength of the repulsive contact interaction and $n_3$ is the number of excited octupole quanta. Our method provides constraints for these quasidegenerate many-body states and gives higher excitation energies that depend linearly on N.

The formation of patterns in two transverse dimensions in photorefractive two-wave mixing with a single feedback mirror is investigated theoretically. We perform numerical simulations of the full (3+1)-dimensional nonlinear model equations, displaying the breakup of the unstable annulus of active modes into hexagonal spots. Analytically we derive amplitude equations of the Landau type for patterns with rhombic- and hexagonal-mode interaction and discuss the stability and coexistence of transverse planforms in the photorefractive feedback system. A strong renormalization for the hexagon amplitude is determined, and its consequences for pattern formation using Landau formalism are discussed. In particular, the stability of regular substructures of a dodecagonal spot arrangement is investigated and square-hexagon competition is predicted. We use an invasive Fourier-filtering technique for the selection of unstable patterns, such as stripes and squares. The longitudinal propagation of the critical and higher-order modes of the self-organized structures and the impact of a Fourier filter on the mode propagation within a nonlinear bulk photorefractive medium is studied in detail.

We report the direct observation of a type of rainbow caustic. In contrast to known examples, this caustic originates from a dissipative, stochastic process. We have observed this when using cold ${}^{87}\mathrm{Rb}$ atoms bouncing inelastically on an evanescent-wave atom mirror. The caustic appears as a sharp peak at the lower edge of an asymmetric velocity distribution of the bouncing atoms. The stochastic process is a spontaneous Raman transition due to photon scattering during the bounce. The results are in good agreement with a classical calculation.

We show that by virtue of the Röntgen interaction, a vortex of order n in a Bose-Einstein condensate (BEC), in which the constituent atoms are characterized by an electric dipole, gives rise to a magnetic monopole distribution, which correctly preserves magnetic charge neutrality. If, on the other hand, the BEC atoms are characterized by a magnetic dipole, we show that the Aharonov-Casher interaction term leads to the prediction of an electric charge distribution associated with the vortex state, which too, exhibits electric charge neutrality. Our theory displays an exact symmetry between the electric and magnetic aspects of the problem and can thus be presented in a unified fashion. Illustrations are given for finite-size atomic gas BECs, superfluid helium, and spin-polarized hydrogen BECs in the $n=1\mathrm{}$ vortex state.

We show how to simplify the computation of the entanglement of formation and the relative entropy of entanglement for states, which are invariant under a group of local symmetries. For several examples of groups we characterize the state spaces, which are invariant under these groups. For specific examples we calculate the entanglement measures. In particular, we derive an explicit formula for the entanglement of formation for $(U\otimes U)$-invariant states, and we find a counterexample of the additivity conjecture for the relative entropy of entanglement.

We investigate the creation of entanglement by the application of phases whose value depends on the state of a collection of qubits. First we give the necessary and sufficient conditions for a given set of phases to result in the creation of entanglement in a state comprising of an arbitrary number of qubits. Then we consider the maximum entanglement generation by global phases. We analyze the creation of entanglement between any two qubits in three-qubit pure and mixed states. We use our result to prove that entanglement is necessary for the Deutsch-Jozsa algorithm to have an exponential advantage over its classical counterpart.

Although key distribution is arguably the most studied context on which to apply quantum cryptographic techniques, message authentication, i.e., certifying the identity of the message originator and the integrity of the message sent, can also benefit from the use of quantum resources. Classically, message authentication can be performed by techniques based on hash functions. However, the security of the resulting protocols depends on the selection of appropriate hash functions, and on the use of long authentication keys. In this paper, we propose a quantum authentication procedure that, making use of just one qubit as the authentication key, allows the authentication of binary classical messages in a secure manner.

Unusual resonance features at high energies were recently discovered in the experimental crossed-beams measurements of the electron-impact ionization of ${\mathrm{Sm}}^{12+}.$ Theoretical calculations were able to confirm that they are due to deep-core excitation with capture into dielectronic states followed by sequential double Auger decay [K. Aichele et al., Phys. Rev. Lett. 86, 620 (2001)]. In this paper additional experimental results are presented, showing more resonances in the single-ionization cross section. Detailed level-to-level calculations of dielectronic capture provide a clear identification of these resonances, as produced by a $3d-4f$ excitation with capture to different $\mathrm{nl}$ orbitals followed by sequential emission of two electrons. By using configuration-average distorted-wave calculations, we estimate the branching ratios for single and double ionization by considering the possible autoionization paths leading to resonant contributions to excitation, single ionization, and double ionization.