We theoretically investigate the effect of an anisotropic trap on the instability of the polar $(m_F=0)$ phase of a spin-1 Bose-Einstein condensate. By considering rigorously the spatial quantization, we show that the growth of the nascent ferromagnetic phase at short times becomes anisotropic, with stronger oscillations in the magnetization correlation function along the unconfined direction.

We have analyzed the conditions for low-power spatiotemporal soliton formation in arrays of evanescently coupled silicon-on-insulator photonic wires. We have verified that pronounced soliton effects can be observed in the presence of realistic loss, two-photon absorption, and higher-order dispersions. A soliton in an $N$-wire array can excite $N$ resonant frequencies, but some of these may be suppressed due to the soliton having zero projection onto the corresponding radiation supermodes. This results in pronounced differences between the radiation spectra observed from solitons excited at the edge and in the center of arrays.

We experimentally realize a high-intensity three-photon Greenberger-Horne-Zeilinger (GHZ) entanglement source directly following the proposal by Rarity and Tapster [J. G. Rarity and P. R. Tapster, Phys. Rev. A 59, R35 (1999)]. The threefold coincidence rate can be more than $200\mathrm{Hz}$ with a fidelity of 0.811, and the intensity can be further improved with moderate fidelity degradation. The GHZ entanglement is characterized by testing the Bell-Mermin inequality and using an entanglement witness operator. To optimize the polarization-entangled source, we theoretically analyze the relationship between the mean photon number of the single-photon source and the probability of parametric down-conversion.

We analyze the momentum entanglement of homogeneous Bardeen–Cooper–Schrieffer (BCS) states between spin-up and spin-down particles at finite temperature. This is achieved by studying the structure of the partial transposition of the two-particle density matrix (denoted by ${\rho }_2^{T_A}$) in momentum space, as well as the corresponding negativity. We show that ${\rho }_2^{T_A}$ consists of infinitely many decoupled $2\times 2$ submatrices, and momentum entanglement is a necessary and sufficient condition for a nonzero order parameter $\Delta$. From the distribution of eigenvalues of ${\rho }_2^{T_A}$, we discover that momentum entanglement is most significantly contributed by pairs with momenta slightly above a surface related to the Fermi energy. In addition, we propose an entanglement witness operator for detecting momentum entanglement in BCS states.

Here we consider a class of $2\otimes 2\otimes d$ density matrices which have positive partial transposes with respect to all subsystems. The entanglement witness approach is used to investigate the entanglement of these density matrices. To demonstrate the approach, the three-qubit case is considered in detail. For constructing entanglement witnesses (EWs) detecting these density matrices, we attempt to convert the problem to an exact convex optimization problem. To this aim, we map the convex set of separable states into a convex region, named feasible region, and consider the cases in which the exact geometrical shape of the feasible region can be obtained. In this way, various linear and nonlinear EWs are constructed. The optimality and decomposability of some of the introduced EWs are also considered. Furthermore, the detection of the density matrices by the introduced EWs are discussed analytically and numerically.

We present and analyze a quantum key distribution protocol based on sending entangled $N$-qubit states instead of single-qubit ones as in the trail-blazing scheme by Bennett and Brassard 1984 (BB84). Since the qubits are sent and acknowledged individually, an eavesdropper is limited to accessing them one by one. In an intercept-resend attack, this fundamental restriction allows one to make the eavesdropper’s information on the transmitted key vanish if even one of the qubits is not intercepted. The implied upper bound $1∕\left(2N\right)$ for this information is further shown not to be the lowest, as the information can be reduced to less than 30% of that in the BB84 scheme in the case $N=2$. In general, the protocol is at least as secure as BB84.

We have employed time-dependent density-functional theory (TDDFT) to calculate the long-range dipole-dipole dispersion coefficient (van der Waals coefficient) $C_6$ of alkali-metal atoms Li, Na, K; alkali-metal atom dimers ${\mathrm{Li}}_2$, ${\mathrm{Na}}_2$, ${\mathrm{K}}_2$; sodium clusters containing even number of atoms ranging from 2 to 20 atoms; and fullerene ${\text{C}}_{60}$. The dispersion coefficient is obtained via Casimir-Polder expression which relates it to the frequency dependent linear polarizability at imaginary frequencies. The frequency-dependent polarizabilities are calculated by employing TDDFT-based complete sum-over-states expressions for the atoms, and direct TDDFT linear response theory for the closed shell dimers and clusters.

$K$-shell x-ray emission measurements of electron capture into Rydberg states of ${\mathrm{Ar}}^{17+}$ and ${\mathrm{Ar}}^{18+}$ ions are carried out as a function of collision energy in order to investigate the energy dependence of angular momentum capture states in slow charge exchange collisions. The highly charged ions are produced using an electron beam ion trap and extracted onto an external argon gas target. A retardation assembly in the beamline allows projectile energies from $\sim 2\mathrm{keV}∕\mathrm{amu}$ down to $\sim 5\mathrm{eV}∕\mathrm{amu}$ to be selected. For decreasing collision energies a shift to electron capture into low orbital angular momentum capture states is observed. Comparative $K$-shell x-ray emission measurements of electron capture by ${\mathrm{Ar}}^{17+}$ and ${\mathrm{Ar}}^{18+}$ ions from background gas in the trap are also presented. The results of the trapping experiments are in discrepancy with those obtained using extracted ions and possible explanations are discussed.

Recently, a method to image molecular electronic orbitals using high-order harmonic generation was introduced by Itatani et al. [Nature 432, 876 (2004)]. We show that, while the tomographic reconstruction of general orbitals with arbitrary symmetry cannot be performed with long laser pulses, this becomes possible when extremely short pulses are used. This statement is shown both in a simplified wave-packet picture and more formally within the strong-field approximation. We present an analytical formula for the wave-packet composition of the recollision electron. An alternative reconstruction equation based on momentum matrix elements, rather than on dipole matrix elements, is proposed. We present simulations of the procedure for two-dimensional model systems based on numerical solutions of the time-dependent Schrödinger equation.

We present a theoretical study of high-order harmonic generation by a Bessel-Gauss laser beam focused in a low-density gas medium. We consider in detail the generation of the 21st-order harmonic of a short-pulse Ti:sapphire laser in an argon gas jet. Within the strong-field approximation for the atomic dipole, and a complete account of the macroscopic propagation, we compute the number of photons produced and the brightness as a function of the medium parameters and the focusing conditions. We show that emission of the 21st-order harmonic can be maximized by adjusting the half-angle of the Bessel-Gauss beam. We find that, at given intensity and confocal parameter, the conversion efficiency is significantly enhanced with a Bessel-Gauss beam, as compared with a Gaussian one. Of particular interest for many applications, we also observe a spectacular increase of the brightness, by two decades, at maximum emission.

The strong-field approximation for ionization of diatomic molecules by a strong laser field [D. B. Milošević, Phys. Rev. A 74, 063404 (2006)] is generalized to include rescattering of the ionized electron wave packet off the molecular centers (the electron’s parent ion or the second atom). There are four rescattering contributions to the ionization rate, which are responsible for the high-energy plateau in the electron spectra and which interfere in a complicated manner. The spectra are even more complicated due to the different symmetry properties of the atomic orbitals of which a particular molecular orbital consists. Nevertheless, a comparatively simple condition emerges for the destructive interference of all these contributions, which yields a curve in the $(E_{{\mathbf{p}}_f},\theta )$ plane. Here $\theta$ is the electron emission angle and $E_{{\mathbf{p}}_f}$ is the electron kinetic energy. The resulting suppression of the rescattering plateau can be strong and affect a large area of the $(E_{{\mathbf{p}}_f},\theta )$ plane, depending on the orientation of the molecule. We illustrate this using the examples of the $3{\sigma }_g$ molecular orbital of ${\mathrm{N}}_2$ and the $1{\pi }_g$ molecular orbital of ${\mathrm{O}}_2$ for various orientations of these molecules with respect to the laser polarization axis. For ${\mathrm{N}}_2$, for perpendicular orientation and the equilibrium internuclear distance $R_0$, we find that the minima of the ionization rate form the curve $E_{{\mathbf{p}}_f}{\cos }^2\theta ={\pi }^2∕\left(2R_0^2\right)$ in the $(E_{{\mathbf{p}}_f},\theta )$ plane. For ${\mathrm{O}}_2$ the rescattering plateau is absent for perpendicular orientation.

Recolliding electrons are responsible for many of the interesting phenomena observed in the interaction of strong laser fields with atoms and molecules. We show that in multielectron targets such as ${\mathrm{C}}_{60}$ an important recollision pathway opens up: the returning electron may excite collective modes even if the laser frequency is far off-resonant. We formulate a simple analytical theory which predicts that the recollision-induced excitation of collective modes should dominate over the “usual” harmonic generation yield at $800\mathrm{nm}$ wavelength. In this case the tomographic imaging of complex multielectron systems may be obscured. We employ a time-dependent density functional model of ${\mathrm{C}}_{60}$ and show that with increasing laser wavelength the dynamics becomes more and more single-active-electron–like, suggesting that long wavelengths are to be preferred for imaging purposes.

Using exact continuous quantum Monte Carlo techniques, we study the zero- and finite-temperature properties of a system of harmonically trapped one-dimensional spin-$\frac{1}{2}$ fermions with short-range interactions. Motivated by experimental searches for modulated Fulde-Ferrel-Larkin-Ovchinikov states, we systematically examine the impact of a spin imbalance on the density profiles. We quantify the accuracy of the Thomas-Fermi approximation, finding that for sufficiently large particle numbers $(N\gtrsim 100)$ it quantitatively reproduces most features of the exact density profile. The Thomas-Fermi approximation fails to capture small Friedel-like spin and density oscillations and overestimates the size of the fully paired region in the outer shell of the trap. Based on our results, we suggest a range of experimentally tunable parameters to maximize the visibility of the double-shell structure of the system and the Fulde-Ferrel-Larkin-Ovchinikov state in the one-dimensional harmonic trap. Furthermore, we analyze the fingerprints of the attractive contact interactions in the features of the momentum and pair momentum distributions.

We present a theory that predicts a boundary electro-optical effect in near-field optics, providing a simple physical picture based on a quasistatic treatment. This optical effect is caused by Maxwell’s boundary conditions and is dominant in the near field of ferroelectric domains on small scales. Our formulation treats the boundary effect and the familiar bulk effect on an equal footing, and could be used to derive and characterize other boundary optical effects in near-field optics. We discuss the observability of boundary electro-optical and magneto-optical effects in near-field optics.

We investigate the dynamics of the instantaneous polarization state of stationary, partially polarized random electromagnetic beamlike fields. An intensity-normalized correlation function of the instantaneous Poincaré vector is introduced for the characterization of the time evolution of the polarization state. This polarization correlation function enables us to define a polarization time and a polarization length over which the polarization state remains substantially unchanged. In the case of Gaussian statistics, the polarization correlation function is shown to assume a simple form in terms of the parameters employed to characterize partial coherence and partial polarization of electromagnetic fields. The formalism is demonstrated for a partially polarized, temporally Gaussian-correlated beam, and black-body radiation. The results are expected to find a range of applications in investigations of phenomena where polarization fluctuations of light play an important role.

We present experimental and theoretical differential cross sections for the elastic scattering of electrons from neon at four incident electron energies from $5\text{to}50\mathrm{eV}$. The magnetic angle-changing device has been used to extend the present measurements from mid-angles to backward angles up to 180°. The results reveal some small differences between experiment and theory at backward angles in some cases; however, the agreement at 5 and $50\mathrm{eV}$ is excellent.

One of the fundamental conditions for one-way quantum computation (1WQC) is the ability to make sequential measurements on isolated qubits that comprise the highly entangled resource for 1WQC, the cluster state. This has been a significant impediment in the implementation of 1WQC with ultracold atoms confined in optical lattices, because the width of the measuring lasers is generally much greater than the atomic (qubit) spacing. We demonstrate that deterministic 1WQC is nevertheless possible, with a polynomial increase in the number of operations, as long as the center of the beams can be positioned with high accuracy and the beam width is reproducible. Extending the number of cluster atoms, the scheme is also able to compensate for accidental measurements of an arbitrary number of nearby qubits.

On the basis of perturbation theory using the fine structure constant $\alpha$ and the ratio of the electron to muon masses, we calculate the one-loop vacuum polarization, electron vertex corrections, and nuclear structure corrections to the hyperfine splitting of the ground state of the muonic helium atom $\left(\mu e{}_2{}^4\mathrm{He}\right)$. We obtain the total result for the ground-state hyperfine splitting $\Delta {\nu }^{\mathrm{HFS}}=4465.526\mathrm{MHz}$, which improves the previous calculation of Lakdawala and Mohr due to the additional corrections taken into account. The remaining difference between the theoretical result and experimental value of the hyperfine splitting, equal to $0.522\mathrm{MHz}$, lies in the range of theoretical error and requires subsequent investigation of higher-order corrections.

The photoelectron satellite structure of rubidium and cesium has been investigated following the photoionization of an $nd$ $(n=3,4)$ inner-shell electron. The intensity ratios of the $n{d}^{-1}ms$ monopole and $n{d}^{-1}{m}^{\prime }p$ conjugated satellite lines have been measured at MAX-lab by using high-resolution electron spectroscopy. For rubidium, moreover, the energy dependence of the $3d_{j}6s∕3d_{j}5s$ and $3d_{j}5p∕3d_{j}5s$ intensity ratios with $j=3∕2$ and $5∕2$ is measured and compared with multiconfiguration Dirac-Fock calculations. A good or at least reasonable agreement is found for both the monopole and conjugated shake-up probabilities if the relaxation of the bound-state electron density is taken into account in the computation of the photoionization cross sections. It is shown that, for the inner-shell ionization of medium and heavy atoms, the orbital relaxation accounts for a significant part of the satellite structure in the photoelectron spectra.

The variation of the energy loss versus the exit angle in channeling experiments using ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{+}$, and ${\mathrm{H}}^{+}$ fragments produced by the incidence of $\mathrm{H}_2{}^{+}$ on thin gold crystals oriented in the ⟨100⟩ direction has been investigated in the low-velocity range, corresponding to energies below $10\mathrm{keV}∕\mathrm{u}$. The experimental results for ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ were compared with computational simulations performed with the MARLOWE code, considering an impact-parameter-dependent energy loss based on electron density calculations and low-energy stopping power models. The comparisons provide information on the impact-parameter dependence of the energy loss for channeled ions and serve as a test of theoretical models in the present low-energy range. A molecular effect is observed for the transmitted ${\mathrm{H}}^{+}$ fragments corresponding to $\mathrm{H}_2{}^{+}$ incidence. This effect is explained based on geometrical considerations and a vicinage effect in the energy loss of correlated protons.