We propose a scheme for quantum secret sharing (QSS) that uses a modulated high-dimensional time-bin entanglement. By modulating the relative phase randomly by $\{0,\pi \}$, a sender with the entanglement source can randomly change the sign of the correlation of the measurement outcomes obtained by two distant recipients. The two recipients must cooperate if they are to obtain the sign of the correlation, which is used as a secret key. We show that our scheme is secure against intercept-and-resend (IR) and beam splitting attacks by an outside eavesdropper thanks to the nonorthogonality of high-dimensional time-bin entangled states. We also show that a cheating attempt based on an IR attack by one of the recipients can be detected by changing the dimension of the time-bin entanglement randomly and inserting two “vacant” slots between the packets. Then, cheating attempts can be detected by monitoring the count rate in the vacant slots. The proposed scheme has better experimental feasibility than previously proposed entanglement-based QSS schemes.

We study the possibility of realizing perfect quantum state transfer in mesoscopic devices. We discuss the case of the Fano-Anderson model extended to two impurities. For a channel with an infinite number of degrees of freedom, we obtain coherent behavior in the case of strong coupling or in weak coupling off resonance. For a finite number of degrees of freedom, coherent behavior is associated with weak coupling and resonance conditions. Finite-temperature and disorder effects are discussed.

We have used the relativistic distorted-wave approximation to calculate the excitation of the lowest metastable states of neon, argon, krypton, and xenon [the $J=0,2$ levels of the $n{p}^5(n+1)s$ configuration] to the ten higher-lying fine-structure levels of the $n{p}^5(n+1)p$ configuration. We compare our results with experimental measurements of the integrated cross section at energies up to $400\mathrm{eV}$ and with other theoretical calculations for these cross sections.

We have studied the transmission through an optically thick ${}^{87}\mathrm{Rb}$ vapor that is illuminated by monochromatic and noise-broadened laser fields in $\Lambda$ configuration. The spectral width of the beat signal between the two fields after transmission through the atomic medium is more than 1000 times narrower than the spectral width of this signal before the medium.

It is shown that a highly-phase-sensitive polarization-squeezed $(2n-1)$-photon state can be generated by subtracting a diagonally polarized photon from the $2n$ photon component generated in collinear type II down-conversion. This polarization wedge state has the interesting property that its photon number distribution in the horizontal and vertical polarizations remains sharply defined for phase shifts of up to $1∕n$ between the circularly polarized components. Phase shifts at the Heisenberg limit are therefore observed as nearly deterministic transfers of a single photon between the horizontal and vertical polarization components.

The emission dynamics of a mode-locked laser oscillator with a nonlinear mirror based on stimulated Brillouin scattering (SBS) has been investigated with regard to its spectrum and to its intensity distribution. The investigation was carried out experimentally as well as by numerical simulations. The laser yields trains of pulses with measured durations of $410\mathrm{ps}$ and energies of the single pulse of up to $2\mathrm{mJ}$. Two theoretical models describing the complex emission dynamics of a mode-locked SBS-laser oscillator are introduced. The first model consists of spectrally resolved laser rate equations and thus describes the mode locking in the frequency domain by the superposition of the longitudinal resonator modes. The SBS-$Q$-switch is incorporated by a phenomenological description of the time dependent SBS reflectivity. Numerical simulations based on this model yield the evolution of a few 100 longitudinal laser modes and the corresponding intensity distribution during the course of a $Q$-switch pulse with $10\text{−}\mathrm{ps}$ resolution. The influences of the different components on the spectrum and thus on the pulse duration will be discussed. The second model describes all occurring dynamics in the time domain providing easy access to the study of misalignment on the output dynamics. Results of numerical simulations of both models and measurement results are compared.

We study geometrical aspects of entanglement, with the Hilbert–Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a “relativistic” formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and nonunitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.

The stepwise behavior of quantum defects along the periodic table of the elements is related to the $(n+\ell ,n)$ building-up rule in the table.

We calculate the neutralization probability of ${\mathrm{H}}^{-}$ ions due to charge transfer in collisions with metal vicinal surfaces. We apply a statistical Thomas-Fermi model with gradient correction to the kinetic energy and a local density approximation for the exchange-correlation energy to compute the ground-state electronic structure of the surface. In comparison with calculations for flat surfaces, we find work-function changes, induced by the vicinal superstructure, in good agreement with published experimental and theoretical data. We evaluate the shift and width of the ${\mathrm{H}}^{-}$ affinity level resonance for fixed positions of the ion near the surface. For incident anions with a kinetic energy of $1\mathrm{keV}$, the calculated ion-neutralization probabilities depend sensitively on the impact direction, point of closest approach of the trajectory, and the surface morphology. We find that the ion survival is more likely if the ${\mathrm{H}}^{-}$ ions approach the step from above, as compared to ions that approach a step from below under otherwise identical scattering conditions. In particular, the electron loss after reflection at a terrace of a monoatomically stepped Al surface is predicted to be resonantly enhanced if the ion approaches a step from below.

We present a quantum-mechanical theory of xuv generation by an elliptically polarized intense laser field. Our approach is valid when the Keldysh parameter $\gamma$ is about unity or less, and the driving ellipticity is less than $\sqrt{2}\gamma$. After the photoionization the motion of the electronic wave packet along the major axis of the driving field polarization ellipse is described quasiclassically, whereas the motion in the transverse direction is considered fully quantum mechanically; we also find the condition that allows the reduction of the motion description to a quantum orbit in the polarization plane of the laser field. We use the ionization rate calculated via numerical solution of the three-dimensional Schrödinger equation (TDSE), and take into account the Coulomb modification of the free electronic wave packet. The predictions of our theory for xuv emission agree well with numerical and experimental results. We study the high harmonic intensities and phases as functions of the driving intensity and ellipticity, and also the ellipticity and the rotation angle of the harmonic field polarization ellipse as functions of the driving ellipticity. The atomic response is decomposed into the contributions of different quantum paths. This allows finding a straightforward explanation for the observed dependencies.

Critical limits of a stationary nonlinear three-dimensional Schrödinger equation with confining power-law potentials $(\sim r^{\alpha })$ are obtained using spherical symmetry. When the nonlinearity is given by an attractive two-body interaction (negative cubic term), it is shown how the maximum number of particles $N_c$ in the trap increases as $\alpha$ decreases. With a negative cubic and positive quintic terms we study a first order phase transition, that occurs if the strength $g_3$ of the quintic term is less than a critical value $g_{3c}$. At the phase transition, the behavior of $g_{3c}$ with respect to $\alpha$ is given by $g_{3c}\sim 0.0036+0.0251∕\alpha +0.0088∕{\alpha }^2$.

We have previously shown that two-photon absorption and the quantum Zeno effect can be used to make deterministic quantum logic devices from an otherwise linear optical system. Here we show that this type of quantum Zeno gate can be used with additional two-photon absorbing media and weak laser pulses to make a heralded single photon source. A source of this kind is expected to have a number of practical advantages that make it well suited for large-scale quantum-information-processing applications.

We consider the phase separation of a trapped atomic mixture of fermions with unequal spin populations near a Feshbach resonance. In particular, we determine the density profile of the two spin states and compare with the recent experiments of Partridge et al. [Science 311, 503 (2006)]. Overall we find quite good agreement. We identify the remaining discrepancies, which provide important clues for the complete understanding of the experiment.

Bipartite entanglement in the ground state of a chain of $N$ quantum spins can be quantified either by computing pairwise concurrence or by dividing the chain into two complementary subsystems. In the latter case the smaller subsystem is usually a single spin or a block of adjacent spins and the entanglement differentiates between critical and noncritical regimes. Here we extend this approach by considering a more general setting: our smaller subsystem $S_A$ consists of a comb of $L$ spins, spaced $p$ sites apart. Our results are thus not restricted to a simple area law, but contain nonlocal information, parametrized by the spacing $p$. For the $XX$ model we calculate the von Neumann entropy analytically when $N\to \infty$ and investigate its dependence on $L$ and $p$. We find that an external magnetic field induces an unexpected length scale for entanglement in this case.

We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk.

We construct a Galilean invariant low-energy effective field theory of boson-fermion mixtures and study bound fermion states on a vortex of boson superfluid. We derive a simple criterion to determine for which values of the fermion angular momentum $l$ there exist an infinite number of bound energy levels. We apply our formalism to two boson-fermion mixed systems: the dilute solution of ${}^3\mathrm{He}$ in ${}^4\mathrm{He}$ superfluid and the cold polarized Fermi gas on the BEC side of the “splitting point.” For the ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$ mixture, we determine parameters of the effective theory from experimental data as functions of pressure. We predict that infinitely many bound ${}^3\mathrm{He}$ states on a superfluid vortex with $l=-2,-1,0$ are realized in a whole range of pressure $0–20\mathrm{atm}$, where experimental data are available. As for the cold polarized Fermi gas, while only $S$-wave $(l=0)$ and $P$-wave $(l=\pm 1)$ bound fermion states are possible in the BEC limit, those with higher negative angular momentum become available as one moves away from the BEC limit.

The possibility of using ultracold atoms to observe strong localization of matter waves is now a subject of great interest, as undesirable decoherence and interactions can be made negligible in these systems. It was proposed that a static-disordered potential can be realized by trapping atoms of a given species in randomly chosen sites of a deep three-dimensional (3D) optical lattice with no multiple occupation. We analyze in detail the prospects of this scheme for observing localized states in 3D for a matter wave of a different atomic species that interacts with the trapped particles and that is sufficiently far detuned from the optical lattice to be insensitive to it. We demonstrate that at low energy a large number of 3D strongly localized states can be produced for the matter wave, if the effective scattering length describing the interaction of the matter wave with a trapped atom is of the order of the mean distance between the trapped particles. Such high values of the effective scattering length can be obtained by using a Feshbach resonance to adjust the free-space interspecies scattering length and by taking advantage of confinement-induced resonances induced by the trapping of the scatterers in the lattice.

We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled Gross-Pitaevskii equations. The unstable modulation grows from initially miscible condensates into various types of vector solitary waves, depending on the combinations of the sign of the coupling constants (intracomponent and intercomponent). We discuss the detailed features of the modulation instability, dynamics of solitary wave formation, and an analogy with the collapsing dynamics in a single-component condensate with attractive interactions.

We examine the basic mode structure of atomic Cooper pairs in an inhomogeneous Fermi gas. Based on the properties of Bogoliubov quasiparticle vacuum, the single particle density matrix and the anomalous density matrix share the same set of eigenfunctions. These eigenfunctions correspond to natural pairing orbits associated with the BCS ground state. We investigate these orbits for a Fermi gas in a spherical harmonic trap and construct the wave function of a Cooper pair in the form of Schmidt decomposition. The issue of spatial quantum entanglement between constituent atoms in a pair is addressed.

The photon density operator function is used to calculate light beam propagation through turbulent atmosphere. A kinetic equation for the photon distribution function is derived and solved using the method of characteristics. Optical wave correlations are described in terms of photon trajectories that depend on fluctuations of the refractive index. It is shown that both linear and quadratic disturbances produce sizable effects for long-distance propagation. The quadratic terms are shown to suppress the correlation of waves with different wave vectors. We examine the intensity fluctuations of partially coherent beams (beams whose initial spatial coherence is partially destroyed). Our calculations show that it is possible to significantly reduce the intensity fluctuations by using a partially coherent beam. The physical mechanism responsible for this pronounced reduction is similar to that of the Hanbury-Braun–Twiss effect.