A method for solving the Byzantine agreement problem [M. Fitzi, N. Gisin, and U. Maurer, Phys. Rev. Lett. 87, 217901 (2001)] and the liar detection problem [A. Cabello, Phys. Rev. Lett. 89, 100402 (2002)] is introduced. The main advantages of this protocol are that it is simpler and is based on a four-qubit singlet state already prepared in the laboratory.

We generalize the perturbation theory of weakly interacting bosons to Bose-Einstein condensates with hyperfine spin $F=1.\mathrm{}$ Analytical expressions of second-order self-energies beyond the mean-field approximation are derived at zero temperature. We further extend the perturbation theory to the finite-temperature case, and derive the corresponding self-energies. We evaluate these self-energies near the poles of the first-order (mean-field) Green’s functions within the on-shell approximation, and expand the results in powers of wave number in the long-wavelength limit. Excitation spectra for each mode are obtained analytically at low temperatures. We also derive the ground-state energy and thermodynamic quantities such as free energy of the system.

The classical theory of the electromagnetic field associated with paraxial Laguerre-Gaussian light is generalized to apply to propagation in a bulk dielectric, and the theory is quantized to obtain expressions for the electric and magnetic field operators. The forms of the Poynting vector and angular momentum density operators are derived and their expectation values for a single-photon wave packet are obtained. The Lorentz force operator in the dielectric is resolved into longitudinal, radial, and azimuthal components. The theory is extended to apply to an interface between two semi-infinite dielectric media, one of which is transparent with an incident single-photon pulse, and the other of which is weakly attenuating. For a pulse that is much shorter than the attenuation length, the theory can separately identify the surface and bulk contributions to the Lorentz force on the attenuating dielectric. Particular attention is given to the transfer of longitudinal and angular momentum to the dielectric from light incident from free space. The resulting expressions for the shift and rotation of a transparent dielectric slab are shown to agree with those obtained from Einstein box theories.

The quantization of the damped one-dimensional harmonic oscillator is carried out. This is implemented by first writing the classical equations of motion that describe the system in a Hamiltonian form, the Hamiltonian being time independent explicitly. Canonical quantization is then implemented by using Heisenberg’s picture. When friction is turned off the results agree with those of the one-dimensional harmonic oscillator.

In this paper, we consider two possible approaches to compute the quantum states of moving magnetically induced anions. We start with the effective Hamiltonian derived in previous works. It has been reduced to the relevant degrees of freedom including those related to the collective motion of the anion across the magnetic field. Multiconfigurational approaches are applied starting with two convenient basis sets which account for the integral of the collective motion, the total angular momentum of the anion along the magnetic field. The coupled-channel equations, resulting from the implementation of these basis states, are derived and many useful relations for the relevant matrix elements are obtained. One of the suggested basis sets comprises the states which describe correctly the limiting case of the detached anion, and is, therefore, amenable to straightforward approximations. The corresponding single-channel approximation is investigated in some detail, and estimates of the eigenenergies of the magnetically induced moving anion are obtained.

In this work, we present model for bichromatic laser emission from laser dye solutions containing randomly distributed scattering particles. We suggest that bichromatic emission is produced by two fluorescent aggregates: monomers and dimers. The shorter-wavelength laser peak was attributed to the monomer emission and the secondary longer-wavelength peak was attributed to the dimer emission. From neat dye solutions, using absorption and emission spectroscopies, the monomer and dimer absorption and emission cross sections were obtained. The partial overlap between the dimer absorption cross section and the monomer emission cross section indicates a unidirectional radiative and nonradiative energy transfers from excited monomers to fundamental dimers. The dynamics of the laser emission was modeled by a set of rate equations, whose solutions agree with our experimental data. It is also shown that nonradiative energy transfer plays a very important role in the dimer laser process, and helps to explain the relatively strong dimer laser peak intensities.

A strongly attractive, two-component Fermi gas of atoms exhibits universal behavior and should be mechanically stable as a consequence of the quantum-mechanical requirement of unitarity. This requirement limits the maximum attractive force to a value smaller than that of the outward Fermi pressure. To experimentally demonstrate this stability, we use all-optical methods to produce a highly degenerate, two-component gas of ${}^6\mathrm{Li}$ atoms in an applied magnetic field near a Feshbach resonance, where strong interactions are observed. We find that gas is stable at densities far exceeding that predicted previously for the onset of mechanical instability. Further, we provide a temperature-corrected measurement of an important, universal, many-body parameter, which determines the stability—the mean-field contribution to the chemical potential in units of the local Fermi energy.

We show that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. If the squeezing parameter is less than or equal to 1, we demonstrate a quantitative relation between the squeezing parameter and the concurrence for the even and odd states. We prove that the even states generated from the initial state with all qubits being spin down, via the one-axis twisting Hamiltonian, are spin squeezed if and only if they are pairwise entangled. For the states generated via the one-axis twisting Hamiltonian with an external transverse field for any number of qubits greater than 1 or via the two-axis countertwisting Hamiltonian for any even number of qubits, the numerical results suggest that such states are spin squeezed if and only if they are pairwise entangled.

The teleportation channel associated with an arbitrary bipartite state denotes the map that represents the change suffered by a teleported state when the bipartite state is used instead of the ideal maximally entangled state for teleportation. This work presents and proves an explicit expression of the teleportation channel for teleportation using Weyl’s projective unitary representation of $(Z/dZ{)}^{2n}$ for integers $d>~2,$ $n>~1,$ which has been known for $n=1.\mathrm{}$ This formula allows any correlation among the n bipartite mixed states, and an application shows the existence of reliable schemes for distillation of entanglement from a sequence of mixed states with correlation.

Quantum walks are expected to provide useful algorithmic tools for quantum computation. This paper introduces absorbing probability and time of quantum walks and gives both numerical simulation results and theoretical analyses on Hadamard walks on the line and symmetric walks on the hypercube from the viewpoint of absorbing probability and time.

We consider situations in which (i) Alice wishes to send quantum information to Bob via a noisy quantum channel, (ii) Alice has a classical description of the states she wishes to send, and (iii) Alice can make use of a finite amount of noiseless classical information. After setting up the problem in general, we focus attention on one specific scenario in which Alice sends a known qubit down a depolarizing channel along with a noiseless classical bit. We describe a protocol that we conjecture is optimal and calculate the average fidelity obtained. A surprising amount of structure is revealed even for this simple case, which suggests that relationships between quantum and classical information could in general be very intricate.

In this work, we report a theoretical study of the role played by chemical environment on the electron-impact resonant core excitations in OCS, ${\mathrm{CO}}_2,$ and ${\mathrm{CS}}_2$ molecules. Calculated differential and integral cross sections for the promotion of a carbon $1s$ electron to the lowest unfilled $p\pi$ orbital of these molecules, or more specifically, the ratios of these cross sections for the corresponding transitions leading to the singlet and the triplet core-excited states in the 300–800 eV incident energy range, are reported. The distorted-wave approximation was applied to these calculations. Our study revealed resonance structures in the calculated ratios for ${\mathrm{CO}}_2,$ in good agreement with the available experimental observation, which is very encouraging. On the other hand, no resonance structure is clearly seen in the calculated ratios for OCS and ${\mathrm{CS}}_2$ molecules. The possible reason for the nonappearance of resonance for these two targets is discussed.

We report calculated photodetachment cross sections from the metastable ${\mathrm{Be}}^{-}$ ${1s}^2{2s2p}^2$ ${}^4{P}^e$ state in the photon energy range 0–10 eV. Outer-shell photodetachment takes place in this energy range, which includes the double-ionization threshold ${\mathrm{Be}}^{+}{(}^2{S}^e)$ at $\sim 7\mathrm{eV}$ as well as doubly excited thresholds of the residual atom up to the $\mathrm{Be}{(1s}^{2}2p4f)$ threshold at $\sim 10\mathrm{eV}.$ Therefore, triply excited states of ${\mathrm{Be}}^{-}$ are reached within the selected photon energy. We have implemented the complex scaled configuration interaction method along with a model potential for the ${1s}^2$ core to uncover the first series of ${\mathrm{Be}}^{-}$ ${}^4{L}^o$ resonant states. In this work, four ${}^4{P}^o,$ seven ${}^4{D}^o,$ and two ${}^4{S}^o$ resonances are reported and we compare our cross section with other previous theoretical calculations, that reported none or, at most, two resonances.

We have investigated the branching ratios and angular distributions of photofragments resulting from the two-frequency multiphoton dissociation of ${\mathrm{HD}}^{+}$ from initial bound level $v_i{=0,J}_i=0\mathrm{}$ induced by linearly polarized parallel laser fields of equal intensity of $1{\mathrm{T}\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ Both the laser frequencies ${\omega }_1$ and ${\omega }_2$ are below the dissociation threshold with ${\omega }_1<{\omega }_2.$ We have used the time-independent close-coupling method. Molecular rotation has been taken into account with $J=0\mathrm{}–9$ in each of the two electronic states GS and ES. The photon absorption channels ${(n}_1{,n}_2)$ with $n_1{,n}_2=0\mathrm{}–3$ have been included when $n_1$ and $n_2$ are the numbers of photons of frequencies ${\omega }_1$ and ${\omega }_2$ absorbed. We have neglected absorption channels when (net) four or more photons are involved. This necessitates the use of 120 channels. All radiative couplings including those due to the intrinsic dipole moments of ${\mathrm{HD}}^{+}$ have been considered in a truncated length gauge form of interaction. In the presence of intermediate photon vibrational resonance with the GS (1,0) channel, dissociation takes place mainly through the ES (1,1) channel. But the channel ES (1,2) dominates for frequency ${\omega }_2$ not satisfying the resonance condition. For linear polarization, preferential photofragment ejection along the field polarization direction (i.e., $\theta =0\mathrm{}°$ or $180°)$ takes place. On resonance, the angular distribution shows prominent rings that are peaks on the photofragment distribution away from $\theta =0\mathrm{}°.$ We have presented the photofragment angular distributions of ${\mathrm{HD}}^{+}$ for different (open) photon channels within the framework of dressed state picture, vibrational trapping and the bond softening, adiabatic path, and the nonadiabatic transition mechanisms.

Above-threshold ionization of Kr atoms in an infinite sequence of circularly polarized few-cycle pulses is studied in the frame of a nonperturbative scattering theory. The photoelectron angular distributions (PADs) in various pulse lengths are obtained. Our study shows that the PADs in circularly polarized few-cycle pulses are not isotropic and the photoelectron rates in a pair of two opposite directions are not always equal to each other. This inversion asymmetry is due to a multichannel transition where the different channels are characterized by different combinations of absorbed-photon numbers in the ionization process. The PADs are symmetric about an axis related to the carrier-envelope (CE) phase. Our study also shows that the position of the maximal emission is related to the CE phase and the pulse length of the short pulses, which makes it possible to control the motion of the ejected photoelectrons by varying the pulses.

Stochastic (Anderson) localization is the spatial localization of the wave function of a quantum particle due to a random spatial potential. We show that a corresponding phenomenon can stabilize dissipative spatial solitons in nonlinear optical resonators: spatial solitons in resonators with randomly distorted mirrors are more stable than those in perfect mirror resonators. We demonstrate the phenomenon numerically, by investigating solitons in lasers with a saturable absorber, and analytically, by deriving and analyzing the coupled equations of spatially coherent and incoherent field components.

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump $\leftrightarrow$ pump, Stokes $\leftrightarrow$ signal, and Raman coherence $\leftrightarrow$ idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

The nonlinear photon-photon interaction mediated by a single two-level atom is studied theoretically based on a one-dimensional model of the field-atom interaction. This model allows us to determine the effects of an atomic nonlinearity on the spatiotemporal coherence of a two-photon state. Specifically, the complete two-photon output wave function can be obtained for any two-photon input wave function. It is shown that the quantum interference between the components of the output state associated with different interaction processes causes bunching and antibunching in the two-photon statistics. This theory may be useful for various applications in photon manipulation, e.g., quantum information processing using photonic qubits, quantum nondemolition measurements, and the generation of entangled photons.

We implement experimentally methods to generate photon-number–path and polarization entangled photon pairs using “beamlike” type-II spontaneous parametric down-conversion, in which the signal-idler photon pairs are emitted as two separate circular beams with small emission angles rather than as two diverging cones.