The leading correction from interactions to the transition temperature $T_c$ for Bose-Einstein condensation can be obtained from a nonperturbative calculation in the critical $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ scalar field theory in three dimensions with $N=2.\mathrm{}$ We show that the linear $\delta$ expansion can be applied to this problem in such a way that in the large-N limit it converges to the exact analytic result. If the principle of minimal sensitivity is used to optimize the convergence rate, the errors seem to decrease exponentially with the order in the $\delta$ expansion. For $N=2,$ we calculate the shift in $T_c$ to fourth order in $\delta .$ The results are consistent with slow convergence to the results of recent lattice Monte Carlo calculations.

The stability regimes and nonlinear dynamics of bright solitons created in a harmonic potential which is transversely attractive and longitudinally expulsive are presented. This choice of potential is motivated by the recent creation of a matter-wave bright soliton from an attractive Bose-Einstein condensate [L. Khaykovich et al., Science 296, 1290 (2002)]. The critical branches for collapse due to the three-dimensional character of the gas and explosion caused by the expulsive potential are derived based on variational studies. Weak excitations of the soliton due to sudden changes in the trapping potential and/or or the scattering length are shown to damp exponentially by the emission of a small fraction of particles. It is shown that higher-order solitons can also be created in present experiments by an abrupt change of a factor of 4 in the scattering length. Finally, it is demonstrated that quantum evaporation occurs by nonlinear tunneling of particles out of the soliton, leading eventually to its explosion.

Noisy pattern precursors have been observed experimentally in a Kerr-like slice subjected to one-dimensional (1D) optical feedback. These noise-induced patterns appear below threshold and anticipate the characteristics of the incoming patterns. In our 1D system, precursors are rolls with an undefined spatial phase which wanders erratically and locks spatially when crossing the threshold. Phase localization allows for a criterion to define the threshold in presence of noise. The experimental observations are well reproduced by the standard model of the Kerr slice medium with optical feedback when Langevin noise terms are included.

The deeply saturated operation of a double-pass Ne-like zinc soft x-ray laser emitting at a wavelength of 21.2 mm is reported, along with results of a study and optimization of its beam parameters and coherence. The active medium is a 3-cm-long plasma column produced by a separately delivered prepulse and a main pulse with a duration of ∼450 ps, supplied by a 1.315-μm laser. To generate plasma with reduced lateral density gradients, the ∼130-μm-wide main pulse focus, producing a pump irradiance of $\sim 2.8\times {10}^{13}{\mathrm{W}\mathrm{}\mathrm{cm}}^{-2},$ is placed on top of a much broader prepulse focus. The x-ray laser emission emerges as a narrowly collimated beam possessing high spatial quality and coherence. The dependence of the output on the prepulse conditions, the pump power, and the setup of the half-cavity mirror are investigated and discussed. The study of the beam transverse coherence demonstrates its strong dependence on pump energy. The large gain-length product attained through half-cavity operation allows for an efficient extraction of the energy stored in the active medium. With a small-signal gain of 7(±0.5) ${\mathrm{cm}}^{\mathrm{-}1}$, the double-pass beam is deeply saturated and provides ∼4 mJ of energy in one pulse, corresponding to peak power in excess of 40 MW, and implies that this system is the most powerful x-ray laser yet demonstrated. The inherent engineering conception of the device is compatible with a repetition rate in a hertz domain.

We study the creation of stationary cold molecules by rapid deceleration of supersonically cooled molecules in a high-intensity pulsed optical lattice. Using the heavy molecule ${\mathrm{I}}_2$ as an example we predict the evolution of the velocity distribution function of the ensemble during the deceleration period, and show that stationary cold molecules with temperatures below 1 K and densities of approximately ${10}^{12}{\mathrm{cm}}^{-3}$ can be produced over length scales of hundreds of micrometers on submicrosecond time scales.

The quantization of the scalar and electromagnetic fields in the presence of a parabolic mirror is further developed in the context of a geometric optics approximation. We extend results in a previous paper to more general geometries, and also correct an error in one section of that paper. We calculate the mean-squared scalar and electric fields near the focal line of a parabolic cylindrical mirror. These quantities are found to grow as inverse powers of the distance from the focus. We give a combination of analytic and numerical results for the mean-squared fields. In particular, we find that the mean-squared electric field can be either negative or positive, depending upon the choice of parameters. The case of a negative mean-squared electric field corresponds to a repulsive van der Waals force on an atom near the focus, and to a region of negative energy density. Similarly, a positive value corresponds to an attractive force and a possibility of atom trapping in the vicinity of the focus.

We create pairs of nondegenerate time-bin entangled photons at telecom wavelengths with ultrashort pump pulses. Entanglement is shown by performing Bell kind tests of the Franson type with visibilities of up to 91%. As time-bin entanglement can easily be protected from decoherence as encountered in optical fibers, this experiment opens the road for complex quantum communication protocols over long distances. We also investigate the creation of more than one photon pair in a laser pulse and present a simple tool to quantify the probability of such events to happen.

We investigate the dynamics of a cold trapped ion coupled to the quantized field inside a high-finesse cavity, considering exact resonance between the ionic internal levels and the field (carrier transition). We derive an intensity-dependent Hamiltonian in which terms proportional to the square of the Lamb-Dicke parameter $\left(\eta \right)$ are retained. We show that different nonclassical effects arise in the dynamics of the ionic population inversion, depending on the initial states of the vibrational motion and field and on the values of $\eta .$

We introduce a general method for the experimental detection of entanglement by performing only few local measurements, assuming some prior knowledge of the density matrix. The idea is based on the minimal decomposition of witness operators into a pseudomixture of local operators. We discuss an experimentally relevant case of two qubits, and show an example how bound entanglement can be detected with few local measurements.

In this paper we propose and analyze a feasible scheme where the detection of a single scattered photon from two trapped atoms or ions performs a conditional unitary operation on two qubits. As examples we consider the preparation of all four Bell’s states, the reverse operation that is a Bell’s measurement, and a controlled-NOT (CNOT) gate. We study the effect of atomic motion and multiple scattering by evaluating Bell’s inequalities violations and by calculating the CNOT gate fidelity.

Recently Ziman et al. [Phys. Rev. A 65, 042105 (2002)] have introduced a concept of a universal quantum homogenizer which is a quantum machine that takes as input a given (system) qubit initially in an arbitrary state $\rho$ and a set of N reservoir qubits initially prepared in the state $\xi .$ The homogenizer realizes, in the limit sense, the transformation such that at the output each qubit is in an arbitrarily small neighborhood of the state $\xi$ irrespective of the initial states of the system and the reservoir qubits. In this paper we generalize the concept of quantum homogenization for qudits, that is, for d-dimensional quantum systems. We prove that the partial-swap operation induces a contractive map with the fixed point which is the original state of the reservoir. We propose an optical realization of the quantum homogenization for Gaussian states. We prove that an incoming state of a photon field is homogenized in an array of beam splitters. Using Simon’s criterion, we study entanglement between outgoing beams from beam splitters. We derive an inseparability condition for a pair of output beams as a function of the degree of squeezing in input beams.

We present an approach for the calculation of relativistic $m{\alpha }^6$ corrections to the lithium ground-state hyperfine splitting. It is based on the effective Hamiltonian derived from relativistic quantum electrodynamic theory. This approach with the help of appropriate nonrelativistic correlated basis sets has the potential to be more accurate than currently available relativistic computational methods such as the relativistic many-body perturbation theory, configuration interaction, or multiconfiguration Dirac-Fock method.

The role of local fields in quantum electrodynamics of isolated quantum dot (QD) has been analyzed. The system is modeled as a strongly confined in space two-level quantum oscillator illuminated by quantum light. Relation between local and acting fields in QD has been derived in the dipole approximation from the integral Maxwell equations for electromagnetic field operators. A formalism of the electromagnetic field quantization in electrically small scatterers has been developed. As a result, Hamiltonian of the system has been formulated in terms of the acting field with a separate term responsible for the effect of depolarization. Schrödinger equation with that Hamiltonian has been solved in linear approximation. Interaction of QD with different quantum states of light, such as Fock states, coherent states, Fock qubits, entangled states, has been analyzed. It has been shown that the local-fields induce a fine structure of the QD absorption (emission) spectrum: instead of a single line with the frequency corresponding to the exciton transition, a doublet appears with one component shifted to the blue (red). The value of the shift depends only on the geometrical and electronic properties of QD while the intensities of components are completely determined by the quantum light statistics. It has been demonstrated that in the limiting cases of classical light and single-photon state the doublet is reduced to a singlet shifted in the former case and unshifted in the latter one. A physical interpretation of the predicted effect has been proposed. Possible ways of experimental observation of the effect has been discussed together with the potentiality of its utilization in the quantum information processing.

We examine a fast decay process that arises in the transition period between the Gaussian and exponential decay processes in quantum decay systems. It is usually expected that the decay is decelerated by a confinement potential barrier. However, we find a case where the decay in the transition period is accelerated by tunneling through a confinement potential barrier. We show that the acceleration gives rise to an appreciable effect on the time evolution of the nonescape probability of the decay system.

High-order harmonic generation has been observed experimentally from ${\mathrm{O}}_2$ molecules at the saturation ionization intensity. The harmonic cutoff extends far beyond the cutoff of Xe despite both have nearly equal ionization potentials. In contrast, the harmonic spectra for ${\mathrm{N}}_2$ and Ar, which have almost the same ionization potentials, are essentially close to each other. We show the extension of harmonic cutoff in ${\mathrm{O}}_2$ is a consequence of ionization suppression. Using a simple modified tunneling ionization model for molecules, we predict both the harmonic cutoff extension and the ionization suppression semiquantitatively.

Two-dimensional central potentials leading to the identical classical and quantum motions are derived and their properties are discussed. Some of zero-energy states in the potentials are shown to cancel the quantum correction $Q=(-{ħ}^2/2m)\Delta R/R$ to the classical Hamilton-Jacobi equation. The Bohr’s correspondence principle is thus fulfilled exactly without taking the limits of high quantum numbers, of $\overrightarrow{ħ}0,$ or of the like. In this exact limit of $Q=0,$ classical trajectories are found and classified. Interestingly, many of them are represented by closed curves. Applications of the found potentials in many areas of physics are briefly commented.

Quantum theory violates Bell’s inequality, but not to the maximum extent that is logically possible. We derive inequalities (generalizations of Cirel’son’s inequality) that quantify the upper bound of the violation, both for the standard formalism and the formalism of generalized observables (POVMs). These inequalities are quantum analogues of Bell inequalities, and they can be used to test the quantum version of locality. We discuss the nature of this kind of locality. We also go into the relation of our results to an argument by Popescu and Rohrlich [Found Phys. 24, 379 (1994)] that there is no general connection between the existence of Cirel’son’s bound and locality.

The Dirac equation is written for the special case of a spinor in a relativistic potential with the even and odd components related by a constraint, and solved exactly with the even component chosen to be the Woods-Saxon potential. The corresponding radial wave functions for the two-component spinor are obtained in terms of the hypergeometric function, and the energy spectrum of the bound states is obtained as a solution to a given equation with boundary constraints in which the nonrelativistic limit reproduces the usual Woods-Saxon potential.

In work by Howell and Yeazell [Phys. Rev. A 62, 012102 (2000)], a proposal is made to generate entangled macroscopically distinguishable states of two spatially separated traveling optical modes. After considering a preparation with nonperfect photodetection, we discuss a random mode of entanglement purification without manual intervention using a number of preparations transmitted over a lossy optical transmission line. An efficiency greater than 1/2 of the purification scheme is required to increase entanglement at all. Furthermore, we study a nondemolition configuration to measure the purity of the state as contrast of interference fringes in a double-slit setup. As a consequence of the relationship between purity and entanglement of formation resulting from treating the entangled coherent states as a state of a bipartite quantum system, the contrast of interference fringes provides a direct means to measure entanglement.

We experimentally investigate time-bin qubits for distributed quantum communication. The robustness of maximal and nonmaximal time-bin entangled qubits (photons) over distances up to 11 km is shown. The entanglement is set by controllable parameters and in all cases is found to be robust, in that the qubits maintain their degree of entanglement after transmission along telecommunication fiber.