We show how to construct a multiqubit control gate on a quantum register of an arbitrary size N. This gate performs a single-qubit operation on a specific qubit conditioned by the state of other $N-1$ qubits. We provide an algorithm how to build up an array of networks consisting of single-qubit rotations and multiqubit control-NOT (CNOT) gates for the synthesis of an arbitrary entangled quantum state of N qubits. We illustrate the algorithm on a system of cold trapped ions. This example illuminates the efficiency of the direct implementation of the multiqubit CNOT gate compared to its decomposition into a network of two-qubit CNOT gates.

We present a realistic purification scheme for pure nonmaximally entangled states. In the scheme, two distant parties Alice and Bob first start with two shared but less entangled photon pairs to produce a conditional four-photon Greenberger-Horne-Zeilinger state, and then perform a $45°$ polarization measurement onto one of the two photons at each location such that the remaining two photons are projected onto a maximally entangled state.

We report an experimental demonstration of an anticorrelation effect in femtosecond-pulse pumped type-II spontaneous parametric down-conversion. Our experimental data, which is different from that of Atatüre et al. [Phys. Rev. Lett. 83, 1323 (2000)], confirmed the shallow symmetric “dip” that is predicted theoretically by Keller and Rubin [Phys. Rev. A 56, 1534 (1997)] and Grice and Walmsley [Phys. Rev. A 56, 1627 (1997)]. We show in this paper that the asymmetric dip observed in the literature is an artifact, which is caused by the asymmetric optical elements introduced into the beam path after the down-conversion process. The “partial distinguishability” theory suggested by Atatüre et al. is therefore incorrect.

Several proposals for a time-of-arrival distribution of ensembles of independent quantum particles subject to an external interaction potential are compared making use of the “crossing state” concept. It is shown that only one of them has the properties expected for a classical distribution in the classical limit. The comparison is illustrated numerically with a collision of a Gaussian wave packet with an opaque square barrier.

We extend the kinetic theory of the laser cooling of atoms to four multilevel atomic schemes: (3+5)-, (5+7)-, (7+9)-, and (9+11)-level atom. In all four atomic schemes the atoms are considered to be excited by two counterpropagating circularly polarized laser waves. A comparison of four multilevel atomic schemes shows that the even-order multiphoton processes are responsible for the narrow structures near zero velocity in the atomic coherences, atomic populations, dipole radiation forces, and the diffusion coefficients. The even-order multiphoton processes in a multilevel atom with a big number of magnetic sublevels are shown to produce the velocity structures, which are much narrower than that produced by the two-photon processes in a (3+5)-level atom. It is found that the multiphoton processes enhance the radiation force at low velocities and the friction produced by the force at a negative detuning. The even-order multiphoton processes caused by the laser waves are identified as the basic physical mechanism responsible for the sub-Doppler laser cooling of atoms. The temperature of laser-cooled atoms is derived for all four models and found to be lower for atomic schemes with a larger number of magnetic sublevels.

The dielectric formalism is used to set up an approximate description of a spatially homogeneous weakly interacting Bose gas in the collisionless regime, which is both conserving and gapless, and has coinciding poles of the single-particle Green’s function and the density autocorrelation function in the Bose-condensed regime. The approximation takes into account the direct and exchange interactions in a consistent way. The fulfillment of the generalized Ward identities related to the conservation of particle number and the breaking of the gauge symmetry is demonstrated. The dynamics at long wavelengths is considered in detail below and above the phase transition, numerically and in certain limits also in analytical approximations. The explicit forms of the density autocorrelation function and the Green’s function are exhibited and discussed.

A theoretical study of the radiative decay of low-lying doubly excited ${}^1{P}^o$ states of Helium in the energy region below the ${\mathrm{He}}^{+}\mathrm{}(N=2\mathrm{})\mathrm{}$ threshold is presented. We calculated the oscillator strength from the ground state, the Auger and radiative decay rates, and the natural widths of these states. These rates are used to obtain the photon emission and metastable atom yield spectra to compare with experimental measurements, including those from Odling-Smee et al. [Phys. Rev. Lett. 84, 2598 (2000)] and Rubensson et al. [Phys. Rev. Lett. 83, 947 (1999)]. We showed that the lifetimes of the long-lived doubly excited states are determined by the radiative rates.

We present the results of generalized measurements of optical polarization designed to provide one of three or four distinct outcomes. This has allowed us to discriminate between nonorthogonal polarization states with an error probability that is close to the minimum allowed by quantum theory. Employing these optimal detection strategies on sets of three (trine) or four (tetrad) equiprobable symmetric nonorthogonal polarization states, we obtain a mutual information that exceeds the maximum value attainable using conventional (von Neumann) polarization measurements.

The resolution in space of processes involving high-energy photons incident on atoms or bare atomic nuclei is investigated. A simple analysis, based on momentum transfer, gives first indications of the length scale being defined by the Compton wavelength of the electron for both the photoeffect and electron-positron pair creation with the electron bound to the atomic nucleus. Since the simple method of converting a momentum transfer q to a distance of $ħ/q$ has potential pitfalls, we continue with a detailed wave-packet study. This study, which is undertaken for the case of the photoeffect, involves the incidence of a photon localized in space and time on a hydrogenlike atom. The wave-packet approach confirms the Compton wavelength, and not the extent of the atomic state, to be the decisive measure for photon energies in excess of the electron rest energy ${\mathrm{mc}}^2.$ In addition, it provides a direct and detailed picture of the impact-parameter dependence of the process. As an introduction to the wave-packet study, we compare calculations based on a plane-wave representation of the unbound lepton to lowest-order perturbative calculations.

For He-like uranium, a state-selective electron-capture study was carried out for relativistic collisions with gaseous targets. In the experiment, the projectile x-ray emission produced by electron capture in collisions of 223-MeV/u ${\mathrm{U}}^{90+}$ ions on ${\mathrm{N}}_2,$ Ar, Kr, and Xe targets was measured in coincidence with ${\mathrm{U}}^{89+}$ projectiles. Due to the large fine-structure splitting in heavy ions, the well-resolved Balmer transitions observed were used to deduce subshell sensitive cross sections for electron capture. For this purpose, a theoretical spectrum analysis and simulation was performed by taking into account electron cascades from states up to $n=40.\mathrm{}$ The state-selective data are compared with theoretical calculations as a function of target atomic number. An overall agreement is found between the experimental data and the theoretical approaches applied except for the j-sensitive part.

We have obtained and characterized a cold atomic beam produced by a simple conical atom funnel, which consists of a conical hollow mirror (axicon) with a small hole at the apex and a single incident laser beam. Atoms trapped in the axicon mirror are ejected by the radiation-pressure imbalance along the extraction column. The atomic beam has a longitudinal velocity in the range of 4 to 6 m/s, a divergence of 150 mrad, and a maximum instantaneous flux of $2.2\times {10}^{10}\hspace{0.5em}\mathrm{atoms}/\mathrm{s}$ in a pulsed operation. The experimental results are in quantitative agreement with the numerical simulations. A continuous atomic beam is also possible with an apex hole smaller than the trapped atomic cloud.

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric-field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented that appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Padé resummation method, with an additional improvement due to utilization of the leading renormalon poles, and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Padé approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.

We calculate the contribution to the damping of condensate collective excitations at finite temperatures arising from the lack of equilibrium between the condensate and thermal atoms. Limiting our attention to collective modes that mainly involve the motion of the condensate, we treat the noncondensate as static as a first approximation. We derive a set of generalized Bogoliubov equations for finite temperatures that contain an explicit damping term due to the collisional exchange of atoms between the two components. We have numerically solved these Bogoliubov equations to obtain the temperature dependence of the damping of the condensate modes in a harmonic trap. These results agree quite well with our recent work based on the Thomas-Fermi approximation but predict a much larger damping near the transition temperature.

We present a method of finding approximate analytical solutions for the spectra and eigenvectors of collective modes in a two-dimensional system of interacting bosons subjected to a linear external potential or the potential of a special form $u(x,y)=\mu -u{\cosh }^{2}x/l,$ where μ is the chemical potential. The eigenvalue problem is solved analytically for an artificial model allowing the unbounded density of the particles. The spectra of collective modes are calculated numerically for the stripe, the rare density valley, and the edge geometry and compared with the analytical results. It is shown that the energies of the modes localized at the rare density region and at the edge are well approximated by the analytical expressions. We discuss Bose-Einstein condensation (BEC) in the systems under investigations at $T\ne 0$ and find that in case of a finite number of the particles the regime of BEC can be realized, whereas the condensate disappears in the thermodynamic limit.

We consider a gas of $N(<~15)$ Bose particles with hard-core repulsion, contained in a quasi-two-dimensional harmonic trap and subjected to an overall angular velocity $\Omega$ about the z axis. Exact diagonalization of the $n\times n$ many-body Hamiltonian matrix in given subspaces of the total (quantized) angular momentum $L_z,$ with $n\sim {10}^5$ (e.g., for $L_z=N=15,\hspace{0.5em}n=240\mathrm{}782)$ was carried out using Davidson’s algorithm. The many-body variational ground-state wave function, as also the corresponding energy and the reduced one-particle density-matrix $\rho (\mathbf{r},{\mathbf{r}}^{\prime })={\sum }_{\mu }{\lambda }_{\mu }{\chi }_{\mu }^{*}\left(\mathbf{r}\right){\chi }_{\mu }\left({\mathbf{r}}^{\prime }\right)$ were determined. With the usual identification of $\Omega$ as the Lagrange multiplier associated with $L_z$ for a rotating system, the $L_z-\Omega$ phase diagram (or the stability line) was determined that gave a number of critical angular velocities ${\Omega }_{\mathrm{ci}},\hspace{0.5em}i=1,2,3,\dots ,$ at which the ground-state angular momentum and the associated condensate fraction, given by the largest eigenvalue of the reduced one-particle density matrix, undergo abrupt jumps. For a given N, a number of (total) angular momentum states were found to be stable at successively higher critical angular velocities ${\Omega }_{\mathrm{ci}},\hspace{0.5em}i=1,2,3,\dots .$ All the states in the regime $N>\mathrm{}{L}_z>0\mathrm{}$ are metastable. For $L_z>N,$ the $L_z$ values for the stable ground states generally increased with increasing critical angular velocities ${\Omega }_{\mathrm{ci}},$ and the condensate was strongly depleted. The critical ${\Omega }_{\mathrm{ci}}$ values, however, decreased with increasing interaction strength as well as the particle number, and were systematically greater than the nonvariational yrast-state values for the $L_z=N$ single vortex state. We have also observed that the condensate fraction for the single vortex state (as also for the higher vortex states) did not change significantly even as the two-body interaction strength was varied over several $\left(\sim 4\right)$ orders of magnitude in the moderately to the weakly interacting regime.

The study of nonlinear dynamical systems is a subject of much interest, one application being in secure communication systems realized through the synchronization of chaotic dynamical systems. In this paper optical coupling is used to effect synchronization between two diode lasers in a master-slave configuration, and we study the effect of frequency detuning between the master and slave lasers on the character of the observed synchronization. Experimental conditions are found under which the synchronization plot (formed by plotting the output power of the slave laser against that of the master at each instant in time) makes a transition from a positive gradient to a negative gradient. The appearance of such a negative gradient is a new phenomenon, to our knowledge, which we term “inverse synchronization.” A rate-equation model is proposed which accounts for light injection into the slave laser, and which agrees with the experimental results. Using this model, we etablish that inverse synchronization is caused by nonresonant coupling between the master and slave lasers.

The analysis of the model quantum clocks proposed by Aharonov et al. [Phys. Rev. A 57, 4130 (1998); e-print quant-ph/9709031] requires considering evanescent components in the transient regime, previously not examined, and consideration of several aspects of the asymptotic regime. We also clarify the meaning of the operational time of arrival distribution that had been investigated. The accuracy limitation due to the back reaction of the clock is not affected.

Unknown quantum pure states of an S-level particle can be transferred onto a group of remote two-level particles with the aid of two-level Einstein-Podolsky-Rosen states. We present a scheme for such kind of teleportation. The unitary transformation to more than two particles, which is needed in the scheme, is written in the product form of two-body unitary transformations.