In order to demonstrate nontrivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 controlled-NOT (CNOT) gates and 15 elementary one-qubit gates. Moreover, if the desired two-qubit gate corresponds to a purely real unitary transformation, we provide a construction that requries at most 2 CNOT and 12 one-qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, $y$-rotation, $z$-rotation, and phase gates.

We show that the security proof of the Bennett 1992 protocol over loss-free channel given by Tamaki, Koashi, and Imoto [Phys. Rev. Lett. 90, 167904 (2003)] can be adapted to accommodate loss. We assumed that Bob’s detectors discriminate between single-photon states on one hand and vacuum state or multiphoton states on the other hand.

Neutral fractions are measured for $\left(0.4–0.8\right)\text{MeV}{\mathrm{H}}^{+}$ ion beams transmitted through aluminum epitaxial foils under the (100) planar channeling condition. Two foils are prepared: the first $\left(\Theta =90°\right)$ is almost perpendicular to the direction of the beam and the second $\left(\Theta =30°\right)$ is inclined at $60°$ compared with the first. The measured neutral fractions, which are in the ${10}^{-3}$ range, exhibit a minimum at the (100) channeling direction, however, the channeling effect is enhanced for the foil with $\Theta =30°$. The fraction is calculated for the two foils from the equilibrium fraction and the charge exchange between the ions and the surface atoms in a vacuum. Both the equilibrium fraction and the charge exchange depend on the exit positions of ions from the midplane of the channel. The measured energy dependence of the ratio (channeling∕random) of the fractions is reproduced by calculation. Thus the results indicate that the transmitted charge-state distributions are modified by the charge exchange after the emergence of ions in a vacuum.

The infinite summations over the complete set of unperturbed atomic states appearing in the $N$th-order perturbation theory for multiphoton ionization are performed using the Dalgarno-Lewis method. The relevant transition matrix elements are written in a closed integral form exhibiting all the analytic properties of the amplitude as a function of incident photon energy. The cross sections for two- and three-photon ionization for atomic hydrogen are calculated for both linearly and circularly polarized light with a wide range of photon energy spectrum including the near resonance, and numerical comparison is made with the values obtained by different methods.

In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose-Einstein condensate selectively loaded into every third site of a one-dimensional optical lattice. The motivation of this work is the recent experimental realization of this system. Patterned loading methods may be useful for quantum computing with trapped atoms. This system also serves to illustrate many basic issues in nonequilibrium quantum-field theory pertaining to the dynamics of quantum correlations and fluctuations which goes beyond the capability of a mean-field theory. By numerically evolving in time the initial-state configuration using the Bose-Hubbard Hamiltonian an exact quantum solution is available for this system in the case of few atoms and wells. One can also use it to test various approximate methods. Under the 2PI CTP scheme with this initial configuration, three different approximations are considered: (a) the Hartree-Fock-Bogoliubov (HFB) approximation, (b) the next-to-leading-order $1∕\mathcal{N}$ expansion of the 2PI effective action up to second order in the interaction strength, and (c) a second-order perturbative expansion in the interaction strength. We present detailed comparisons between these approximations and determine their range of validity by contrasting them with the exact many-body solution for a moderate number of atoms and wells. As a general feature we observe that because the second-order 2PI approximations include multiparticle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution, which a mean-field collisionless approach fails to produce. While the second-order approximations show a clear improvement over the HFB approximation, our numerical results show that they fail at late times, when interaction effects are significant.

We present an experimental and theoretical study of the coherent Rayleigh-Brillouin scattering in gases in the kinetic regime. Gas density perturbation waves were generated by two crossing pump laser beams through optical dipole forces. A probe laser beam was then coherently scattered from the perturbation waves. The line shape of the scattered light was modeled using kinetic theory. The model takes into account the internal energy modes of the gas particles and is applicable to both molecular and atomic gases. We discuss the implication of coherent Rayleigh-Brillouin scattering on kinetic theory and photon matter interaction.

We present the coherent control of the temporal shape of laser pulses obtained by exploiting the propagation dynamics of electromagnetically induced transparency. Temporal compression, as a special case of pulse tailoring, is discussed. We envisage applications in nonlinear optics processes and control of pulse shapes in the vacuum ultraviolet spectral region.

The importance of feedback control is being increasingly appreciated in quantum physics and applications. This paper describes the use of optimal control methods in the design of quantum feedback control systems, and in particular the paper formulates and solves a risk-sensitive optimal control problem. The resulting risk-sensitive optimal control is given in terms of an unnormalized conditional state, whose dynamics include the cost function used to specify the performance objective. The risk-sensitive conditional dynamic equation describes the evolution of our knowledge of the quantum system tempered by our purpose for the controlled quantum system. Robustness properties of risk-sensitive controllers are discussed and an example is provided.

We consider a generalization of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by $N$- or $d$-dimensional systems (qudits). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf’s formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of qudit generalizations of the Ekert’s protocol for qubits.

Stripping and excitation cross sections are calculated, using a time-dependent discrete-variable approach, for collisions of protons with energies from $0.5\text{keV}$ to $2\text{MeV}$ with ${\text{He}}^{+}$ initially in the $1s$, $2s$, $2p$, $3s$, $3p$, and $3d$ states. This quantum-semiclassical approach takes trajectory curvature into account. The spatial and temporal convergence properties of the method are analyzed for the ground and higher states. The results are in good agreement with existing accurate calculations and experimental cross sections, available for $E_p⩾3.73\text{keV}$. Results are also obtained for lower-energy collisions where the cross sections are still significant but trajectory curvature is important.

We study solitons in the condensate trapped in a double-well potential with far-separated wells, when the $s$-wave scattering length has different signs in the two parts of the condensate. By employing the coupled-mode approximation it is shown that there are unusual stable bright solitons in the condensate, with the larger share of atoms being gathered in the repulsive part. Such unusual solitons derive their stability from the quantum tunneling and correspond to the strong coupling between the parts of the condensate. The ground state of the system, however, corresponds to weak coupling between the condensate parts, with the larger share of atoms being gathered in the attractive part of the condensate.

We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local-oscillator angle; for $n$-mode systems they depend on $n$ heterodyne mixing angles. The canonical formalism realizes nontrivial mixing of pairs of conjugate quadratures of the electromagnetic field in terms of homodyne variables for single-mode systems, and in terms of heterodyne variables for multimode systems. In the first instance the transformations yield nonquadratic model Hamiltonians of degenerate multiphoton processes and define a class of non-Gaussian, nonclassical multiphoton states that exhibit properties of coherence and squeezing. We show that such homodyne multiphoton squeezed states are generated by unitary operators with a nonlinear time evolution that realizes the homodyne mixing of a pair of conjugate quadratures. Tuning of the local-oscillator angle allows us to vary at will the statistical properties of such states. We discuss the relevance of the formalism for the study of degenerate (up-)down-conversion processes. In a companion paper [F. Dell’Anno, S. De Siena, and F. Illuminati, 69, 033813 (2004)], we provide the extension of the nonlinear canonical formalism to multimode systems, we introduce the associated heterodyne multiphoton squeezed states, and we discuss their possible experimental realization.

Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper [F. Dell’Anno, S. De Siena, and F. Illuminati, Phys. Rev. A 69, 033812 (2004)], we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of Hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing nondegenerate and degenerate multiphoton processes. We determine the coherent states associated with the canonical transformations, which generalize the nondegenerate two-photon squeezed states. Such heterodyne multiphoton squeezed states are defined as the simultaneous eigenstates of the transformed, coupled annihilation operators. They are generated by nonlinear unitary evolutions acting on two-mode squeezed states. They are non-Gaussian, highly nonclassical, entangled states. For a quadratic nonlinearity the heterodyne multiphoton squeezed states define two-mode cubic phase states. The statistical properties of these states can be widely adjusted by tuning the heterodyne mixing angles, the phases of the nonlinear couplings, as well as the strength of the nonlinearity. For quadratic nonlinearity, we study the higher-order contributions to the susceptibility in nonlinear media and we suggest possible experimental realizations of multiphoton conversion processes generating the cubic-phase heterodyne squeezed states.

Clauser-Horne-Shimony-Holt inequality for bipartite systems of four dimensions is studied in detail by employing the unbiased eight-port beam splitters measurements. The uniform formulas for the maximum and minimum values of this inequality for such measurements are obtained. Based on these formulas, we show that an optimal nonmaximally entangled state is about $6\%$ more resistant to noise than the maximally entangled one. We also give the optimal state and the optimal angles which are important for experimental realization.

We analyze the properties of the second-order correlation functions of the electromagnetic field in atom-cavity systems that approximate two-level systems. It is shown that a recently developed polariton formalism can be used to account for all the properties of the correlations, if the analysis is extended to include two manifolds—corresponding to the ground state and the states excited by a single photon—rather than just two levels.

Using photoelectron spectroscopy, we demonstrate how the self-assembling process of cluster formation in an adiabatic expansion leads to radial segregation and layering as well as to variable surface composition for binary Ar∕Xe clusters. The radial structuring can be qualitatively understood from the different interatomic bonding strengths of the two components.

We present efficient circuits that can be used for the phase-space tomography of quantum states. The circuits evaluate individual values or selected averages of the Wigner, Kirkwood, and Husimi distributions. These quantum gate arrays can be programmed by initializing appropriate computational states. The Husimi circuit relies on a subroutine that is also interesting in its own right: the efficient preparation of a coherent state, which is the ground state of the Harper Hamiltonian.

Results from measurements of absolute $K$-shell ionization cross sections and $L\alpha$ x-ray production cross sections of Ge by impact of electrons with kinetic energies ranging from the ionization threshold up to $40\text{keV}$ are presented. The cross sections were obtained by measuring $K\alpha$ and $L\alpha$ x-ray intensities emitted from ultrathin Ge films deposited onto self-supporting carbon backing films. Recorded x-ray intensities were converted to absolute cross sections by using estimated values of the sample thicknesses, the number of incident electrons, and the detector efficiency. Experimental data are compared with the results of widely used simple analytical formulas, with calculated cross sections obtained from the plane-wave and distorted-wave Born approximations and with experimental data from the literature.

We consider the problem of an atomic beam propagating quantum mechanically through an atom beam splitter. Casting the problem in an adiabatic representation (in the spirit of the Born-Oppenheimer approximation in molecular physics) sheds light on explicit effects due to nonadiabatic passage of the atoms through the splitter region. We are thus able to probe the fully three-dimensional structure of the beam splitter, gathering quantitative information about mode mixing, splitting ratios, and reflection and transmission probabilities.

We consider a rotating Bose-Einstein condensate confined in combined harmonic and quartic traps, following recent experiments [V. Bretin, S. Stock, Y. Seurin, and J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004)]. We investigate numerically the behavior of the wave function which solves the three-dimensional Gross Pitaevskii equation and analyze in detail the structure of vortices. For a quartic-plus-harmonic potential, as the angular velocity increases, the vortex lattice evolves into a vortex array with hole. The merging of vortices into the hole is highly three dimensional, starting from the top and bottom of the condensate to reach the center. We also investigate the case of a quartic-minus-harmonic potential, not covered by experiments or previous numerical works. For intermediate repulsive potentials, we show that the transition to a vortex array with hole takes place for lower angular velocities, when the lattice is made up of a small number of vortices. For the strong repulsive case, a transition from a giant vortex to a hole with a circle of vortices around is observed.