We present measurements of electron-impact excitation cross sections into levels of the $4p^{5}5p$ configuration from the $J=0$ and $J=2$ metastable levels of krypton. Metastable-atom targets were generated using two different sources, a hollow-cathode discharge and via charge-exchange collisions between a fast ${\mathrm{Kr}}^{+}$ beam and Cs atoms. The metastable atoms are excited to $4p^{5}5p$ levels by a monoenergetic electron beam and the fluorescence from the levels are used to determine the excitation cross sections. Laser quenching of the hollow-cathode target is used to separate the signal contributions from excitation of the two metastable levels. Like excitation from the metastable levels of Ar, cross sections for dipole-allowed excitations are generally larger than ones for dipole-forbidden excitations. Krypton differs from Ar and Ne, however, in having a larger spin-orbit coupling for the $4p^5$ core so that the energy levels of each excited configuration segregate into two tiers based on the value of the core angular momentum. Cross sections for dipole-allowed excitation with a change in the core angular momentum are not only much smaller than their core-preserving counterparts, but also have different energy dependence. The measured cross sections are compared with recent theoretical calculations and with previous experimental work.

State selective $nl$-electron capture cross sections are presented for highly charged ions with $Z=6–10$ colliding with atoms and molecules. The energy range investigated was from $1\mathrm{eV}∕\mathrm{amu}(v=0.006\mathrm{a.u.})\text{to}100\mathrm{keV}∕\mathrm{amu}(v=2.0\mathrm{a.u.})$. The energy dependence of the $l$-level populations is investigated. The $K$ shell x-ray emission cross sections are determined by using the calculated state-selective electron capture results as input and then applying hydrogenic branching and cascading values for the photon emission. A major shift in the line emission from being almost solely Lyman-$\alpha$ transitions at the highest collisions energies to strong high-$n$ to $1s$ transitions at the lowest energies is observed. The calculated cross sections are in reasonable accord with measurements made by Greenwood et al. [Phys. Rev. A 63, 062707 (2001)], using ${\mathrm{O}}^{8+}$ and ${\mathrm{Ne}}^{10+}$ on various targets at $3\mathrm{keV}∕\mathrm{amu}$. The calculations are also in accord with x-ray emission cross section data obtained on the EBIT machine at Lawrence Livermore National Laboratory (LLNL) where ${\mathrm{O}}^{8+}$ and ${\mathrm{Ne}}^{10+}$ high resolution measurements were made at a temperature of $10\mathrm{eV}∕\mathrm{amu}$ for a series of targets with varying ionization potentials. The ${\mathrm{Ne}}^{10+}$ data clearly shows the contribution from multiple capture followed by Auger autoionization in the line emission spectra. Our calculated line emission cross sections are used to provide an ab initio determination of the soft x-ray spectrum of comet C/Linear 1999 S4 that was observed on the Chandra X-ray Observatory. The calculations show that the spectrum is due to the charge exchange of the neutral gases in the comet’s coma with the ions of the slow solar wind.

We have performed a detailed calculation of the double-differential angular–kinetic-energy distribution of photofragments in above threshold dissociation (ATD) of $\mathrm{D}_2{}^{+}$ from initial vibrational-rotational levels $v_i=4,5$ and $J_i=0,1$ in an intense linearly polarized laser field of wavelength $400\mathrm{nm}$ and intensity $3\times {10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$. The calculation used a time-independent close-coupling (CC) formalism with eight (ten) electronic states included in the basis-set expansion of the molecular wave function. The molecular electronic states included, apart from the two lowest $1s{\sigma }_g$ and $2p{\sigma }_u$ states, were $2p\pi _u{}^{\pm }$, $2s{\sigma }_g$, $3p{\sigma }_u$, $3d{\sigma }_g$, $3d\pi _g{}^{\pm }$, and $4f{\sigma }_u$. All the higher electronic states dissociate to the atomic state $\mathrm{D}\left(2\ell \right)$. A sufficient number of photon absorption channels, $n=0–7$, and molecular rotational quantum numbers $J=0–11$ were taken into account to ensure the convergence of the multiphoton ATD probability. Altogether 198 coupled channels had to be considered in the calculation. The calculations reveal signatures of significant ejection of the photodissociation fragments away from the laser polarization direction due to the inclusion of the higher excited electronic states. The ratio of the photofragments perpendicular to and along the polarization axis shows good quantitative agreement with the experimental result. The angular distributions show considerable structures depending on the relative kinetic energies of the photofragments, and the fragments with different kinetic energies show peaks at different dissociation angles.

We study Bragg scattering at one-dimensional atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated inside a laser-driven cavity. The atoms arrange themselves into an array of lens-shaped layers located at the antinodes of the standing wave. Light incident on this array at a well-defined angle is partially Bragg reflected. We measure reflectivities as high as $30\%$. In contrast to a previous experiment devoted to the thin grating limit [S. Slama et al., Phys. Rev. Lett. 94, 193901 (2005)] we now investigate the thick grating limit characterized by multiple reflections of the light beam between the atomic layers. In principle, multiple reflections give rise to a photonic stop band, which manifests itself in the Bragg diffraction spectra as asymmetries and minima due to destructive interference between different reflection paths. We show that close to resonance however disorder favors diffuse scattering, hinders coherent multiple scattering and impedes the characteristic suppression of spontaneous emission inside a photonic band gap.

We investigate within a self-consistent theory the molecular instabilities arising in the normal state of a homogeneous degenerate Fermi gas, covering the whole Bose-Einstein condensate (BEC) to BCS crossover. These are the standard instability for molecular formation, the BCS instability which corresponds to the formation of Cooper pairs, and the related Bose-Einstein instability. These instabilities manifest themselves in the properties of the particle-particle vertex, which we calculate in a ladder approximation. To find the critical temperatures corresponding to these various instabilities, we handle the properties of the interacting Fermi gas on the same footing as the instabilities by making use of the same vertex. This approximate treatment is shown to be quite satisfactory in a number of limiting situations where it agrees with known exact results. The results for the BCS critical temperature and for the BE condensation are found to be in fair agreement with earlier results. The threshold for formation of molecules at rest undergoes a sizable shift toward the BEC side, due to quantum effects arising from the presence of the degenerate Fermi gas. This should make its experimental observation fairly easy. This shift remains important at least up to temperatures comparable to the Fermi energy of the gas.

The mean-field dynamics of a Bose-Einstein condensate is studied in the presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show that the method of complex scaling can be used to obtain a quantitative description of this decay process. A real-time propagation approach that is applied to the complex-scaled Gross-Pitaevskii equation allows us to calculate the chemical potentials and lifetimes of the metastably trapped Bose-Einstein condensate. The method is applied to a one-dimensional harmonic confinement potential combined with a Gaussian envelope, for which we compute the lowest symmetric and antisymmetric quasibound states of the condensate. A comparison with alternative approaches using absorbing boundary conditions as well as complex absorbing potentials shows good agreement.

We report the observation of the cosine modulation in the coincidence rates from a Hong-Ou-Mandel (HOM) interferometer. Spatial interference fringes are seen by minute rotations of one mirror about the vertical axis, while the beam splitter is fixed in the center position. The results show that the maximum visibility of the fringe is 0.81, and the photon pairs separated by less than $1.52\mathrm{mm}$ in the source plane are measured to be indistinguishable. It turns out that it is possible to invert the HOM dips to peaks by the rotation of the mirror.

We present the physical principles of a quantum key distribution system that opens the possibility of parallel quantum key distribution and, therefore, of a substantial improvement in the bit rate of such systems. Quantum mechanics allows for multiple measurements at different frequencies and thus we exploit this concept by extending the concept of frequency coding to the case where more than one radio-frequency subcarrier is used for independently encoding the bits onto an optical carrier. Taking advantage of subcarrier multiplexing techniques we demonstrate that the bit rate can be greatly improved as parallel key distribution is enabled.

Femtosecond dynamics are observed by resonant x-ray Raman scattering (RXS) after excitation along the dissociative $\mathrm{Cl}1s\to 6{\sigma }^{*}$ resonance of gas-phase $\mathrm{HCl}$. The short core-hole lifetime results in a complete breakdown of the common nondispersive behavior of soft-x-ray transitions between parallel potentials. We evidence a general phenomenon of RXS in the hard-x-ray region: a complete quenching of vibrational broadening. This opens up a unique opportunity for superhigh resolution x-ray spectroscopy beyond vibrational and lifetime limitations.

We have measured the absolute photoionization cross section of the ${\mathrm{Fe}}^{4+}$ ion between 59 and $140\mathrm{eV}$ photon energy, including the region of the $3p\to 3d$ excitations. To interpret the data we have performed calculations using a code developed for the determination of the spectral opacity of hot plasmas. We have also compared our measurements with the results of several $R$-matrix calculations. In short, both theoretical approaches describe qualitatively the results of the experiment in the $3p\text{−}3d$ excitation region.

We consider a one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in experiments with ultracold boson and fermion isotopes in optical lattices. We use the Bethe-ansatz technique to find the ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We prove that the mixture is always stable against demixing. Combining exact solution with the local density approximation, we calculate density profiles and collective oscillation modes in a harmonic trap. In the strongly interating regime, we use exact wave functions to calculate correlation functions for bosons and fermions under periodic boundary conditions.

We show experimentally that spectral phase manipulation of ultrashort extreme-uv light pulses can induce and control coherent transient excitation of the $\mathrm{He}\left(1s3p\right)$ excited state by the nonresonant components of the broadband extreme-ultraviolet light. The spectral phase manipulation of the 15th harmonic of an intense $805\mathrm{nm}$, $80\mathrm{fs}$ pulse is achieved by propagation of the euv light through a variable optical density of He gas. The acquired spectral phase due to the dispersive interaction of the off-resonance components in the euv pulse with the $\mathrm{He}\left(1s3p\right)$ resonance enhances and modifies the transient excitation. The temporal evolution of the coherently prepared transient $\mathrm{He}\left(1s3p\right)$ amplitude is probed by ionization to the continuum with a $400\mathrm{nm}$, $80\mathrm{fs}$ pulse.

We address the problem of measuring the relative angle between two “quantum axes” made out of $N_1$ and $N_2$ spins. Closed forms of our fidelitylike figure of merit are obtained for an arbitrary number of parallel spins. The asymptotic regimes of large $N_1$ and/or $N_2$ are discussed in detail. The extension of the concept “quantum axis” to more general situations is addressed. We give optimal strategies when the first quantum axis is made out of parallel spins whereas the second is a general state made out of two spins.

Optimal control is formulated based on a noncommutative calculus of operator derivatives. The use of optimal control methods in the design of quantum systems relies on the differentiation of an operator-valued function with respect to the relevant operator. Noncommutativity between the operator and its derivative leads to a generalization of the conventional method of control for classical systems. This formulation is applied to quantum networks of both spin and bosonic particles for the purpose of quantum state control via quantum random walks.

We develop a framework to implement the dynamical decoupling of open quantum systems using continuous pulse sequences. By exploiting the geometric perspective of the continuous dynamical decoupling, we show that the decoupling pulses can be intuitively designed in the basis of the structure function of the $\mathrm{SU}\left(n\right)$ corresponding to the control Hamiltonian. Several examples are given to illustrate the basic idea. We argue that in practice the efficiency of the decoupling is determined by the minimum attainable decoupling cycle time $T_c$ instead of the order of the discrete decoupling group.

Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of an $NP$-complete problem. Errors inherent to truncations of the exact action of interacting gates are controlled by the size of the matrices in the representation. The property of finding the right solution for an instance and the expected value of the energy (cost function) are found to be remarkably robust against these errors. As a symbolic example, we simulate the algorithm solving a 100-qubit hard instance, that is, finding the correct product state out of $\sim {10}^{30}$ possibilities. Accumulated statistics for up to $60$ qubits seem to point at a subexponential growth of the average minimum time to solve hard instances with highly truncated simulations of adiabatic quantum evolution.

A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor to approximate a set of unitary operators to a specified level of precision. We measure how well an operation is performed by the process fidelity between the desired operation and the operation produced by the processor. We show how to find the program for a given processor that produces the best approximation of a particular unitary operation. We also place bounds on the dimension of the program space that is necessary to approximate a set of unitary operators to a specified level of precision.

Here we deal with a nonlocality argument proposed by Cabello, which is more general than Hardy’s nonlocality argument, but still maximally entangled states do not respond. However, for most of the other entangled states, maximum probability of success of this argument is more than that of the Hardy’s argument.

We study the time evolution of localized (local bond) excitations in a symmetric quantum trimer molecule. We relate the dynamical properties of localized excitations such as their spectral intensity and their temporal evolution (survival probability and tunneling of bosons) to their degree of overlap with quantum tunneling pair states. We report on the existence of degeneracy points in the trimer eigenvalue spectrum for specific values of parameters due to avoided crossings between tunneling pair states and additional states. The tunneling of localized excitations which overlap with these degenerate states is suppressed at all times. As a result local bond excitations may be strongly localized forever, similar to their classical counterparts.