Absolute $M$-shell x-ray production cross sections have been measured and calculated for Au and Bi for electron incident energies from close to the ionization threshold up to $38\mathrm{keV}$. The experimental cross sections were deduced from $M\alpha$ x-ray intensities emitted from ultrathin Au and Bi samples deposited on self-supporting C films. The measurements were performed on an electron microprobe using several wavelength-dispersive spectrometers. The x-ray production cross sections were also evaluated theoretically using ionization cross sections calculated from the plane-wave and the distorted-wave Born approximations. Experimental results are compared with the calculated cross sections and also with the results of two analytical formulas widely used in many applications. Good agreement is found between the measured cross sections and the predictions from the distorted-wave Born approximation, which indicates that this approximation is suited for the calculation of $M$-shell ionization cross sections of heavy elements.

We have recently shown [J. Mikosch et al., Phys. Rev. Lett. 98, 223001 (2007)] that the storage time of a thermal ensemble of ions in a multipole radiofrequency (rf) ion trap is ultimately limited by ion evaporation. An analysis of the evaporation rate was used to determine an effective trap depth as a function of the rf amplitude. This revealed that already for moderate rf amplitudes and low average stability parameter $\eta$ the loss of ions is driven by nonadiabatic motion of the fastest ions in the rf field. Here we present the details of the experimental procedure together with our experimental apparatus, which combines a 22-pole rf ion trap with tandem time-of-flight mass spectrometry for ion selection and product analysis. We furthermore describe in detail the numerical and analytical models used in the interpretation of our results, which allows one to predict the most favorable trapping conditions in multipole rf ion traps. From a fit to our data we obtain a maximal value of the multipole stability parameter of ${\eta }_{\mathit{max}}=0.36\pm 0.02$ for adiabatic ion motion.

We demonstrate that dynamical symmetry plays a crucial role in determining the structure of the eigenspectra of spinor Bose-Einstein condensates (BECs). In particular, the eigenspectra of spin-1 and spin-2 BECs in the single-mode approximation are shown to be completely determined by dynamical symmetries, where a spin-2 BEC corresponds to the U(5) limit of the interacting boson model in nuclear physics. The eigenspectrum of a spin-3 BEC is solved analytically for a specific class of coupling constants, while it is shown that dynamical symmetry alone is not sufficient to determine the spectrum for arbitrary coupling constants. We also study the low-lying eigenspectra of spin-1 and spin-2 BECs in the absence of external magnetic field, and find, in particular, that the quasidegenerate spectra emerge for antiferromagnetic and cyclic phases. This implies that these systems are highly susceptible to external perturbations and may undergo symmetry-breaking transitions to other states upon increasing the system’s size.

We study a two-level atom coupled to a Bose-Einstein condensate. We show that the rules governing the decoherence of mesoscopic superpositions involving different classical-like states of the condensate can be probed using this system. This scheme is applicable irrespective of whether the condensate is initially in a coherent, thermal, or more generally, in any mixture of coherent states. The effects of atom loss and finite temperature to the decoherence can therefore be studied. We also discuss the various noise sources causing the decoherence.

We develop a Fock-space WKB method for a Bose-Einstein condensate (BEC) in a double-well trap, using an analogy with a single particle of either positive or negative mass in a quantum potential. The usual mean-field approach is the classical limit, and the inverse number of atoms plays the role of Planck constant. The ground state of positive-mass particles corresponds to the mean-field fixed point of lower energy, while that of negative mass to the excited fixed point. In the case of attractive BECs above the threshold for symmetry breaking, the ground state is the Schrödinger cat state and we relate this to the double-well shape of the potential in Fock space. In the repulsive case, we identify the quantum states corresponding to the mean-field macroscopic self-trapping phenomenon. In particular, the phase-locked ($\pi$ phase) macroscopic quantum self-trapping of BECs is related to the double-well shape of the potential in Fock space. The running-phase macroscopic quantum self-trapping state is found to be subject to quantum collapses and revivals. The phase dispersion grows exponentially, reaching the absolute maximum just before the first collapse of the running phase, which may explain the growth of the phase fluctuations seen in the experiment on macroscopic quantum self-trapping.

A generalized description of Talbot-Lau interference with matter waves is presented, which accounts for arbitrary grating interactions and realistic beam characteristics. The dispersion interaction between the beam particles and the optical elements strongly influences the interference pattern in this near-field effect, and it is known to dominate the fringe visibility if increasingly massive and complex particles are used. We provide a general description of the grating interaction process by combining semiclassical scattering theory with a phase space formulation. It serves to systematically improve the eikonal approximation used so far, and to assess its regime of validity.

We investigate the radiation of a blackbody in a cavity of finite size. For a given geometry, we use semiclassical techniques to obtain explicit expressions of the modified Planck and Stefan-Boltzmann blackbody radiation laws as a function of the size and shape of the cavity. We determine the range of parameters (temperature and size and shape of the cavity) for which these effects are accessible to experimental verification. Finally we discuss potential applications of our findings in the physics of the cosmic microwave background and sonoluminescence.

We report the observation of three-mode optoacoustic parametric interactions of the type predicted to cause parametric instabilities in a $77\text{−}\mathrm{m}$-long, high-optical-power cavity that uses suspended sapphire mirrors. Resonant interaction occurs between two distinct optical modes and an acoustic mode of one mirror when the difference in frequency between the two optical cavity modes is close to the frequency of the acoustic mode. Experimental results validate the theory of parametric instability in high-power optical cavities, and demonstrate tunable parametric gain $\sim {10}^{-2}$ and more than $20\mathrm{dB}$ amplification of a high-order optical mode power generated by an applied acoustic signal.

We describe experimental results of the generation of superposition states in a two-level system, $4s{S}_{1∕2}$ and $3d{D}_{5∕2}$ states, of a single calcium ion. The generation method is based on population transfer via rapid adiabatic passage (RAP), proposed by Vitanov and Shore [Phys. Rev. A 73, 053402 (2006)]. The coherence of the generated superposition state is evaluated with a Ramsey-like interferometry method and a fringe visibility of up to 0.93 is obtained. The state generation shows strong robustness with respect to the RAP pulse parameters, including frequency chirp width and Rabi frequency.

The generalization of the concept of coherent states for a Morse potential based on the real or complex displacements of the equilibrium position of the ground-state wave function yields a natural framework for their generation via Franck-Condon transitions. We study the relevance of including continuum states in the proper treatment of these displaced states, particularly for the description of their time evolution. It is shown that displaced Morse states may exhibit mathematical and physical temporal stability manifested through the presence of revivals in spite of the unbound character of the included continuum states. The Wigner function of these states is presented as well as relations to previous constructions. The time evolution of particular phase space properties such as mean values of position and momentum as well as their uncertainties are also analyzed.

The properties of cavity solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback from a diffraction grating are characterized and analyzed. The solitons have a typical width of $10\mu \mathrm{m}$ and a linewidth of down to $10\mathrm{MHz}$, i.e., they represent small microlasers. Their equilibrium spatial location arises from an interplay of spatial inhomogeneities in the device and a grating-induced force which depends on detuning. Transients involve the passage through a self-pulsing state. Due to the grating-induced advection, drifting excitations are found, which might have applications in all-optical delay lines though their solitonic nature remains to be established.

We suggest and analyze a technique for efficient and robust creation of dense ultracold molecular ensembles in their ground rovibrational state. In our approach a molecule is brought to the ground state through a series of intermediate vibrational states via a multistate chainwise stimulated Raman adiabatic passage technique. We study the influence of the intermediate states decay on the transfer process and suggest an approach that minimizes the population of these states, resulting in a maximal transfer efficiency. As an example, we analyze the formation of ${}^{87}\mathrm{Rb}_2$ starting from an initial Feshbach molecular state and taking into account major decay mechanisms due to inelastic atom-molecule and molecule-molecule collisions. Numerical analysis suggests a transfer efficiency $>90\%$, even in the presence of strong collisional relaxation as are present in a high density atomic gas.

The early stage of entanglement growth in a Bose system on a lattice is studied by means of analytical methods. A local unitary transformation is established which allows us to introduce Bose-Einstein condensation and the related weak-coupling approximation. We calculate both the entanglement of each lattice site with all other sites and the entanglement between pairs of sites. The first quantity weakly depends on the system size, while the second one exhibits peculiar oscillations within the time range of validity of our approximation.

We study the symmetric-side-channel-assisted private capacity of a quantum channel, for which we provide a single-letter formula. This capacity is additive, convex, and, for degradable channels, equal to the unassisted private capacity. While a channel’s (unassisted) capacity for private classical communication may be strictly larger than its quantum capacity, we will show that these capacities are equal for degradable channels, thus demonstrating the equivalence of privacy and quantum coherence in this context. We use these ideas to find new bounds on the key rate of quantum key distribution protocols with one-way classical post-processing. For the Bennett-Brassard 1984 protocol, our results demonstrate that collective attacks are strictly stronger than individual attacks.

Random number generators are important components of information security systems. In particular, cryptography standards require that the numbers generated by quantum key distribution applications meet a rigorous set of standardized randomness tests. To date, implementations of entangled quantum key distribution (EQKD) have not included any randomness assessment. We report on the results of randomness tests and highlight how typical EQKD system operation affects the successes and failures in meeting the fundamental test criteria.

We present an analysis of spectroscopic data concerning the long-range molecular state $(6s_{1∕2}+6p_{1∕2})0_u^{+}$ of ${}^{133}\mathrm{Cs}_2$ [M. Pichler, H. Chen, and W. C. Stwalley, J. Chem. Phys. 121, 1796 (2004)] by using the Lu-Fano method coupled to the improved LeRoy-Bernstein formula. The obtained Lu-Fano graph exhibits the coupling of molecular series to the $(6s_{1∕2}+6p_{3∕2})0_u^{+}$ state. The coupling is due to the spin effects in the molecule. A two-channel model involving the improved LeRoy-Bernstein formula allows us to characterize the molecular series, to localize the perturbing levels, to evaluate the coupling in the vicinity of each perturbing level (five observed for Cs) in a two-level approach and in a more accurate multilevel description. Furthermore, we predict the energy and the width of the first predissociated level.

We report total cross sections for positron scattering from two primary alcohols, methanol $\left(\mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}\right)$ and ethanol $\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{O}\mathrm{H}\right)$. The energy range of the present study is $0.1–40\mathrm{eV}$. The ethanol measurement appears to be original while for methanol we compare our data to the only previous result from Kimura and colleagues [Adv. Chem. Phys. 111, 537 (2000)], with a significant discrepancy between them being found at the lower energies. Positronium formation threshold energies for both species, deduced from the present respective total cross section data sets, are found to be consistent with those expected on the basis of their known ionization energies. There are currently no theoretical results against which we can compare our total cross sections.

The coexistence of superfluid and Mott insulator, due to the quadratic confinement potential in current optical lattice experiments, makes the accurate detection of the superfluid–Mott-insulator transition difficult. Studying alternative trapping potentials which are experimentally realizable and have a flatter center, we find that the transition can be better resolved, but at the cost of a more difficult tuning of the particle filling. When mapping out the phase diagram using local probes and the local density approximation we find that the smoother gradient of the parabolic trap is advantageous.

We use a two-mode Bose-Hubbard Hamiltonian to determine the ground state and dynamical evolution for a Bose Josephson junction realized by an ultracold Bose gas in a double-well trap. We identify Mott-like lobes where number fluctuations are suppressed and the interference fringes in the momentum distribution are strongly reduced. Different from superconducting Josephson junctions, the lobes size increases at increasing wells imbalance. Upon a sudden rise of the barrier between the two wells, an initially phase-coherent state evolves into a coherent superposition of phase states, leading to destructive interference in the time-dependent momentum distribution.

We study a gas of strongly polarized cold fermions in an optical lattice when the excited $p$ bands are populated. We derive the relevant Hamiltonian and discuss the expected phase diagram for both repulsive and attractive interactions. In the parameter regime covered here, checkerboard antiferromagnetic ordering is found to be possible for repulsive interactions, while for attractive interactions, transitions between different types of paired phases are predicted.