We discuss the ground state entanglement of the $E\otimes ϵ$ Jahn-Teller model in the presence of a strong transverse magnetic field as a function of the vibronic coupling strength. A complete characterization is given of the phenomenon of entanglement sharing in a system composed by a qubit coupled to two bosonic modes. Using the residual $I$ tangle, we find that three-partite entanglement is significantly present in the system in the parameter region near the bifurcation point of the corresponding classical model.

We derive exact expressions for the mean value of Meyer-Wallach entanglement $Q$ for localized random vectors drawn from various ensembles corresponding to different physical situations. For vectors localized on a randomly chosen subset of the basis, $⟨Q⟩$ tends for large system sizes to a constant which depends on the participation ratio, whereas for vectors localized on adjacent basis states it goes to zero as a constant over the number of qubits. Applications to many-body systems and Anderson localization are discussed.

We explore the rich internal structure of ${\text{Cs}}_2$ Feshbach molecules. Pure ultracold molecular samples are prepared in a ${\text{CO}}_2$-laser trap, and a multitude of weakly bound states is populated by elaborate magnetic-field ramping techniques. Our methods use different Feshbach resonances as input ports and various internal level crossings for controlled state transfer. We populate higher partial-wave states of up to eight units of rotational angular momentum ($l$-wave states). We investigate the molecular structure by measurements of the magnetic moments for various states. Avoided level crossings between different molecular states are characterized through the changes in magnetic moment and by a Landau-Zener tunneling method. Based on microwave spectroscopy, we present a precise measurement of the magnetic-field-dependent binding energy of the weakly bound $s$-wave state that is responsible for the large background scattering length of Cs. This state is of particular interest because of its quantum-halo character.

Dynamics of multilevel molecules and pulse propagation is studied near the two-photon resonance. We have found a strict solution of this problem beyond the rotating wave approximation. Our analytical solution is in close agreement with the strict numerical solution for the $4,4^{\prime }$-bis(dimethylamino) stilbene molecule. The compensation of the dynamical Stark shift is studied for fixed-in-space molecules. It is shown that the orientational disorder does not allow complete compensation of the dynamical Stark shift.

We demonstrate theoretically and experimentally that under suitable conditions high-$Q$ microspheres can exhibit anomalous dispersion, which permits phase and energy matching for nonlinear optical interactions. We use such dispersion control to produce either Raman or four-wave mixing parametric oscillations by changing the size of the microsphere.

In the case of the nonlinear Schrödinger equation with designed group velocity dispersion, variable nonlinearity, and gain or loss, we analytically demonstrate the phenomenon of chirp reversal crucial for pulse reproduction. Two different scenarios are exhibited, where the pulses experience identical dispersion profiles, but show entirely different propagation behavior. Exact expressions for dynamical quasisolitons and soliton bound states relevant for fiber communication are also exhibited.

We study the two-dimensional discrete Ginzburg-Landau equation. In the linear limit, the dispersion and gain curves as well as the diffraction pattern are determined analytically. In the nonlinear case, families of two-dimensional discrete solitons are found numerically as well as approximately in the high-confinement limit. The instability dynamics are analyzed by direct simulations.

We produce large numbers of low-energy ions by photoionization of laser-cooled atoms inside a surface-electrode-based Paul trap. The isotope-selective trap’s loading rate of $4\times {10}^5{\mathrm{Yb}}^{+}\mathrm{ions}∕\mathrm{s}$ exceeds that attained by photoionization (electron-impact ionization) of an atomic beam by three (six) orders of magnitude. Traps as shallow as $0.13\mathrm{eV}$ are easily loaded with this technique. The ions are confined in the same spatial region as the laser-cooled atoms, which will allow the experimental investigation of interactions between cold ions and cold atoms or Bose-Einstein condensates.

The modular multiplication operator, a central subroutine in Shor’s factoring algorithm, is shown to be a coherent superposition of two quantum baker’s maps when the multiplier is 2. The classical limit of the maps being completely chaotic, it is shown that there exist perturbations that push the modular multiplication operator into regimes of generic quantum chaos with spectral fluctuations that are those of random matrices. For the initial state of relevance to Shor’s algorithm we study fidelity decay due to phase and bit-flip errors in a single qubit and show exponential decay with shoulders at multiples or half-multiples of the order. A simple model is used to gain some understanding of this behavior.

A characterization of qubit quantum channels is introduced. In analogy to what happens in the context of bosonic channels we exploit the possibility of representing the states of the system in terms of characteristic function. The latter are functions of noncommuting variables (Grassmann variables) and are defined in terms of generalized displacement operators. In this context we introduce the set of Gaussian channels and show that they share similar properties with the corresponding bosonic counterpart.

Rigorous treatment is presented for antiproton capture by helium ions, i.e., $\overline{p}+{\text{He}}^{+}\to {\left(\overline{p}{\text{He}}^{+}\right)}^{\ast \ast }\to \overline{p}{\text{He}}^{2+}+e$, by using $R$-matrix theory. The present work applies the $R$-matrix method to an exotic collision system containing an antiproton, a nucleus, and an electron. The eigenvalue problem in the $R$-matrix method is solved by the discrete-variable-representation algorithm without use of any decoupling approximation. The probability of antiproton capture is calculated for the total angular momentum $J=30$. A huge number of the overlapping resonances are found to be prominent everywhere over a wide range of energies. As suggested in a time-dependent wave-packet propagation calculation [K. Sakimoto, Phys. Rev. A 74, 022709 (2006)], the resonances make a dominant contribution to the antiproton capture. It is found that the nonadiabatic coupling is always weak in off-resonance collisions, but can be very strong in resonance collisions.

This paper reports ab initio calculations of rare gas ($\mathrm{RG}=\text{Kr}$, Ar, Ne, and He) dimer quadrupoles at the second order of Møller-Plesset perturbation theory (MP2). The study reveals the crucial role of the dispersion contribution to the ${\mathrm{RG}}_2$ quadrupole in the neighborhood of the equilibrium dimer separation. The magnitude of the dispersion quadrupole is found to be much larger than that predicted by the approximate model of Hunt. As a result, the total MP2 quadrupole moment is significantly smaller than was assumed in virtually all previous related studies. An analytical model for the distance dependence of the ${\mathrm{RG}}_2$ quadrupole is proposed. The model is based on the effective-electron approach of Jansen, but replaces the original Gaussian approximation to the electron density in an $\mathrm{RG}$ atom by an exponential one. The role of the nonadditive contribution in ${\mathrm{RG}}_3$ quadrupoles is discussed.

Angular distributions of photoelectrons in the photodetachment from ${\mathrm{OH}}^{-}\left({}^1\Sigma ^{+}\right)+h\nu \to \mathrm{OH}({}^2\Pi _i;\upsilon =0)+e^{-}$ process were measured at four discrete wavelengths $(440–266\mathrm{nm})$ using a crossed anion-laser interaction and a linear time-of-flight photoelectron spectrometer. The asymmetry parameters determined from the measured angular distributions at these wavelengths were fitted to a model that accounts for the dipole interaction between the final-state particles and to a free-electron form of the Cooper-Zare model. The observed spectral dependence of the asymmetry parameter shows no significant influence of the dipole interaction. The spectral dependences of the asymmetry parameter in the photodetachment from ${\mathrm{OH}}^{-}$ and the previously studied ${\mathrm{O}}^{-}$ are found to be very similar.

A method is described for extracting double ionization amplitudes from a quantum wave packet for an atom after a short radiation pulse, but while the electrons are still interacting. The procedure involves the use of exterior complex scaling to effectively propagate the field-free solution to infinite times, and allows the use of existing integral formulas for double ionization amplitudes for two electron atoms and molecules.

Tunable, polarized, microfocused x-ray pulses were used to record x-ray absorption spectra across the $K$ edges of ${\text{Kr}}^{+}$ and ${\text{Kr}}^{2+}$ produced by laser ionization of Kr. Prominent $1s\to 4p$ and $5p$ excitations are observed below the $1s$ ionization thresholds in accord with calculated transition energies and probabilities. Due to alignment of $4p$ hole states in the laser-ionization process, the ${\text{Kr}}^{+}$ $1s\to 4p$ cross section varies with respect to the angle between the laser and x-ray polarization vectors. This effect is used to determine the ${\text{Kr}}^{+}$ $4p_{3∕2}$ and $4p_{1∕2}$ quantum state populations, and these are compared with results of an adiabatic strong-field ionization theory that includes spin-orbit coupling.

We investigate the behavior of ultracold bosons in optical lattices with a disorder potential generated via a secondary species frozen in random configurations. The statistics of disorder is associated with the physical state in which the secondary species is prepared. The resulting random potential, albeit displaying algebraic correlations, is found to lead to localization of all single-particle states. We then investigate the real-time dynamics of localization for a hardcore gas of mobile bosons which are brought into sudden interaction with the random potential. Regardless of their initial state and for any disorder strength, the mobile particles are found to reach a steady state characterized by exponentially decaying off-diagonal correlations and by the absence of quasicondensation; when the mobile particles are initially confined in a tight trap and then released in the disorder potential, their expansion is stopped and the steady state is exponentially localized in real space, clearly revealing Anderson localization.

We describe an achromatic, phase-stable, broadband source of polarization-entangled photon pairs with high spectral brightness that uses four-wave mixing in a fiber Sagnac interferometer. We achieved a polarization-entangled two-photon coincidence rate of $7\mathrm{kHz}$ per $0.5\mathrm{THz}$ $\left(0.9\mathrm{nm}\right)$ of bandwidth per $300\mathrm{\mu }\mathrm{W}$ of average pump power. At this rate, we observed two-photon fringe interference visibilities greater than 97%, over a $10\mathrm{THz}$ $(\approx 21\mathrm{nm})$ spectral range. We measured violations of Bell’s inequality by more than 22 standard deviations for each of the four Bell states in less than $3\text{minutes}$ per state. The high spectral brightness $\left(26\mathrm{kHz}{\mathrm{nm}}^{-1}{\mathrm{mW}}^{-1}\right)$, large tunable wavelength range, single spatial mode, and phase stability make this source a promising candidate for a wide range of quantum-information applications.

We calculate the frequency and damping of the scissors mode in a classical gas as a function of temperature and coupling strength. Our results show good agreement with the main features observed in recent measurements of the scissors mode in an ultracold gas of ${}^6\mathrm{Li}$ atoms. The comparison between theory and experiment involves no fitting parameters and thus allows an identification of nonclassical effects at and near the unitarity limit.

A method is presented for quantitative phase-contrast tomography using unfiltered radiation from a small polychromatic source. The three-dimensional distribution of complex refractive index in a monomorphous object is reconstructed given a single projection image per view angle. The reconstruction algorithm is achromatic and stable with respect to high-spatial-frequency noise, in contrast to conventional tomography. The density distribution in a test sample was accurately reconstructed from polychromatic phase-contrast data collected with a point-projection x-ray microscope.

An exact treatment of the relativistic plane-wave Born (RPWB) cross section for electron-impact excitation is provided for an arbitrary atom or ion. This result represents an improvement over the cross section obtained from the widely used Bethe high-energy theory developed in the 1930s. The results obtained from this RPWB approach can be applied to a broad class of problems in fundamental electron-impact scattering theory. As an illustration, the approach is used to approximate the high-$\ell$, partial-wave contribution in more accurate calculations of the excitation cross section, a problem which has been lacking a fully relativistic treatment for more than $20\text{years}$.