In a rapidly rotating Bose-Einstein condensate (BEC) the condensate wave function is analogous to that of a type II superconductor close to the critical magnetic field $H_{c2}$. This wave function is a superposition of the lowest Landau levels (LLL) of a charged particle in a magnetic field and corresponds to a vortex lattice. This leads to the inverted-parabola density profile of the BEC in the parabolic trap similar to slower rotation outside the LLL regime. Then one can apply the continuum theory of the Tkachenko modes (transverse sound modes in the vortex lattice) suggested for slower rotation, but with another shear modulus also known for type II superconductors at $H_{c2}$. The theory yields a simple expression for the Tkachenko eigenfrequencies of the BEC cloud. The comparison with experiment shows that the experimental conditions have not yet reached the LLL regime.

We analyze the quantum entanglement between two interacting atoms trapped in a spherical harmonic potential. At ultracold temperature, ground-state entanglement is generated by the dominated $s$-wave interaction. Based on a regularized pseudopotential Hamiltonian, we examine the quantum entanglement by performing the Schmidt decomposition of low-energy eigenfunctions. We indicate how the atoms are paired and quantify the entanglement as a function of a modified $s$-wave scattering length inside the trap.

We present a detailed analysis and design of a neutral atom quantum logic device based on atoms in optical traps interacting via dipole-dipole coupling of Rydberg states. The dominant physical mechanisms leading to decoherence and loss of fidelity are enumerated. Our results support the feasibility of performing single- and two-qubit gates at MHz rates with decoherence probability and fidelity errors at the level of ${10}^{-3}$ for each operation. Current limitations and possible approaches to further improvement of the device are discussed.

We critically review earlier works on Hardy’s nonlocality argument for two spin-$s$ systems and show that solutions previously found in this regard were restricted due to imposition of some conditions which have no role in the argument of nonlocality. We provide a compact form of the nonlocality condition for two spin-$s$ particles, and we also extend it to $n$ number of spin-$s$ particles. Finally we apply a more general kind of nonlocality argument, still without an inequality, to higher-spin systems.

We develop a direct diagrammatic construction scheme for the inelastic propagator, which describes inelastic scattering processes. Starting from the previously presented “direct approach” to the inelastic propagator, which involves a higher-order elastic Green’s function, we show how one can obtain the inelastic propagator for simple excitations without actually evaluating all the diagrams for the higher-order Green’s function. The three cases where either the target molecule itself or its cation or anion is a closed-shell system are discussed. A generalization of the method to obtaining inelastic propagators between higher excitations is briefly addressed.

The lowest energy structures and electronic properties of ${\mathrm{Al}}_n\mathrm{N}(n=2–12)$ clusters were studied using density-functional theory. The equilibrium geometries of ${\mathrm{Al}}_n\mathrm{N}$ clusters with up to $n=12$ were determined from a number of possible structural isomers at each size. The ${\mathrm{Al}}_7\mathrm{N}$ cluster was found be particularly stable with higher binding energy and larger electronic gap. For all the ${\mathrm{Al}}_n\mathrm{N}$ clusters studied, we found charge transfers from the Al to N site and co-existence of ionic and covalent bonding characteristics.

In order to use a collection of trapped ions for experiments where a well-defined preparation of vibrational states is necessary, all vibrational modes have to be cooled to ensure precise and repeatable manipulation of the ions quantum states. A method for simultaneous sideband cooling of all axial vibrational modes is proposed. By application of a magnetic field gradient the absorption spectrum of each ion is modified such that sideband resonances of different vibrational modes coincide. The ion string is then irradiated with monochromatic electromagnetic radiation, in the optical or microwave regime, for sideband excitation. This cooling scheme is investigated in detailed numerical studies. Its application for initializing ion strings for quantum information processing is extensively discussed.

The dynamics of the ethylene molecule in femtosecond laser pulses is studied as a function of the laser parameters using an ab initio time-dependent approach, called nonadiabatic quantum molecular dynamics. We predict that, by choosing different femtosecond pulses with well-defined excitation frequencies, one can selectively induce either the isomerization process or different fragmentation phenomena.

We present a scheme, based on coherent Raman scattering, to transfer the complete information content of an optical field from one spectral band to another with good efficiency, high fidelity, and large bandwidth. We demonstrate the transfer of both amplitude and phase modulation to new frequencies by scattering in a coherently prepared sodium vapor. The scattering process for this system has a bandwidth of at least tens of MHz and preserves the field envelope with a fidelity of 98%.

There are two different approaches for describing the slowing down of charged particles in solids, commonly used in a separate way. Either one treats the energy transfer to the target or considers the dragging force due to the induced potential (“wake”). We herewith present a classical many-body calculation which intrinsically allows simultaneously both descriptions. For the first time, we can follow in detail the development of the stopping power, the projectile’s charge and excitation state, as well as the formation of the wake, for ions entering into a solid. We further show that in nonequilibrium, stopping the development of the wake contributes much stronger to the change in stopping power than one could expect from the corresponding change of the projectile’s charge or excitation state. This is exemplified by the explanation of an experimentally observed surface enhancement in the stopping power, which sheds new light on analysis tools with single atomic depth resolution. We underline our findings by simulating also anti-Ni ions, which are found to form a pressure wave in contrast to trailing wakes in the case of Ni ions.

We report the exact entanglement cost of a class of multiqubit bound entangled states, computed in the context of a universal model for multipartite state preparation. The exact amount of entanglement needed to prepare such states are determined by first obtaining lower bounds using a cut-set approach, and then providing explicit local protocols achieving the lower bound.

We show that entangled radiation-matter states with broken symmetries can be prepared by using nonclassical light in the coherent control techniques. We demonstrate the method by realizing the entanglement in degenerate continuum electronic momentum states of opposite directionality and discrete states of opposite handedness in chiral molecules. When the material system is excited simultaneously by classical light and quantum light in a state with several semiclassical phases, the interference conditions guide the system to such entangled radiation-matter states.

A class of architectures is advanced for cluster-state quantum computation using quantum dots. These architectures include using single and multiple dots as logical qubits. Special attention is given to supercoherent qubits introduced by Bacon et al. [Phys. Rev. Lett. 87, 247902 (2001)] for which we discuss the effects of various errors and present a means of error protection.

We study theoretically the quantum dynamics of two interacting electrons in the symmetric double-dot structure under the influence of a bichromatic resonant pulse. The state vector evolution is studied for two different pulse designs. It is shown that the laser pulse can generate an effective exchange coupling between electron spins localized in different dots. Possible applications of this effect to quantum-information processing (entanglement generation, quantum-state engineering) are discussed.

We investigate quantum communication between the sites of a spin ring with twisted boundary conditions. Such boundary conditions can be achieved by a magnetic flux through the ring. We find that a nonzero twist can improve communication through finite odd-numbered rings and enable high-fidelity multiparty quantum communication through spin rings (working near perfectly for rings of five and seven spins). We show that in certain cases, the twist results in the complete blockage of quantum-information flow to a certain site of the ring. This effect can be exploited to interface and entangle a flux qubit and a spin qubit without embedding the latter in a magnetic field.

Calculations of leptonic and hadronic annihilation rates in the hydrogen-antihydrogen molecule are presented. Both the leptonic potential and leptonic wave function are evaluated within the Born-Oppenheimer approximation employing the Ritz variational principle. Nonadiabatic corrections to the leptonic potential are also obtained. Explicitly correlated Gaussians are employed as basis functions, which describe accurately the hydrogen-antihydrogen interaction. Given the leptonic potential the hadronic part of the wave function for each molecular level of the hydrogen-antihydrogen quasimolecule is calculated by solving the corresponding Schrödinger equation by means of precise $B$-spline representations. The decay rates of the quasimolecule into separate positronium and protonium systems are estimated for a number of molecular levels. Utilizing the leptonic and hadronic wave functions the leptonic- and hadronic-annihilation rates for different molecular levels are computed.

$Ll,L\alpha ,L\beta ,L\gamma ,L{\gamma }_{1+5},L{\gamma }_{2+3},L{\gamma }_{4+4^{\prime }}$ x-ray production cross sections of ${}_{58}\mathrm{Ce}$, ${}_{60}\mathrm{Nd}$ and ${}_{71}\mathrm{Lu}$ induced by 4-, 6-, 8-, and $10\text{−}\mathrm{MeV}$ carbon ions were measured. For Lu, $L{\gamma }_{2+3}$ is separated from $L{\gamma }_{2+3+6}$ after revision of the technique of Datz et al. so that $L{\gamma }_{1+5}$ was used instead of $L{\gamma }_1$, the $L{\gamma }_{4+4^{\prime }}∕L{\gamma }_{1+5}$ ratio was corrected for multiple ionization, and uncertainties in $L{\gamma }_{4+4^{\prime }}$ were incorporated in the fitting process. $L$-subshell ionization cross sections were extracted as a weighted average from two combinations of these cross sections, $\{L\alpha ,L{\gamma }_{1+5},L{\gamma }_{2+3}\}$ and $\{L\alpha ,L{\gamma }_{1+5},L\gamma \}$. It is shown that, to within a few percent, the first of these two combinations results in the identical cross sections as this weighted average. Within 10%, permutations of different sets of single-hole atomic parameters yielded the same ionization cross sections. These cross sections are typically within 15% and at most 35% of the cross sections obtained with atomic parameters that were altered in two different ways for multiple ionization. Extracted subshell and total $L$-shell ionization cross sections as well as Ce and Nd data of Braziewicz et al. are compared with the ECPSSR theory of Brandt and Lapicki that accounts for the energy-loss (E), Coulomb-deflection (C), perturbed-stationary-state (PSS) and relativistic (R) effects. These measurements are also compared with the ECPSSR theory after its corrections—in a separated and united atom (USA) treatment, and for the intrashell (IS) transitions with the factors of Sarkadi and Mukoyama normalized to match $L$-shell cross section with the sum of $L$-subshell cross sections—as well as with the similarly improved semiclassical approximation of Trautmann. For Ce and Nd, the agreement of the extracted ionization cross sections with these theories is poor for $L_1$ and good for $L_2$, $L_3$, and total $L$ shell ionization. For the $L_2$ subshell, this agreement is better for Ce and Nd than for Lu. The ECPSSR theory corrected for the USA and IS effects is surprisingly good for the $L_1$-subshell ionization of Lu, while at $4\mathrm{MeV}$ a similarly corrected semiclassical approximation is in excellent agreement with $L_2$ and $L_3$ data but overestimates the $L_1$ measurement by almost a factor of 2.

The distorted-wave approximation (DWA) is applied to study $K$-shell excitation in ${\mathrm{C}}_2{\mathrm{H}}_2$ by electron impact. More specifically, calculated differential and integral cross sections for the $X{}^1\Sigma _g^{+}\to {}^{1,3}\Pi _g(1s{\sigma }_g\to 1p{\pi }_g)$ and $X{}^1\Sigma _g^{+}\to {}^{1,3}\Pi _u(1s{\sigma }_u\to 1p{\pi }_g)$ transitions in this target in the $300–800\mathrm{eV}$ incident energy range are reported. The triplet-to-singlet ratios of respective integral cross sections, namely, RI(3:1), calculated by dividing the integral cross sections for transitions leading to the triplet core-excited states by those leading to the corresponding singlet states, are also reported as a function of incident energies. In general, our calculated sums of the generalized oscillator strength for transitions leading to the ${}^1\Pi _g$ and ${}^1\Pi _u$ excited states are in good agreement with the available experimental data. On the other hand, the present calculated integral cross sections and the corresponding data for its isoelectronic species CO are significantly different. Possible physical origins for this difference are discussed.

Quantum-mechanical calculations are performed of the dynamic alignment of linear molecules induced by a strong nonresonant laser field. Within this framework we have treated in a unified fashion the alignment with laser pulses of varying duration from the short pulse impulsive limit $({\tau }_{\text{pulse}}⪡T_{\mathrm{rot}})$ to the long pulse adiabatic limit $({\tau }_{\text{pulse}}>T_{\mathrm{rot}})$. The temporal behavior of the alignment in both these limits, and in the intermediate pulse duration regime, have been analyzed. For the impulsive limit the dependence of the degree of maximum alignment upon the laser pulse duration was examined and the intensity-dependent optimum pulse duration explained. A comparison between the degree of alignment under the same conditions of pulse intensity and rotational temperature was performed between the impulsive and adiabatic cases. The adiabatic case was found to always provide a better degree of alignment for a given intensity which we show is due to the zero relative phasing between the component states of the superposition that form the pendular states. We have explicitly calculated the angular distribution of an ensemble of linear molecules as it evolves through a rotational revival; a rich structure is found that may be useful in guiding future experiments that utilize the field free alignment in a revival.

We investigate the Bose-Einstein condensation of fermionic pairs in a uniform two-component Fermi gas, obtaining an explicit formula for the condensate density as a function of the chemical potential and the energy gap. We analyze the condensate fraction in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly interacting Cooper pairs to the Bose-Einstein condensate of molecular dimers. By using the local-density approximation we study confined Fermi vapors of alkali-metal atoms for which there is experimental evidence of condensation also on the BCS side of the Feshbach resonance. Our theoretical results are in agreement with these experimental data and give the behavior of the condensate on both sides of the Feshbach resonance at zero temperature.