A Bethe-ansatz spin-density functional approach is developed to evaluate the ground-state density profile in a system of repulsively interacting spin-$1∕2$ fermions inside a quasi-one-dimensional harmonic well. The approach allows for the formation of antiferromagnetic quasiorder with increasing coupling strength and reproduces with high accuracy the exact solution that is available for the two-fermion system.

We propose a communication-assisted local-hidden-variable model that yields the correct outcome for the measurement of any product of Pauli operators on an arbitrary graph state, i.e., that yields the correct global correlation among the individual measurements in the Pauli product. Within this model, communication is restricted to a single round of message passing between adjacent nodes of the graph. We show that any model sharing some general properties with our own is incapable, for at least some graph states, of reproducing the expected correlations among all subsets of the individual measurements. The ability to reproduce all such correlations is found to depend on both the communication distance and the symmetries of the communication protocol.

Nonclassical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization qubit. In the process we highlight some of subtleties involved in common methods for generating decoherence in quantum optics.

We propose a size-consistent method to combine small active space multiconfigurational self-consistent-field (MCSCF) wave functions with standard correlation energy density functionals. The correlation energy is not evaluated from the standard spin densities but from a pair of alternative densities obtained from the natural orbitals and occupation numbers. The method substantially improves the MCSCF estimates of the spectroscopic constants of a set of 11 diatomics, with an accuracy comparable to that from Becke three-parameter Lee-Yang-Parr (B3LYP) hybrid functional and Becke–Lee-Yang-Parr (BLYP) functional spin-unrestricted Kohn-Sham density functional theory (DFT) calculations. The method also provides estimates in good agreement with multireference coupled-cluster calculations for the diradical-involved automerization barrier of cyclobutadiene, with deviations $\sim 0.3-1.7\mathrm{kcal}{\mathrm{mol}}^{-1}$ as compared to deviations $\sim 14–15\mathrm{kcal}{\mathrm{mol}}^{-1}$ provided by B3LYP or BLYP spin-restricted Kohn-Sham DFT calculations. It also yields rather good estimates of energy differences between triplet and open-shell singlet states in the helium atom and the methylene molecule.

We report high precision calculations of nonrelativistic energies of the hydrogen molecular ion $\mathrm{H}_2{}^{+}$ in some low-lying states, using a variational method in multiple Hylleraas basis sets. For the ground state, for example, the energy is established to an accuracy of 8 parts in ${10}^{30}$, which represents 8 orders of magnitude improvement over the best previous value of Cassar and Drake [J. Phys. B 37, 2485 (2004)]. Our calculations lay a firm foundation for studying higher-order relativistic and QED effects.

We theoretically explore photoassociation by adiabatic passage of two colliding cold ${}^{85}\mathrm{Rb}$ atoms in an atomic trap to form an ultracold ${\mathrm{Rb}}_2$ molecule. We consider the incoherent thermal nature of the scattering process in a trap and show that coherent manipulations of the atomic ensemble, such as adiabatic passage, are feasible if performed within the coherence time window dictated by the temperature, which is relatively long for cold atoms. We show that a sequence of $\sim 2\times {10}^7$ pulses of moderate intensities, each lasting $\sim 750\mathrm{ns}$, can photoassociate a large fraction of the atomic ensemble at temperature of $100\mu \mathrm{K}$ and density of ${10}^{11}\text{atoms}∕{\mathrm{cm}}^3$. Use of multiple pulse sequences makes it possible to populate the ground vibrational state. Employing spontaneous decay from a selected excited state, one can accumulate the molecules in a narrow distribution of vibrational states in the ground electronic potential. Alternatively, by removing the created molecules from the beam path between pulse sets, one can create a low-density ensemble of molecules in their ground rovibrational state.

We present an optical system designed to capture and observe a single neutral atom in an optical dipole trap, created by focusing a laser beam using a large-numerical-aperture $(\mathrm{NA}=0.5)$ aspheric lens. We experimentally evaluate the performance of the optical system and show that it is diffraction limited over a broad spectral range $(\sim 200\mathrm{nm})$ with a large transverse field $(\pm 25\mu \mathrm{m})$. The optical tweezer created at the focal point of the lens is able to trap single atoms of ${}^{87}\mathrm{Rb}$ and to detect them individually with a large collection efficiency. We measure the oscillation frequency of the atom in the dipole trap and use this value as an independent determination of the waist of the optical tweezer. Finally, we produce with the same lens two dipole traps separated by $2.2\mu \mathrm{m}$ and show that the imaging system can resolve the two atoms.

In the last several years considerable efforts have been devoted to developing Bose-Einstein-condensate-based devices for applications such as fundamental research, precision measurements, and integrated atom optics. Such devices, capable of complex functionality, can be designed from simpler building blocks as is done in microelectronics. One of the most important components of microelectronics is a transistor. We demonstrate that a Bose-Einstein condensate in a three-well potential structure where the tunneling of atoms between two wells is controlled by the population in the third shows behavior similar to that of an electronic field-effect transistor. Namely, it exhibits switching and both absolute and differential gain. The role of quantum fluctuations is analyzed, and estimates of the switching time and parameters for the potential are presented.

When it comes to laser phenomena in quantum-dot-based systems, usually atomic models are employed to analyze the characteristic behavior. We introduce a semiconductor theory, originating from a microscopic Hamiltonian, to describe lasing from quantum dots embedded in microcavities. The theory goes beyond two-level atomic models and includes modified contributions of spontaneous and stimulated emission as well as many-body effects. An extended version, which incorporates carrier-photon correlations, provides direct access to the photon autocorrelation function and thereby on the statistical properties of the laser emission. In comparison to atomic models, we find deviations in the dependence of the input/output curve on the spontaneous emission coupling $\beta$. Modifications of the photon statistics are discussed for high-quality microcavities with a small number of emitters.

The Dicke model describing an ensemble of two-state atoms interacting with a single quantized mode of the electromagnetic field (with omission of the ${\widehat{A}}^2$ term) exhibits a zero-temperature phase transition at a critical value of the dipole coupling strength. We propose a scheme based on multilevel atoms and cavity-mediated Raman transitions to realize an effective Dicke model operating in the phase transition regime. Optical light from the cavity carries signatures of the critical behavior, which is analyzed for the thermodynamic limit where the number of atoms is very large.

The properties of an entangled two-photon state antisymmetric in frequencies are studied. At a beam splitter, two entangled photons are perfectly anticorrelated. In addition, they cannot be detected at the same time instant despite the fact that their detection times are confined to a narrow time window, i.e., they are temporally antibunched. Using nonlinear photonic-band-gap structures made of $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$, two schemes for generating such states are described.

Three distinct types of behavior have recently been identified in the two-dimensional trapped bosonic gas, namely, a phase-coherent Bose-Einstein condensate (BEC), a Berezinskii-Kosterlitz-Thouless-type (BKT) superfluid, and normal gas phases in order of increasing temperature. In the BKT phase the system favors the formation of vortex-antivortex pairs, since the free energy is lowered by this topological defect. We provide a simple estimate of the free energy of a dilute Bose gas with and without such vortex dipole excitations and show how this varies with particle number and temperature. In this way we can estimate the temperature for crossover from the coherent BEC to the (only) locally ordered BKT-like phase by identifying when vortex-dipole excitations proliferate. Our results are in qualitative agreement with recent, numerically intensive, classical field simulations.

We study the growth of an elongated phase-fluctuating condensate from a nonequilibrium thermal cloud in the axially hydrodynamic regime, obtained by shock cooling. Quantitative measurements using momentum Bragg spectroscopy reveal the evolution of the phase coherence as the condensate grows to equilibrium. We find no delay between the population growth and the development of the phase coherence. We also compare the growth of the condensate with numerical simulations based on kinetic theory, revealing quantitative agreement except for an unexplained time delay.

We study the Loschmidt echo (LE) of a coupled system consisting of a central spin and its surrounding environment described by a general $XY$ spin-chain model. The quantum dynamics of the LE is shown to be remarkably influenced by the quantum criticality of the spin chain. In particular, the decaying behavior of the LE is found to be controlled by the anisotropy parameter of the spin chain. Furthermore, we show that due to the coupling to the spin chain, the ground-state Berry phase for the central spin becomes nonanalytical and its derivative with respect to the magnetic parameter $\lambda$ in spin chain diverges along the critical line $\lambda =1$, which suggests an alternative measurement of the quantum criticality of the spin chain.

In high precision Penning trap mass spectrometry the cyclotron frequency of a polarizable ion is perturbed due to the Stark interaction with the motional electric field. For polar diatomic molecular ions, which have adjacent rotational levels of opposite parity, these shifts can be particularly large—especially for the lowest rotational levels, which are those occupied by ions stored for many hours in cryogenic Penning traps. In order to provide corrections to precision atomic mass measurements, we consider the calculation of orientation polarizabilities of $\mathrm{C}{\mathrm{O}}^{+}$ and the positive ions of the first and second row diatomic hydrides, $\mathrm{Li}{\mathrm{H}}^{+}$ to $\mathrm{Ar}{\mathrm{H}}^{+}$. Dipole moments for these ions have been calculated using the restricted coupled cluster method with perturbative triples and large basis sets. Using these dipoles and an effective Hamiltonian, we have obtained rotational-state dependent polarizabilities of the open-shell diatomic ions $\mathrm{C}{\mathrm{O}}^{+}$, $\mathrm{N}{\mathrm{H}}^{+}$, $\mathrm{O}{\mathrm{H}}^{+}$, $\mathrm{F}{\mathrm{H}}^{+}$, $\mathrm{P}{\mathrm{H}}^{+}$, $\mathrm{S}{\mathrm{H}}^{+}$, and $\mathrm{Cl}{\mathrm{H}}^{+}$. Results are given for those rotational levels that are significantly populated at $4.2\mathrm{K}$, for magnetic fields up to $10\mathrm{T}$. For the remaining first and second row hydride cations, polarizabilities at the magnetic fields of interest can be obtained from a simple formula valid for closed-shell molecules. Conversely, in cases where the polarizability shifts can be measured, our results enable experimental determination of dipole moments.

The Breit-Pauli $R$-matrix method with 17 fine-structure levels is used to calculate integral cross sections with magnetic sublevels for electron-impact excitation of He-like Cl ions from the ground state. The integral cross sections are obtained for transitions from the ground state to the fine-structure levels of all the excited states of the $1s2l$ $(l=0,1)$ configurations. Polarization degrees for the $w$ $(1s^2{}^{1}S_0-1s2p{}^{1}P_1)$, $y$ $(1s^2{}^{1}S_0-1s2p{}^{3}P_1)$, and $x$ $(1s^2{}^{1}S_0-1s2p{}^{3}P_2)$ lines of low and moderately charged He-like ions are also obtained for a systematic investigation of the atomic number dependence. Our results for the polarization degree of He-like Cl ions are found to be in excellent agreement with experimental and other theoretical results.

We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the $\mathrm{Rb}\left({}^{1}S\right)+\mathrm{O}\mathrm{H}\left({}^2\Pi _{3∕2}\right)$ system, including fine-structure and hyperfine effects. We have developed a set of five potential energy surfaces for $\mathrm{Rb}\text{−}\mathrm{O}\mathrm{H}\left({}^2\Pi \right)$ from high-level ab initio electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of ${10}^{-13}{\mathrm{cm}}^2$ are predicted for temperatures typical of Stark decelerators. We conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.

The Casimir-Polder potential for interaction between an excited atom and a ground-state one in the retarded case is obtained with the help of perturbation technique. The potential drops as $R^{-2}$ with the distance between the atoms [E. A. Power and T. Thirunamachandran, Phys. Rev. A 47, 2539 (1993)]. It results in divergent integrals for interaction between an excited atom and a dilute gas medium. We investigate interaction between two atoms embedded in a dielectric medium with the help of a method that enables us to make calculations beyond the perturbation technique. We take into account absorption of photons in the medium. This approach solves the problem of divergence. We consider interaction between an excited atom and a planar dielectric gas medium of ground-state atoms. We show that the retarded interaction between an excited atom and a gas of ground-state atoms is not oscillating but follows a simple power law. We show that to obtain a conventional nonretarded expression for the van der Waals force between an excited atom and a dilute gas, the distance between the atom and the interface should be much smaller than the free mean path of a photon in the medium. Interaction between an excited atom and a hemisphere of ground-state atoms is considered.

A first-principles density functional theory based B3LYP (Becke’s hybrid three-parameter exchange functional with the LYP correlation functional) method with aug-cc-pVDZ(-PP) [Dunning’s augumented correlation consistent valence double zeta with polarization function on Al and pseudopotential for Pb] basis set has been used to search the most stable structures and study the electronic properties of neutral $\mathrm{Al}{\mathrm{Pb}}_n$ and cationic $\mathrm{Al}\mathrm{Pb}_n{}^{+}$ clusters $(n=1–12)$. The evolution of energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, binding energies, and vertical ionization potentials of these clusters have been investigated. Several cationic clusters, such as $\mathrm{Al}\mathrm{Pb}_9{}^{+}$, $\mathrm{Al}\mathrm{Pb}_{10}{}^{+}$, and $\mathrm{Al}\mathrm{Pb}_{12}{}^{+}$ with enhanced stability have been identified. Molecular orbital analyses reveal that the special stability of $D_{4d}$ $\mathrm{Al}\mathrm{Pb}_{10}{}^{+}$ with 42 valence electrons may arise from the closed-shell nature of the $\pi$ subsystem, which is subjected to the $2{(N_{\pi }+1)}^2$ rule with $N_{\pi }=1$. The large nucleus-independent chemical shift (NICS) values indeed demonstrate the high stability of the cationic $\mathrm{Al}\mathrm{Pb}_{10}{}^{+}$. Meanwhile, the big cavity and large NICS values of isoelectronic $D_{4d}$ $\mathrm{Pb}_{10}{}^{2-}$ suggest that it can encapsulate other appropriate metal atoms successfully. As to the $C_{3v}$ $\mathrm{Al}\mathrm{Pb}_9{}^{+}$ cluster, its large stability may also arise from the closed-shell nature of the $\pi$ subsystem with 8 $\pi$ electrons, further confirmed by the large NICS values. Additionally, the nine-atom Pb clusters $\mathrm{Pb}_9{}^{2-}$, $\mathrm{Pb}_9{}^{3-}$, and $\mathrm{Pb}_9{}^{4-}$ possess strong aromatic character. Especially, the $D_{3h}$ $\mathrm{Pb}_9{}^{4-}$ cluster exhibits double spherically aromatic character and the largest NICS value at the center of the cage. These pure Pb clusters with large cavities and their encapsulating clusters should be good candidates for making new cluster-assembled nanostructured materials.