We discuss how to construct tight-binding models for ultracold atoms in honeycomb potentials, by means of the maximally localized Wannier functions (MLWFs) for composite bands introduced by Marzari and Vanderbilt [Phys. Rev. B 56, 12847 (1997)]. In particular, we work out the model with up to third-nearest neighbors, and provide explicit calculations of the MLWFs and of the tunneling coefficients for the graphenelike potential with two degenerate minima per unit cell. Finally, we discuss the degree of accuracy in reproducing the exact Bloch spectrum of different tight-binding approximations, in a range of typical experimental parameters.

We address measurement schemes where certain observables $X_k$ are chosen at random within a set of nondegenerate isospectral observables and then measured on repeated preparations of a physical system. Each observable has a probability $z_k$ to be measured, with ${\sum }_k{z}_k=1$, and the statistics of this generalized measurement is described by a positive operator-valued measure. This kind of scheme is referred to as quantum roulettes, since each observable $X_k$ is chosen at random, e.g., according to the fluctuating value of an external parameter. Here we focus on quantum roulettes for qubits involving the measurements of Pauli matrices, and we explicitly evaluate their canonical Naimark extensions, i.e., their implementation as indirect measurements involving an interaction scheme with a probe system. We thus provide a concrete model to realize the roulette without destroying the signal state, which can be measured again after the measurement or can be transmitted. Finally, we apply our results to the description of Stern-Gerlach-like experiments on a two-level system.

We address the joint estimation of the two defining parameters of a displacement operation in phase space. In a measurement scheme based on a Gaussian probe field and two homodyne detectors, it is shown that both conjugated parameters can be measured below the standard quantum limit when the probe field is entangled. We derive the most informative Cramér-Rao bound, providing the theoretical benchmark on the estimation, and observe that our scheme is nearly optimal for a wide parameter range characterizing the probe field. We discuss the role of the entanglement as well as the relation between our measurement strategy and the generalized uncertainty relations.

Initial calculations to explore the role of pressure on generalized oscillator strengths (GOSs) for the hydrogen atom are presented. Our work is based on models of quantum confinement where the hydrogen atom is assumed to be spatially confined in a spherical cavity bounded by a barrier potential of finite height. For a given confinement radius and barrier height the energy spectrum for all available bound states and a number of continuum states (pseudocontinuum) is obtained by solving the Schrödinger equation using a finite-differences method. In contrast with the free atom case, the GOS momentum-transfer distribution for the $1s\to nl$ transitions is enhanced in amplitude and width as pressure increases. A turnover of this behavior takes place at a critical pressure, indicating the approach to the limit of confining capacity for the system to hold the $nl$ state. As a consequence of this behavior, the corresponding dipole oscillator strength (DOS) values provide a useful way to characterize the critical pressures for the fading and ultimate bleaching of the spectroscopic emission lines. It is also found that the height of the barrier—simulating different confining media—also affects these properties. These findings may be equally applicable to the study of inelastic energy loss from swift bare ions incident on matter under high pressures, photoabsorption, and photoionization cross sections of caged atoms as well as on optical properties of hydrogenic impurities trapped in spherical quantum dots.

We report the measurement of the hyperfine structure in the 7$d$ ${}^2{D}_{3/2}$ state of ${}^{133}$Cs isotope by Doppler-free two-photon fluorescence spectroscopy in a gas cell. The hyperfine level separations were measured using a frequency-stabilized Ti:sapphire laser locked to one of the hyperfine transitions and an acousto-optic modulator locked to another hyperfine transition. The frequency separation between various hyperfine levels has been measured with a precision of ∼100 kHz. From the measured hyperfine separations of the excited state, we have determined the magnetic dipole coupling constant ($A$) and electric quadrupole coupling constant ($B$) for the 7$d$ ${}^2{D}_{3/2}$ state. The determined hyperfine structure constants are $A=7.38$ (0.01) MHz and $B=-0.18$ (0.1) MHz. The values measured are found to be in good agreement with the earlier reported results using stepwise excitation process.

The photoionization cross section of the Ca atom, confined by a spherical annular potential, has been calculated using a modification to the Belfast $R$-matrix code for a variety of depths of the confining potential. The results show that the external potential affects the cross section, which is dominated by doubly excited autoionizing states, quite significantly, causing much of the oscillator strength to move into the discrete region of the spectrum. In addition, increasing well depth causes a level crossing between the first two excited states of Ca${}^{+}$, thereby changing the ordering of resonances dramatically. The calculation for free Ca shows excellent agreement with experiment.

We study the Bloch-Zener oscillation, which is a superposition of Bloch oscillation and Landau-Zener tunneling between Bloch bands, for a quantum particle in a frustrated sawtooth lattice with and without uniform magnetic field. Under the single-band tight-binding approximation, the sawtooth lattice is a two-miniband system and may have a flat band structure. The presence of magnetic field can make the gap between two minibands close, and around the touch point the dispersion is an asymmetric Dirac cone. We analyze in detail the Landau-Zener tunneling and Bragg scattering in the Bloch-Zener oscillation and the effect of magnetic field. Our results also give a clear picture of the dynamical localization in real space induced by the flat band structure of the lattice.

A two-body correlated basis set is used to develop a many-body theory which is valid for any number of bosons in the trap. The formalism incorporates the van der Waals interaction and two-body correlations in an exact way. The theory has successfully been applied to Bose-Einstein condensates—dilute weakly interacting and also dilute but having a large scattering length. Even in the extreme dilute condition, we observe the breakdown of the shape-independent approximation and the interatomic correlation plays an important role in the large particle-number limit. This correlated many-body calculation can handle, within the two-body correlation approximation, the entire range of atom number of experimentally achieved condensates. Next we successfully push the basis function for large scattering lengths where the mean-field results are manifestly bad. The sharp increase in correlation energy clearly shows the beyond-mean-field effect. We also calculate one-particle densities for various scattering lengths and particle numbers. Our many-body calculation exhibits the finite-size effect in the one-body density.

Impulsive stimulated Raman scattering (ISRS) plays a key role in coherent control of low-energy rotational resonances. Femtosecond laser pulses are widely employed to utilize ISRS because they are broadband and can cover the needed frequencies in a single pulse. Here, we show theoretically that the ISRS process is expressed as a linear response to the instantaneous Stokes parameters (ISPs) of the laser pulse. These IPSs expressed in rotational coordinates are then shown to be responsible for the angular momentum transfer from light to matter. These relationships have led to the designs of spectral profiles and polarization states of light pulses that should selectively excite particular rotational modes.

In their recent paper, Williams et al. [Phys. Rev. A 85, 022701 (2012)] report on the apparatus and experimental method for the measurement of the Stokes parameter $P_2$ associated with spin-polarized electron impact $\left(3d^{10}{s}^2\right){}^1{S}_0\to \left(3d^{10}4s5s\right){}^3{S}_1$ excitation of zinc. On the basis of a qualitative semiclassical argument, they make the following claim regarding the discrepancy between theory and experiment for $P_2$: “The task remains for theory to include a topological nondynamical phase.” We analyze the validity of this assertion.

A recent article by Williams et al. [Phys. Rev. A 85, 022701 (2012)] highlights a discrepancy between experiment and theory for the linear light polarization $P_2$ measured after impact excitation of zinc atoms by a spin-polarized electron beam. The claim is made that current collision theories must be modified by including a geometric (Berry) phase in the calculations in order to reproduce the experimental data for Zn and similar data from the Münster group for Hg. We show that the $e$-Hg data can be qualitatively reproduced by our fully relativistic $B$-spline $R$-matrix approach without any further modification.

The Comments by Bartschat and Zatsarinny and by Bostock et al. on our paper [Phys Rev A 85, 022701 (2011)] are addressed. We clarify our original statement and point out that we only suggested that theory should include topological phase and did not say how to include it.

Fermions, as a major class of quantum particles, provide platforms for quantum information processing beyond the possibilities of spins or bosons, which have been studied more extensively. One particularly interesting model to study, in view of recent progress in manipulating ultracold fermion gases, is the fermionic version of measurement-based quantum computation (MBQC), which implements full quantum computation with only single-site measurements on a proper fermionic many-body resource state. However, it is not known which fermionic states can be used as the resource states for MBQC and how to find them. In this paper, we generalize the framework of spin MBQC to fermions. In particular, we provide a general formalism to construct many-body entangled fermion resource states for MBQC based on the fermionic projected entangled pair state representation. We give a specific fermionic state which enables universal MBQC and demonstrate that the nonlocality inherent in fermion systems can be properly taken care of with suitable measurement schemes. Such a framework opens up possibilities of finding MBQC resource states which can be more readily realized in the laboratory.

We propose and analyze a scheme to observe topological phenomena with ions in microtraps. We consider a set of trapped ions forming a regular structure in two spatial dimensions and interacting with lasers. We find phonon bands with nontrivial topological properties, which are caused by the breaking of time-reversal symmetry induced by the lasers. We investigate the appearance of edge modes, as well as their robustness against perturbations. Long-range hopping of phonons caused by the Coulomb interaction gives rise to flat bands which, together with induced phonon-phonon interactions, can be used to produce and explore strongly correlated states. Furthermore, some of these ideas can also be implemented with cold atoms in optical lattices.

We show that the uncertainty relation as expressed in the Robertson-Schrodinger generalized form can be used to detect the mixedness of three-level quantum systems in terms of measurable expectation values of suitably chosen observables when prior knowledge about the basis of the given state is known. In particular, we demonstrate the existence of observables for which the generalized uncertainty relation is satisfied as an equality for pure states and a strict inequality for mixed states corresponding to single as well as bipartite systems of qutrits. Examples of such observables are found for which the magnitude of uncertainty is proportional to the linear entropy of the system, thereby providing a method for measuring mixedness.

We investigate magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of ${}^{40}$K and ${}^{87}$Rb atoms, where we can create ${}^{40}$K${}^{87}$Rb molecules with a conversion efficiency as high as 45%. In the limit of fast magnetic sweeps and small molecule fraction, we find that the time scale of molecule production is accurately predicted by a parameter-free model that uses only the atomic densities, masses, and the known Feshbach resonance parameters. We find that molecule production efficiency saturates for slower magnetic sweeps, at which point the maximum number of Feshbach molecules depends primarily on the atoms’ phase-space density. At higher temperatures, our measurements agree with a phenomenological model that successfully describes the formation of bosonic molecules from either Bose or Fermi gases. However, for quantum degenerate atom gas mixtures, we measure significantly fewer molecules than this model predicts.

Within the weak-field asymptotic theory, the dependence of the tunneling ionization rate of a molecule in a static electric field on its orientation with respect to the field is determined by the structure factor for the highest occupied molecular orbital (HOMO). An accurate determination of this factor, and hence the ionization rate, requires accurate values of the HOMO in the asymptotic region. Techniques for calculating the structure factors for molecules in the Hartree-Fock approximation are discussed. For diatomics, grid-based numerical Hartree-Fock calculations which reproduce the correct asymptotic tail of the HOMO are possible. However, for larger molecules, to solve the Hartree-Fock equations one should resort to basis-based approaches with too rapidly decaying Gaussian basis functions. A systematic study of the possibility to reproduce the asymptotic tail of the HOMO in calculations with Gaussian basis sets is presented. We find that polarization-consistent basis sets with quadruple or pentuple-zeta quality greatly improve the tail of the HOMO, but only when used with variationally optimized exponents. This methodology is validated by considering the CO molecule for which reliable grid-based calculations can be performed. The optimized Gaussian basis sets are used to calculate the structure factors for the triatomic molecules CO${}_2$ and OCS. The results are compared with available experimental and theoretical results.