Progress on the evaluation of systematic frequency shifts is described in the development of the optical frequency standard based on single-trapped ${}^{40}$Ca${}^{+}$ with a “clock” transition at 729 nm. The overall systematic uncertainty of the 4$s$ ${}^2$$S_{1/2}$-3$d$ ${}^2$$D_{5/2}$ clock resonance has been characterized to be 7.8 × 10${}^{-16}$. This uncertainty is at a level similar to the Cs fountain primary standard, while the potential stability for the ${}^{40}$Ca${}^{+}$ clock exceeds that of Cs.

We present a full quantum theory to study the transient evolution of photon pairs. We introduce a method which gives exact time-dependent solutions of the coupled quantum Langevin equations for a multilevel quantum particle driven by arbitrary time-dependent laser fields. The analytical solutions are used to develop a numerical code for computing exact time evolution of the two-photon correlation function. We analyze the effects of laser pulses sequence, pulse duration, chirping, and initial internal quantum states on the nonclassicality of the photon correlation through the violation of the Cauchy-Schwarz inequality. The results provide a promising possibility of controlling the generation of highly correlated photon pairs using tailored short laser pulses.

We study transitions between ground and low-energy excited states of heavy ions corresponding to $s-d$ single-electron transitions or $s^2-d^2$ double-electron transitions. The large nuclear charge $Z$ and significant change in angular momentum of electron orbitals make these transitions highly sensitive to a potential variation in the fine-structure constant $\alpha$. The transitions may be considered as candidates for laboratory searches for space-time variation of $\alpha$.

We have calculated the $s$-wave scattering length of all the even isotopes of calcium (Ca) and barium (Ba) in order to investigate the prospect of Bose-Einstein condensation (BEC). For Ca we have used an accurate molecular potential based on detailed spectroscopic data. Our calculations show that Ca does not provide other isotopes alternative to the recently Bose condensed ${}^{40}$Ca that suffers strong losses because of a very large scattering length. For Ba we show by using a model potential that the even isotopes cover a broad range of scattering lengths, opening the possibility of BEC for at least one of the isotopes.

Photoionization of an atom via interatomic correlations to $N$ neighboring atoms may be strongly enhanced due to constructive interference of quantum pathways. The ionization proceeds via resonant photoexcitation of a neighbor atom and subsequent interatomic Coulombic decay. The enhancement can scale with $N^2$, leading to “superenhanced photoionization.”

We show that conical intersections can be created in laboratory coordinates by dressing a parabolic trap for ultracold atoms or molecules with a combination of optical and static magnetic fields. The resulting ring trap can support single-particle states with half-integer rotational quantization and many-particle states with persistent flow. Two well-separated atomic or molecular states are brought into near resonance by an optical field and tuned across each other with an inhomogeneous magnetic field. Conical intersections occur at the nodes in the optical field.

The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum-information theory. Here, we completely characterize genuine multiparticle entanglement for four-qubit states diagonal in the cluster-state basis. In addition, we give a complete characterization of multiparticle entanglement for all five-qubit graph states mixed with white noise, for states diagonal in the basis corresponding to the five-qubit $\mathsf{Y}$-shaped graph, and for a family of graph states with an arbitrary number of qubits.

We examine the entanglement induced by an angular momentum coupling between two harmonic systems. The Hamiltonian corresponds to that of a charged particle in a uniform magnetic field in an anisotropic quadratic potential or, equivalently, to that of a particle in a rotating quadratic potential. We analyze both the vacuum and thermal entanglement, thereby obtaining analytic expressions for the entanglement entropy and negativity through the Gaussian state formalism. It is shown that vacuum entanglement diverges at the edges of the dynamically stable sectors, increasing with the angular momentum and saturating for strong fields, whereas at finite temperature entanglement is nonzero just within a finite field or frequency window and no longer diverges. Moreover, the limit temperature for entanglement is finite in the whole stable domain. The thermal behavior of the Gaussian quantum discord and its difference from the negativity is also discussed.

We observed an electromagnetically induced transparency signal in a four-level system with optically selected rubidium atoms at specific velocities in a room-temperature vaporized cell. Since the atoms behave like cold atoms in the selected atomic view, the observed signals coincide with a trapped atomic system. According to this result, we can observe Doppler-free signals, which correspond from 1.2 to 1.0 K in a Doppler-broadened medium. And the selected atoms have velocity components of ±(131 ± 3) MHz per wave number. Our experimental results can provide insight for research in cold media.

Molecular ion-pair states are analogs of electronic Rydberg states, but with the electron replaced by a much heavier ion. We calculate ab initio the long-range vibrational H${}^{+}$H${}^{-}$ ion-pair states in H${}_2$ for ungerade ${}^1{\Sigma }_u^{+}$ symmetry, corresponding to recent observations by Ekey and McCormack [Phys. Rev. A 84, 020501 (2011)]. The overall trends in the experiment are reproduced and many peaks can be assigned. The calculations yield interloper resonances corresponding to vibrational states trapped inside the barriers on the potential-energy curves 5,6${}^1{\Sigma }_u^{+}$.

We obtain analytically the exact nonretarded dispersive interaction energy between an atom and a perfectly conducting disk. We consider the atom in the symmetry axis of the disk and assume that the atom is predominantly polarizable in the direction of this axis. For this situation we discuss the finite-size effects on the corresponding interaction energy. We follow the recent procedure introduced by Eberlein and Zietal together with the old and powerful Sommerfeld's image method for nontrivial geometries. For the sake of clarity we present a detailed discussion of Sommerfeld's image method. Comparing our results for the atom-disk system with those recently obtained for an atom near a conducting plane with a circular aperture, we discuss the nonadditivity of the van der Waals interactions involving an atom and two complementary surfaces. We show that there is a given ratio $z/a$ between the distance $z$ from the atom to the center of the disk (aperture) and the radius of the disk $a$ (aperture) for which nonadditivity effects vanish. Qualitative arguments suggest that this quite unexpected result will occur not only for a circular hole, but for any other symmetric hole.

We present fully differential cross section (FDCS) calculations for electron-impact excitation-ionization of helium using the four-body distorted wave-exchange (4DWE) model. This model includes both the direct and exchange amplitudes, which account for the indistinguishability of the free electrons in the final state. The results of the 4DWE model are compared with absolute experimental results, and we find that the exchange amplitude has a minimal impact in determining the shape and magnitude of the FDCS.

The formulation of the parabolic adiabatic expansion approach to the problem of ionization of atomic systems in a static electric field, originally developed for the axially symmetric case [Phys. Rev. A 82, 023416 (2010)], is generalized to arbitrary potentials. This approach is used to rederive the asymptotic theory of tunneling ionization in the weak-field limit. In the atomic case, the resulting formulas for the ionization rate coincide with previously known results. In addition, the present theory accounts for the possible existence of a permanent dipole moment of the unperturbed system and, hence, applies to polar molecules. Accounting for dipole effects constitutes an important difference of the present theory from the so-called molecular Ammosov-Delone-Krainov theory. The theory is illustrated by comparing exact and asymptotic results for a set of model polar molecules and a realistic molecular ion HeH${}^{2+}$ in the $2p\sigma$ state.

We investigate the number fluctuations of spatially split many-boson systems employing a theorem about the maximally and minimally attainable variances of an observable. The number fluctuations of many-boson systems are given for different numbers of lattice sites and both mean-field and many-body wave functions. It is shown which states maximize the particle number fluctuations, both in lattices and double wells. The fragmentation of the states is discussed, and it is shown that the number fluctuations of some fragmented states are identical to those of fully condensed states.

We study the dynamics of vortex nucleation and lattice formation in a Bose–Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross–Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by R. A. Williams et al. [Phys. Rev. Lett. 104, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.

We describe a nonlinear optical mechanism that leads to a decrease of the degree of (transverse) spatial coherence of a laser beam as a function of propagation distance. This prediction is in direct contrast with those of the van Cittert-Zernike theorem, which applies to propagation through a linear, homogeneous material. The mechanism by which coherence is lost is the growth of small phase irregularities initially present on the laser wave front. We develop a detailed theoretical model of this effect and present experimental results that validate this model. The practical importance of this result is that by being able to controllably decrease the spatial coherence of a laser beam, one can limit the maximum intensity that is produced in its focal region. By limiting the intensity, one can prevent laser damage to bulk optical components or to sensitive photodetectors. This mechanism thus provides an alternative to current approaches of sensor protection based on optical power limiting.

We investigate the response of a harmonically confined mirror to an optical pulse in cavity optomechanics. We show that when the pulsed coupling strength takes the form of a chirped pulse, thermal fluctuations of the mirror can be significantly transferred to the cavity field. In addition, the frequency modulation of the pulse could enable a better cooling performance by suppressing the sensitivity of the dependence of detuning and pulse areas. Using numerical investigations, we find that the pulsed cooling is mainly limited by the cavity-field decay rate.

We provide an analytical proof of the entropic uncertainty relations presented by J. I. de Vicente and J. Sánchez-Ruiz [Phys. Rev. A 77, 042110 (2008)] and also show that the replacement of Eq. (27) by Eq. (29) in that reference introduces solutions that do not take fully into account the constraints of the problem, which in turn lead to some mistakes in their treatment.

We discuss a model of dipolar bosons trapped in a weakly coupled planar array of one-dimensional tubes. We consider the situation where the dipolar moments are aligned by an external field, and we find a rich phase diagram as a function of the angle of this field exhibiting quantum phase transitions between solid, superfluid, and supersolid phases. In the low energy limit, the model turns out to be identical to one describing quasi-one-dimensional superconductivity in condensed matter systems. This opens the possibility of using bosons as a quantum analog simulator of electronic systems, a scenario arising from the intricate relation between statistics and interactions in quasi-one-dimensional systems.