We put forward a versatile and highly scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small number of simple optical components arranged in a multipath Mach-Zehnder-like configuration, where a weak coherent state is injected. Environmental effects (decoherence) are generated by a spatial light modulator, which introduces pure dephasing in the transverse spatial plane perpendicular to the direction of propagation of the light beam. By controlling the characteristics of this dephasing, one can explore a great variety of scenarios of quantum random walks: pure quantum evolution (ballistic spread), fast fluctuating environment leading to a diffusive classical random walk, and static disorder resulting in the observation of Anderson localization.

We report calculations of accurate high-lying energy resonances of the 4$s^2$4$p^2$ (${}^1{D}_2$)$nd$ and 4$s^2$4$p^2$ (${}^1{S}_0$)$nd$ Rydberg series originating from the $4s{}^{2}4p^3{}^2{P}_{1/2,3/2}^0$ and $4s{}^{2}4p^3{}^2{D}_{3/2,5/2}^0$ metastable states of Se${}^{+}$. The calculations are performed using the screening constant by unit nuclear charge (SCUNC) method up to $n=40$. The results obtained are compared with the first theoretical $R$-matrix calculations [McLaughlin and Ballance, J. Phys. B: At. Mol. Phys. 45, 095202 (2012)] and with recent ALS measurements [Esteves et al., Phys. Rev. A 84, 013406 (2011)]. Analysis of the present results is achieved in the framework of the standard quantum-defect theory and of the SCUNC procedure by calculating the effective charge. It is shown that the SCUNC method reproduces excellently the ALS results up to $n=25$. Our predicted data up to $n=40$ may be of great importance for the atomic physics community in connection with the modeling of plasma and astrophysical systems.

We use configuration interaction technique to calculate parity nonconservation in metastable Xe and Hg [proposal of the experiment in L. Bougas et al., Phys. Rev. Lett. 108, 210801 (2012)]. Both nuclear-spin-independent and nuclear-spin-dependent (dominated by the nuclear anapole moment) parts of the amplitude are considered. The amplitudes are strongly enhanced by the proximity of states of opposite parity.

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing an inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analyzed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the correctness and usefulness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the $\exp (-\gamma r_{12})$ term.

Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high-precision calculations for diatomic molecules. A compact one-dimensional integral representation is found, which is suited for the numerical evaluation. Together with recurrence relations, it makes possible the calculation of the two-center two-electron integral with arbitrary powers of electron distances. An alternative approach via the Taylor series in the internuclear distance is also investigated. Although numerically slower, it can be used in cases when recurrences lose stability. Separate analysis is devoted to molecular integrals with integer powers of interelectronic distances $r_{12}$ and the vanishing corresponding nonlinear parameter. Several methods of their evaluation are proposed.

We propose a method for the measurements of the ${}^{17}$O/${}^{16}$O isotope amount ratio in water, based upon the use of a pair of offset-frequency locked extended-cavity diode lasers at 1.39 $\mu$m. This method enables one to acquire absorption spectra with an extremely high fidelity, exploiting the highly accurate, absolute, and repeatable frequency axis. One of the two lasers, namely the so-called slave laser, is continuously scanned across a pair of H${}_2$${}^{16}$O and H${}_2$${}^{17}$O lines at 7183.5 cm${}^{-1}$ and it interacts with a water vapor sample inside a multiple reflections cell, thus producing absorption spectra with a signal-to-noise ratio of the order of 4000 for a detection bandwidth of 1 kHz. The determination of the isotope amount ratio is performed through a careful analysis of the acquired spectra, by using semiclassical line profiles. In this respect, the influence of the choice of the line shape model is investigated. The experimental reproducibility of the spectrometer has been carefully assessed by means of an Allan variance analysis. Finally, the application of the Kalman filtering technique has shown that a precision of 0.6‰ can be achieved, from repeated spectral acquisitions over a time span of 6000 s.

We calculate shallow three-body bound states in the universal regime, defined by Efimov, with inclusion of both scattering length and effective range parameters. We find corrections to the universal scaling laws for large binding energies. For narrow resonances we find a distinct nonmonotonic behavior of the threshold at which the lowest Efimov trimer merges with the three-body continuum. The origin of the three-body parameter is related to the two-body atom-atom interactions in a physically clear model. Our results demonstrate that experimental information from narrow Feshbach resonances and/or mixed systems are of vital importance to pin down the relation of two- and three-body physics in atomic systems.

The integral relations formalism introduced in [P. Barletta et al., Phys. Rev. Lett. 103, 090402 (2009); C. Romero-Redondo et al., Phys. Rev. A 83, 022705 (2011)] and designed to describe $1+N$ reactions is extended here to collision energies above the threshold for the target breakup. These two relations are completely general, and in this work they are used together with the adiabatic expansion method for the description of $1+2$ reactions. The neutron-deuteron breakup, for which benchmark calculations are available, is taken as a test of the method. The $s$-wave collision between the ${}^4$He atom and ${}^4$He${}_2$ dimer above the breakup threshold and the possibility of using soft-core two-body potentials plus a short-range three-body force will be investigated. Comparisons to previous calculations for the three-body recombination and collision dissociation rates will be shown.

We formulate the dynamics of electron-wave propagation in photoionization microscopy for nonhydrogenic atoms, based on a frame transformation between the spherical and parabolic coordinates used in Harmin's Stark-effect theory. An expression for the wave function for photoelectrons ejected from the nonhydrogenic atomic source has been derived. The spatial distributions of electron current densities or differential cross sections for Na are computed and compared to those from a recently developed coupled-channel theory. The difference between these two approaches is analyzed and attributed to the frame transformation for irregular wave functions. Since more detailed physical information can be extracted by comparing differential cross sections, rather than total cross sections, photoionization microscopy is proposed to test the Stark-effect theory.

We report on a study of the optical dipole force in a ladderlike three-level atomic system induced by the trains of few-cycle-pulse laser fields. In the present study, we consider the nonresonant as well as the chirped pulse excitation of three-level atoms. The so-called optical dipole force is calculated by numerically solving the force equation and the density matrix equations self-consistently beyond the rotating wave approximations. By analyzing the center-of-mass motion, it is shown that under nonresonant excitation, the optical dipole force induced by the trains of few-cycle pulses may be used for focusing and defocusing of atoms in an atomic beam. Moreover, we have demonstrated that the chirped nanosecond pulses may be used for both coherent population transfer and focusing or defocusing of atoms simultaneously.

We examine two approaches for significantly extending the velocity range of the optical bichromatic force (BCF), to make it useful for laser deceleration of atomic and molecular beams. First, we present experimental results and calculations for BCF deceleration of metastable helium using very large BCF detunings and discuss the limitations of this approach. We consider in detail the constraints, both inherent and practical, that set the usable upper limit of the BCF. We then show that a more promising approach is to utilize a BCF profile with a relatively small velocity range in conjunction with chirped Doppler shifts, to keep the force resonant with the atoms as they are slowed. In an initial experimental test of this chirped BCF method, helium atoms are slowed by $\sim$370 m/s using a BCF profile with a velocity width of $\lesssim$125 m/s. Straightforward scaling of the present results indicates that a decelerator for He* capable of loading a magneto-optical trap can yield a brightness comparable to a much larger Zeeman slower.

We have developed a simple heuristic method for determining the polarization of an optically pumped alkali-metal vapor. A linearly polarized probe beam traverses a vapor cell perpendicular to the pump-beam propagation direction, and the transmitted beam intensity is monitored for orthogonal linear polarizations. As the probe beam is scanned in frequency across the $D_1$ transition, its linear-polarization-dependent transmission can be used as a measure of the atomic orientation of the vapor. We analyze these transmission differences and their dependence on the alkali-metal number density in the vapor.

Orientation-dependent nonadiabatic molecular high-order-harmonic generation (MHOHG) is studied for the one-electron polar diatomic molecular ion HeH${}^{2+}$ exposed to short, linearly polarized, intense laser fields. The fully dimensional time-dependent Schrödinger equation is solved numerically. The resonance of excited states is maximal in the parallel orientation, while it is minimal in the perpendicular case for the nonsymmetric molecular ion. The resulting redshift and the overall intensity of MHOHG strongly depend on the electronic symmetry and charge transfer of the resonant excited states. These results are used to confirm the proposed four-step model in MHOHG involving intermediate resonance states.

We studied the high-harmonic generation of H${}_2$${}^{+}$ ions in an intense laser field by solving the time-dependent Schrödinger equation in prolate spheroidal coordinates. By analyzing the power spectra of the harmonics with the electric field polarized along the molecular axis, we found that the yield of the third-order harmonic drops by several orders of magnitude at a specified aligned angle between the laser polarization direction and the molecular axis. The laser polarization angle of the minimum depends on the internuclear distance and it disappears both in the separated- and united-atom limits. This infers that the minimum is associated with the molecular symmetry. By decomposing individual contributions of the $\sigma$ and $\pi$ states, we identified that the minimum is attributed to the cancellation of the induced dipole moments of the $\sigma$ and $\pi$ states, like a dynamical Cooper minimum, but the position of the minimum can be tuned by the laser intensity for a given internuclear distance.

We demonstrate a scheme for the preparation of molecular alignment and angular momentum orientation using a hybrid combination of two limits of Raman scattering. First a weak, impulsive pump pulse initializes the system via the nonresonant dynamic Stark effect. Then, having overcome the influence of the vacuum fluctuations, an amplification pulse selectively enhances the initial coherences by transient stimulated Raman scattering, generating alignment and angular momentum orientation of molecular hydrogen. The amplitude and phase of the resulting coherent dynamics are experimentally probed, indicating an amplification factor of $4.5$. An analytic theory is developed to model the dynamics.

The effective staggered coupling between two hyperfine ground states of ultracold atoms trapped in a one-dimensional optical lattice is produced by the Raman processes induced by additional light fields. The induced staggered coupling can be applied to quantum information processing and to the preparation of an antiferromagnetic state for a system of ultracold atoms with two hyperfine internal states.

We study theoretically Bose-Einstein condensates with polarized dipolar interactions in anisotropic traps. We map the parameter space by varying the trap frequencies and dipolar interaction strengths and find an irregular-shaped region of parameter space in which density-oscillating condensate states occur, with maximum density away from the trap center. These density-oscillating states may be biconcave (red-blood-cell-shaped), or have two or four peaks. For all trap frequencies, the condensate becomes unstable to collapse for sufficiently large dipole interaction strength. The collapse coincides with the softening of an elementary excitation. When the condensate mode is density oscillating, the character of the softening excitation is related to the structure of the condensate. We classify these excitations by linear and angular characteristics. We also find excited solutions to the Gross-Pitaevskii equation, which are always unstable.

We present a simple mechanism to produce vortices at any desired spatial locations in harmonically trapped Bose-Einstein condensates (BECs) with multicomponent spin states coupled to external transverse and axial magnetic fields. The vortices appear at the spatial points where the spin-transverse field interaction vanishes and, depending on the multipolar magnetic field order, the vortices can acquire different predictable topological charges. We explicitly demonstrate our findings, both numerically and analytically, by analyzing a 2D BEC via the Gross-Pitaevskii equation for atomic systems with either two or three internal states. We further show that by a spontaneous symmetry-breaking mechanism, vortices can appear in any spin component, unless symmetry is externally broken at the outset by an axial field. We suggest that this scenario may be tested using an ultracold gas of ${}^{87}$Rb occupying all three $F=1$ states in an optical trap.

We study the dynamics of ultracold bosons in a double-well potential within the two-mode Bose-Hubbard model by means of semiclassical methods. By applying a Wentzel-Kramers-Brillouin (WKB) quantization we find analytical results for the energy spectrum, which are in excellent agreement with numerically exact results. They are valid in the energy range of plasma oscillations, both in the Rabi and the Josephson regime. Adopting the reflection principle and the Poisson summation formula we derive an analytical expression for the dynamics of the population imbalance depending only on the few relevant parameters of the system. This allows us to discuss its characteristic dynamics, especially the oscillation frequency and the collapse and revival time, as a function of the model parameters, leading to a deeper understanding of Josephson physics. We find that our formulas match previous experimental observations.

The properties of an $F=1$ spinor Bose-Einstein condensate trapped in a double-well potential are discussed using both a mean-field two-mode approach and a two-site Bose-Hubbard Hamiltonian. We focus on the region of phase space in which spin effects lead to symmetry breaking of the system, favoring the spatial localization of the condensate in one well. To model this transition we derive, using perturbation theory, an effective Hamiltonian that describes $N/2$ spin singlets confined in a double-well potential.