$4d^{-1}$ photoelectron and subsequent $N_{4,5}\mathit{OO}$ Auger electron spectra of Sb have been measured using synchrotron radiation. Features created by an open shell electronic structure of atomic Sb in the spectra have been interpreted using multiconfigurational Dirac-Fock calculations. The results are compared with the molecular Sb${}_4$ and the comparison shows that the relaxation pathways of the hole states in atomic and molecular Sb are very different, so that different groups of states are populated in the corresponding Auger spectra.

We propose a pump scheme for quantum circulations, including countercirculations for superposition states, of a spinor Bose-Einstein condensate. Our scheme is efficient and can be implemented within current experimental technologies and setups. It remains valid for nonclassical atomic states, such as pseudo-spin-squeezed states and maximally entangled $N$-particle Greenberger-Horne-Zeilinger ($|N,0\rangle +|0,N\rangle$) states. Moreover, it is capable of transforming several enhanced sensing protocols relying on reduced fluctuations from quantum correlation and entanglement of atomic internal states to enhanced measurement of spatial interference and rotation.

We describe standing-wave patterns induced by an attractive finite-ranged external potential inside a large Bose-Einstein Condensate (BEC). As the potential depth increases, the time-independent Gross-Pitaevskii equation develops pairs of solutions that have nodes in their wave function. We elucidate the nature of these states and study their dynamical stability. Although we study the problem in a two-dimensional BEC subject to a cylindrically symmetric square well potential of a radius that is comparable to the coherence length of the BEC, our analysis reveals general trends that are valid in two and three dimensions, independent of the symmetry of the localized potential well, and suggestive of the behavior in general short-range and large-range potentials. One set of nodal BEC wave functions resembles the single particle $n$-node bound-state wave function of the potential well, the other wave functions resemble the $n-1$-node bound-state wave function with a kink state pinned by the potential. The second state, though corresponding to the lower free energy value of the pair of $n$-node BEC states, is always unstable, whereas the first can be dynamically stable in intervals of the potential well depth, implying that the standing-wave BEC can evolve from being dynamically unstable to stable and back to unstable as the potential well is adiabatically deepened—a phenomenon that we refer to as “reentrant dynamical stability.”

We theoretically investigate the dynamics of two-photon excitation by correlated photons with energy anticorrelation in terms of how the excitation efficiency depends on incident pulse width. A three-level atomic system having an intermediate state is used to evaluate the efficiency of two-photon excitation. It is shown that for shorter pulses closer to a monocycle pulse the excitation efficiency by correlated photons is enhanced to become $100$ times as large as that by uncorrelated photons.

We develop the quantum theory of transverse angular momentum of light beams. The theory applies to paraxial and quasiparaxial photon beams in vacuum and reproduces the known results for classical beams when applied to coherent states of the field. Both the Poynting vector, alias the linear momentum, and the angular-momentum quantum operators of a light beam are calculated including contributions from first-order transverse derivatives. This permits a correct description of the energy flow in the beam and the natural emergence of both the spin and the angular momentum of the photons. We show that for collimated beams of light, orbital angular-momentum operators do not satisfy the standard commutation rules. Finally, we discuss the application of our theory to some concrete cases.

A general framework for regarding oracle-assisted quantum algorithms as tools for discriminating among unitary transformations is described. This framework is applied to the Deutsch-Jozsa problem and all possible quantum algorithms which solve the problem with certainty using oracle unitaries in a particular form are derived. It is also used to show that any quantum algorithm that solves the Deutsch-Jozsa problem starting with a quantum system in a particular class of initial, thermal equilibrium-based states of the type encountered in solution-state NMR can only succeed with greater probability than a classical algorithm when the problem size $n$ exceeds $~{10}^5.$

We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function and translate the problem in terms of the distribution of the eigenvalues of random matrices. We investigate the appearance of two phase transitions, one at a positive temperature, associated with very entangled states, and one at a negative temperature, signaling the appearance of a significant factorization in the many-body wave function. We also focus on the presence of metastable states (related to two-dimensional quantum gravity) and study the finite size corrections to the saddle point solution.

It is known that relative entropy of entanglement for an entangled state $\rho$ is defined via its closest separable (or positive partial transpose) state $\sigma$. Recently, it has been shown how to find $\rho$ provided that $\sigma$ is given in a two-qubit system. In this article we study the reverse process, that is, how to find $\sigma$ provided that $\rho$ is given. It is shown that if $\rho$ is of a Bell-diagonal, generalized Vedral-Plenio, or generalized Horodecki state, one can find $\sigma$ from a geometrical point of view. This is possible due to the following two facts: (i) the Bloch vectors of $\rho$ and $\sigma$ are identical to each other; (ii) the correlation vector of $\sigma$ can be computed from a crossing point between a minimal geometrical object, in which all separable states reside in the presence of Bloch vectors, and a straight line, which connects the point corresponding to the correlation vector of $\rho$ and the nearest vertex of the maximal tetrahedron, where all two-qubit states reside. It is shown, however, that these properties are not maintained for the arbitrary two-qubit states.

A mixed quantum-classical method aimed at the study of nonadiabatic dynamics in the presence of external electromagnetic fields is developed within the framework of time-dependent density functional theory. To this end, we use a trajectory-based description of the quantum nature of the nuclear degrees of freedom according to Tully’s fewest switches trajectories surface hopping, where both the nonadiabatic coupling elements between the different potential energy surfaces, and the coupling with the external field are given as functionals of the ground-state electron density or, equivalently, of the corresponding Kohn-Sham orbitals. The method is applied to the study of the photodissociation dynamics of some simple molecules in gas phase.

$3s_{1/2}$-$3p_{3/2}$ and $3p_{1/2}$-$3d_{3/2}$ transitions have been studied in potassiumlike ${\mathrm{W}}^{55+}$ through neonlike ${\mathrm{W}}^{64+}$ ions at the electron-beam ion trap facility in Livermore. The wavelengths of the lines have been measured in high resolution relative to well known reference lines from oxygen and nitrogen ions. Using the high-energy SuperEBIT electron-beam ion trap and an $R=44.3$ m grazing-incidence soft-x-ray spectrometer, the lines were observed with a cryogenic charge-coupled device camera. The wavelength data for the sodiumlike and magnesiumlike tungsten lines are compared with theoretical predictions for ions along the isoelectronic sequences.

We extend our analysis of two electrons on a sphere [Phys. Rev. A 79, 062517 (2009);  Phys. Rev. Lett. 103, 123008 (2009)] to electrons on concentric spheres with different radii. The strengths and weaknesses of several electronic structure models are analyzed, ranging from the mean-field approximation (restricted and unrestricted Hartree-Fock solutions) to configuration interaction expansion, leading to near-exact wave functions and energies. The Møller-Plesset energy corrections (up to third-order) and the asymptotic expansion for the large-sphere regime are also considered. We also study the position intracules derived from approximate and exact wave functions. We find evidence for the existence of a long-range Coulomb hole in the large-sphere regime and infer that unrestricted Hartree-Fock theory overlocalizes the electrons.

Processes for charge transfer into ${\mathrm{He}}^{2+}$ colliding with the atomic isotopes hydrogen (H), deuterium (D), and tritium (T) are theoretically studied at collision energies as low as 30 eV/amu. Probabilities and cross sections for electron capture into different shells of the projectile are calculated using an ab initio approach which solves the time-dependent Schrödinger equation. The results are interpreted in terms of radial and rotational couplings between molecular orbitals. The probabilities exhibit strong Stueckelberg oscillations for charge transfer into shells with the principal quantum numbers $n=2$ and 3 due to radial coupling mechanisms in specific ranges of the impact parameter. The total cross sections for charge transfer, evaluated for a given shell, differ by orders of magnitude, as different isotopes are used in the collisions. The isotope effect increases significantly for decreasing $n=3$, 2, and 1. This finding is attributed to the influence of the rotational coupling mechanism, which is strongly affected by the distance of closest approach between the collision partners.

We study the statics and dynamics of dark solitons in a cigar-shaped Bose-Einstein condensate confined in a double-well potential. Using a mean-field model with a noncubic nonlinearity, appropriate to describe the dimensionality crossover regime from one- to three-dimensional, we obtain branches of solutions in the form of single and multiple dark soliton states, and study their bifurcations and stability. It is demonstrated that there exist dark soliton states which do not have a linear counterpart and we highlight the role of anomalous modes in the excitation spectra. Particularly, we show that anomalous mode eigenfrequencies are closely connected to the characteristic soliton frequencies as found from the solitons’ equations of motion, and how anomalous modes are related to the emergence of instabilities. We also analyze in detail the role of the height of the barrier in the double-well setting, which may lead to instabilities or decouple multiple dark soliton states.

We consider a cavity optomechanical system consisting of a Bose-Einstein condensate (BEC) interacting with two counterpropagating traveling-wave modes in an optical ring cavity. In contrast to the more familiar case where the condensate is driven by the standing-wave field of a high-$Q$ Fabry-Pérot cavity we find that both symmetric and antisymmetric collective density side modes of the BEC are mechanically excited by the light field. In the semiclassical, mean-field limit where the light field and the zero-momentum mode of the condensate are treated classically the system is found to exhibit a rich multistable behavior, including the appearance of isolated branches of solutions (isolas). We also present examples of the dynamics of the system as input parameters such as the frequency of the driving lasers are varied.

We demonstrate that the optical response of a periodically modulated dynamic slab exhibits infinite resonances for frequencies $\omega =(\Omega /2)(2l+1)$, namely, odd multiples of one-half of the modulating frequency $\Omega$ of the dielectric function $\epsilon (t)$. These frequencies coincide partially with the usual condition of parametric amplification. However, the resonances occur only for certain normalized slab thicknesses $L_R$. These resonances follow from detailed numerical studies based on our recent paper [Zurita-Sánchez, Halevi, and Cervantes-González, Phys. Rev. A 79, 053821 (2009)]. As the thickness $L$ nearly matches a resonance thickness $L_R$, the amplitudes of counterpropagating modes in the slab obey a condition implying that both have the same modulus and their phases match a condition related to $L_R$ and the bulk wave vectors. When this condition is met, the electric field profile inside the slab is a superposition of standing waves with odd and even symmetries, and the reflection and transmission coefficients can reach great values and become infinite at exact resonance. Numerical simulations of the optical response are shown for a sinusoidal $\epsilon (t)$ with either moderate or strong modulation. As expected, as the modulation strength increases, higher-order harmonics $\omega -n\Omega$ ($n=0,\pm 1,\pm 2,\dots$) become more noticeable, and short-wavelength bulk modes contribute significantly. However, we found that, regardless of the excitation frequency $\omega =(\Omega /2)(2l+1)$, the dominant spectral component of the generated fields is $\Omega /2$. Also, as the excitation frequency increases, the parity of the standing waves is conserved.

We demonstrate that an intense single-cycle terahertz (THz) pulse can act as a time lens to phase modulate and compress a copropagating ultrashort laser pulse. By using the THz-induced phase modulation as a time lens and a glass plate as a group velocity dispersive element, we have compressed an unchirped $~165$ fs laser pulse to $~45$ fs.

Electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting are two phenomena that could be featured in a variety of three-level atomic systems. The considered phenomena, EIT and AT, are similar “looking” in the sense that they are both characterized by a reduction in absorption of a weak field in the presence of a stronger field. In this paper, we explicitly set the threshold of separation between EIT and AT splitting in a unified study of four different three-level atomic systems. Two resonances are studied and compared in each case. A comparison of the magnitudes of the resonances reveals two coupling-field regimes and two categories of three-level system.

High-order harmonic generation (HHG) from molecules produces spectra that are modulated by interferences that encode both the static structure and the electron dynamics initiated by interaction with the laser field. Using a midinfrared (mid-IR) laser at $1300$ nm, we are able to study the region of the harmonic spectrum containing such interferences in ${\mathrm{CO}}_2$ over a wide range of intensities. This allows for isolation and characterization of interference minima arising due to subcycle electronic dynamics triggered by the laser field, which had previously been identified but not systematically separated. Our experimental and theoretical results demonstrate important steps toward combining attosecond temporal and angstrom-scale spatial resolution in molecular HHG imaging.

We report on measurements performed on an apparatus aimed to study the Casimir force in the cylinder-plane configuration. The electrostatic calibrations evidence anomalous behaviors in the dependence of the electrostatic force and the minimizing potential upon distance. We discuss analogies and differences of these anomalies with respect to those already observed in the sphere-plane configuration. At the smallest explored distances we observe frequency shifts of non-Coulombian nature preventing the measurement of the Casimir force in the same range. We also report on measurements performed in the parallel-plane configuration, showing that the dependence on distance of the minimizing potential, if present at all, is milder than in the sphere-plane or cylinder-plane geometries. General considerations on the interplay between the distance-dependent minimizing potential and the precision of Casimir force measurements in the range relevant to detect the thermal corrections for all geometries are finally reported.

Photons can carry spin angular momentum (SAM) and orbital angular momentum (OAM), which can be used to realize a qubit system and a high-dimension system, respectively. This spin-orbital system is very suitable for implementing one-dimensional discrete-time quantum random walks. We propose a simple scheme of quantum walks on the spin-orbital angular momentum space of photons, where photons walk on the infinite OAM space controlled by their SAM. By employing the recent invention of an optical device, the so-called “$q$-plate,” our scheme is more simple and efficient than others because there is no Mach-Zehnder interferometer in the scheme.