We apply the time-dependent R-matrix method to investigate harmonic generation from Ne${}^{+}$ at a wavelength of 390 nm and intensities up to ${10}^{15}$ W cm${}^{-2}$. The $1s^{2}2s^{2}2p^4$ ${(}^3{P}^e,{}^1{D}^e,$ and ${}^1{S}^e)$ states of Ne${}^{2+}$ are included as residual-ion states to assess the influence of interference between photoionization channels associated with these thresholds. The harmonic spectrum is well approximated by calculations in which only the ${}^3{P}^e$ and ${}^1{D}^e$ thresholds are taken into account, but no satisfactory spectrum is obtained when a single threshold is taken into account. Within the harmonic plateau, extending to about 100 eV, individual harmonics can be suppressed at particular intensities when all Ne${}^{2+}$ thresholds are taken into account. The suppression is not observed when only a single threshold is accounted for. Since the suppression is dependent on intensity, it may be difficult to observe experimentally.

The multichannel recombination in high-order-harmonic generation (HHG) from the asymmetric molecular ion HeH${}^{2+}$ has been investigated by numerically solving the time-dependent Schrödinger equation based on the non-Born-Oppenheimer approximation. In this paper, not only has the physical image in harmonic emission from the asymmetric molecular ion been established, but also the distinguishing of recombination channels has been achieved. Moreover, our quantitative calculations show that the recombination channels from different electronic states make different contributions to HHG. Furthermore, by means of the time-frequency maps, electron-nuclear probability density distributions, and the laser dressed state picture, the physical mechanism of the multichannel recombination has been revealed.

We study bright solitons in the Gross-Pitaevskii equation as they are split and recombined in a low-energy system. We present analytic results determining the general region in which a soliton may not be split on a potential barrier and confirm these results numerically. Furthermore, we analyze the energetic regimes where quantum fluctuations in the initial center-of-mass position and momentum become influential on the outcome of soliton splitting and recombination events. We then use the results of this analysis to determine a parameter regime where soliton interferometry is practicable.

We introduce a mechanism to develop a turbulent flow in a spinor Bose-Einstein condensate, consisting in the stirring of a single line vortex by means of an external magnetic field. We find that density and velocity fluctuations have white-noise power spectra at large frequencies and that the energy spectrum obeys Kolmogorov 5/3 law in the turbulent region. As the stirring is turned off, the flow decays to an agitated nonequilibrium state that shows an energy bottleneck crossover at small length scales. We demonstrate our findings by numerically solving two-state spinor coupled three-dimensional Gross-Pitaevskii equations. We suggest that this mechanism may be experimentally implemented in spinor ultracold gases confined by optical traps.

To improve precision measurements made with atom interferometers, the effect of de Broglie wave-front curvature induced by a lens inside an atom interferometer is experimentally demonstrated and theoretically analyzed. Electrostatic lenses shift, magnify, and distort atom interference fringes, which modifies the phase and the contrast of the interference signals. Informed by these observations, an improved method is presented for analyzing measurements of atomic beam velocity distributions using phase choppers [W. F. Holmgren, I. Hromada, C. E. Klauss, and A. D. Cronin, New J. Phys. 13, 115007 (2011)].

We discuss theoretically the ground state of a Bose-Einstein condensate with attractive atom-atom interactions in a double-well trap as a starting point of Heisenberg-limited atom interferometry. The dimensionless parameter governing the quality of the ground state for this purpose is identified. The near degeneracy between the ground state and the first excited state severely curtails the prospects of the thermally prepared ground state in quantum metrology.

Conventional Glauber coherent states (CS) can be defined in several equivalent ways, e.g., by displacing the vacuum or, explicitly, by their infinite Poissonian expansion in Fock states. It is well known that these definitions become inequivalent if applied to finite $d$-level systems (qudits). We present a comparative Wigner-function description of the qudit CS defined (i) by the action of the truncated displacement operator on the vacuum and (ii) by the Poissonian expansion in Fock states of the Glauber CS truncated at $(d-1)$-photon Fock state. These states can be generated from a classical light by its optical truncation using nonlinear and linear quantum scissors devices, respectively. We show a surprising effect that a macroscopically distinguishable superposition of two qudit CS (according to both definitions) can be generated with high fidelity by displacing the vacuum in the qudit Hilbert space. If the qudit dimension $d$ is even (odd), then the superposition state contains Fock states with only odd (even) photon numbers, which can be referred to as the odd (even) qudit CS or Schrödinger's cat state. This phenomenon can be interpreted as an interference of a single CS with its reflection from the highest-energy Fock state of the Hilbert space, as clearly seen via phase-space interference of the Wigner function. We also analyze nonclassical properties of the qudit CS including their photon-number statistics and nonclassical volume of the Wigner function, which is a quantitative parameter of nonclassicality (quantumness) of states. Finally, we study optical tomograms, which can be directly measured in the homodyne detection of the analyzed qudit cat states and enable the complete reconstructions of their Wigner functions.

We experimentally investigate the quantum-correlated twin beams generated through stimulated nondegenerate four-wave mixing in the double-lambda atomic system. A 2.5-dB noise reduction of intensity difference with 18.4-GHz frequency difference at the cesium $D_1$ line is observed in a Cs vapor cell. The quantitative theoretical analysis reveals the experimental difficulty in getting high quantum correlation in Cs atoms because of the large hyperfine splitting of the ground states. However, it is favorable for obtaining quantum correlation in a wide range of pump detunings and relative long lengths of vapor cells. This quantum correlation provides a potential resource for possible coherent interfaces between atomic and solid-state systems due to its wavelength at the Cs $D_1$ line which lies well within the wavelength regime of the exciton emission from InAs quantum dots.

We predict that narrow beams, reflecting from flat subwavelength diffraction gratings, can focus. The effect is shown for the beams of electromagnetic radiation; however, it should be observable for beams of waves of arbitrary nature (microwaves, surface plasmons, and acoustic and mechanical waves). We present analytical estimations of the focusing performance obtained by multiple scattering calculations and demonstrate the focusing effect numerically for an optical system (reflections from an array of dielectric cylinders), using the finite-difference time-domain calculations.

We present a theoretical model to describe polarization-entanglement generation by spontaneous parametric down conversion in a transverse pump configuration. It takes into account the effect of a resonant microcavity for the pump beam and gives a direct link between the level of generated entanglement and the spatial profile of the pump beam. A pumping scheme leading to the generation of high quality Bell states is proposed.

A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures, and root infidelity to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we recover the Landau-Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare alternative uncertainty relations when using other known fidelity-based metrics.

The authors call attention to a previous work [Kelin Wang, Mang Feng, and Juhao Wu, Phys. Rev. A 52, 1419 (1995)] for quantum-mechanically studying the stability region of the Paul trap, where the calculation does not work for the case of zero dc voltage. But the ions can be confined experimentally at zero dc voltage which is understandable via the Mathieu equation. We present a quantum-mechanical study for such a case as a supplement.

We present theoretically and generate experimentally a vector optical field with parabolic symmetry of linear polarization. We extend the study to the modified parabolic-symmetry vector fields. We explore their tightly focusing behaviors, in particular, a modified parabolic-symmetry vector field can be tightly focused into a high-performance subwavelength sharp line.

We propose a mechanism of electron localization and molecular symmetry breaking in dissociative photoionization of the H${}_2$ molecule. The Coulomb field of the ejected electron can induce the transition of the remaining H${}_2$${}^{+}$ ion from the gerade ${}^2{\Sigma }_g^1\left(1s{\sigma }_g\right)$ to the ungerade ${}^2{\Sigma }_u^1\left(2p{\sigma }_u\right)$ electronic state when the nuclei in a bound vibrational state are near the outer turning point. The superposition of this process with a direct transition to the vibrational continuum should produce a nongerade ionic state, which results in observed asymmetry in the $p$-H ejection relative to the electron ejection direction at a small kinetic energy release.

We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported by Oxman and Khoury [Phys. Rev. Lett. 106, 240503 (2011)] is detailed and extended to qudits of different dimensions. The topological nature of the phase evolution and its restriction to fractional values are related to both the structure of the projective space of states and entanglement. For maximally entangled states of qudits with the same Hilbert-space dimension, the fractional geometric phases are the only ones attainable under local SU($d$) operations, an effect that can be experimentally observed through conditional interference.

We calculate correlation functions for a relativistic Einstein-Podolsky-Rosen–type experiment with massive Dirac particles. We take into account the influence of the Newton-Wigner localization and perform the calculations for a couple of physically interesting states. In particular, we show that localization inside detectors does not significantly affect correlation functions in the case when localization regions are macroscopic or in the case when Einstein-Podolsky-Rosen particles are in a definite momentum state (irrespectively of the size of localization regions).

A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A method for mapping the spin-squeezing inequalities for spin-$\frac{1}{2}$ particles to entanglement conditions for spin-$j$ particles is also presented. We apply our mapping to obtain a generalization of the original spin-squeezing inequality to higher spins. We show that, for large particle numbers, a spin-squeezing parameter for entanglement detection based on one of our inequalities is strictly stronger than the original spin-squeezing parameter defined in Sørensen et al. [Nature (London) 409, 63 (2001)]. We present a coordinate system independent form of our inequalities that contains, besides the correlation and covariance tensors of the collective angular momentum operators, the nematic tensor appearing in the theory of spin nematics. Finally, we discuss how to measure the quantities appearing in our inequalities in experiments.

In this work we present very accurate quantum-mechanical calculations of all bound pure vibrational states of the ${\mathrm{HD}}^{+}$ ion performed without the Born-Oppenheimer (BO) approximation. All three particles forming the system are treated on equal footing. The approach involves separating the center-of-mass motion from the laboratory-frame nonrelativistic Hamiltonian and expending the wave function of each considered state in terms of all-particle explicitly correlated Gaussian functions. The Gaussian exponential parameters are variationally optimized with the aid of the analytical energy gradient calculated with respect to these parameters. For each state the leading relativistic corrections are calculated as expectation values of the corresponding operators with the non-BO wave function of the state. The non-BO approach allows us to directly describe the charge asymmetry in ${\mathrm{HD}}^{+}$ which is due to the nuclear-mass asymmetry. The effect increases with the vibrational excitation and affects the values of the relativistic corrections. This phenomenon is the focus of the present study.

We measured by laser spectroscopy the isotope shifts between naturally occurring even isotopes of strontium ions for both the $5s{}^2{S}_{1/2}\to 5p{}^2{P}_{1/2}$ (violet) and the $4d{}^2{D}_{3/2}\to 5p{}^2{P}_{1/2}$ (infrared) dipole-allowed optical transitions. Fluorescence spectra were taken by simultaneous measurements on a two-component Coulomb crystal in a linear Paul trap containing ${10}^3$–${10}^4$ laser-cooled ${\mathrm{Sr}}^{+}$ ions. The isotope shifts are extracted from the experimental spectra by fitting the data with the analytical solution of the optical Bloch equations describing a three-level atom interacting with two laser beams. This technique allowed us to increase the precision with respect to previously reported data obtained by optogalvanic spectroscopy or fast atomic-beam techniques. The results for the $5s{}^2{S}_{1/2}\to 5p{}^2{P}_{1/2}$ transition are ${\nu }_{88}-{\nu }_{84}=+378\left(4\right)$ MHz and ${\nu }_{88}-{\nu }_{86}=+170\left(3\right)$ MHz, in agreement with previously reported measurements. In the case of the previously unexplored $4d{}^2{D}_{3/2}\to 5p{}^2{P}_{1/2}$ transition we find ${\nu }_{88}-{\nu }_{84}=-828\left(4\right)$ MHz and ${\nu }_{88}-{\nu }_{86}=-402\left(2\right)$ MHz. These results provide more data for stringent tests of theoretical calculations of the isotope shifts of alkali-metal-like atoms. Moreover, they simplify the identification and the addressing of ${\mathrm{Sr}}^{+}$ isotopes for ion frequency standards or quantum-information-processing applications in the case of multi-isotope ion strings.

We derive algebraic expressions for the atomic multipole moments $m_{k,q}\left(F\right)$ describing the steady-state polarization of an atomic ensemble with angular momentum $F$ in a static magnetic field of arbitrary direction and general multipole relaxation rates ${\Gamma }_q^{\left(k\right)}$. The longitudinal moments $m_{k,0}$ are given in terms of truncated continued fractions, while the transverse moments $m_{k,q\ne 0}$, representing the ensemble coherence, are given by products of truncated continued fractions. The special case of isotropic relaxation leads to particularly simple and elegant expressions. Our results are relevant for all domains of physics that consider the evolution of a spin system interacting with vector-type perturbations.