We investigate the influence of atomic motion on precision Rabi spectroscopy of ultracold fermionic atoms confined in a deep one-dimensional optical lattice. We analyze the spectral components of longitudinal sideband spectra and present a model to extract information about the transverse motion and sample temperature from their structure. Rabi spectroscopy of the clock transition itself is also influenced by atomic motion in the weakly confined transverse directions of the optical lattice. By deriving Rabi flopping and Rabi line shapes of the carrier transition, we obtain a model to quantify trap-state-dependent excitation inhomogeneities. The inhomogeneously excited ultracold fermions become distinguishable, which allows $s$-wave collisions. We derive a detailed model of this process and explain observed density shift data in terms of a dynamic mean-field shift of the clock transition.

Differential, integral, and momentum-transfer cross sections for the elastic scattering of electrons by ${\text{SiF}}_2$ have been calculated for the incident electron energy range of 0–10 eV. These results are obtained by using the $R$-matrix method. The close-coupling expansion of the wave function of the scattering used in the $R$-matrix formalism includes the lowest six target states. We have also calculated the excitation cross sections from the ground state $X{{}^{1}A}_1$ to the first five excited states ${{}^{3}B}_1$, ${{}^{1}B}_1$, ${{}^{3}B}_2$, ${{}^{3}A}_1$, and ${{}^{1}B}_2$ from their respective thresholds up to 10 eV. The target states are represented by configuration-interaction wave functions that account for correlation effects. We detect a shape resonance in ${{}^{2}B}_1$ symmetry and a core-excited shape resonance in ${{}^{2}A}_2$ symmetry. We have included up to $g$-partial waves in the scattering calculation. For this polar molecule, higher partial wave contribution is accounted for by invoking a Born-closure approximation. Elastic cross-section results are compared with the other theoretical works available.

We numerically investigate the dynamics of recollision of an electron in high-order harmonic generation (HHG) for an H atom and a molecular ion $\text{H}_2{}^{+}$ using a short (ten optical cycles), and intense $\left(I_0\ge {10}^{14}\text{W}/{\text{cm}}^2\right)$, $z$-polarized linear laser pulse with wavelength 800 nm by accurately solving the three-dimensional time-dependent Schrödinger equation. A time-frequency analysis obtained via Gabor transforms is employed to identify electron recollision and recombination times responsible for the generation of harmonics. We find that the HHG spectra are mainly attributed to the recollision of an inner electron wave packet with the parent ion in agreement with the classical recollision model. A time delay of the electron recollision occurs between wave packets in inner and outer regions, near to and far from the parent ion, due to different phase of the acceleration (as well as dipole velocity) of the electron. Inner wave packets at recollision contain mainly short and long trajectories whereas outer wave packets contain only single trajectories. Lower-order harmonics are generated mainly by single recollisions near field extrema, i.e., in strong electric fields whereas higher-order harmonics are generated by double trajectories with different intensities. In the case of $\text{H}_2{}^{+}$ at a critical nuclear distance for charge resonance enhanced ionization, we also find that HHG mainly comes from contributions of the inner electron wave packet, but with more complex recollision trajectories due to the presence of more than one Coulomb center. Triple recollision trajectories are shown to occur generally for the latter.

The alignment-dependent nonsequential double ionization (NSDI) of diatomic molecule ${\text{N}}_2$ in intense fields is studied using the $S$-matrix theory. Our results show that the valence orbitals play an important role in alignment-dependent NSDI process: in addition to the contribution from the outmost $1{\pi }_u$ orbital of $\text{N}_2{}^{+}$ in all the alignment angles, the suboutmost $3{\sigma }_g$ orbital plays an important role at small alignment angles, which is more pronounced at high intensity. Taking into account the experimental alignment condition, the ratio of $\text{N}_2{}^{2+}:\text{N}^{+}{}_2$ for the parallel alignment to that for perpendicular alignment obtained, including the $3{\sigma }_g$ orbital, is closer to the experimental result than that without considering this orbital.

We study the temperature dependence of optical properties of dilute gases of alkali-metal atoms in the state with Bose-Einstein condensates. The description is constructed in the framework of the microscopic approach that is based on the Green’s-functions formalism. We find the expressions for the scalar Green’s functions describing a linear response of a condensed gas to a weak external electromagnetic field (laser). It is shown that these functions depend on the temperature, other physical properties of a system, and on the frequency detuning of a laser. We compare the relative contributions of the condensate and noncondensate particles in the system response. The influence of the temperature effects is studied by the example of two- and three-level systems. We show that in these cases, which are most commonly realized in the present experiments, the group velocity and the absorption rate of pulses practically do not depend on the gas temperature in the region from the absolute zero to the critical temperature. We discuss also the cases when the temperature effects can play a significant role in the phenomenon of slowing of electromagnetic pulses in a gas of alkali-metal atoms with Bose-Einstein condensates.

A single down-spin fermion with an attractive zero-range interaction with a Fermi sea of up-spin fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wave function in the molecular limit, we determine the critical value for the polaron-to-molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof’ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirotzek et al. [Phys. Rev. Lett. 102, 230402 (2009)]. In addition, we calculate the contact coefficient of the strongly imbalanced gas, using the adiabatic theorem of Tan and discuss the implications of the polaron-to-molecule transition for the phase diagram of the attractive Fermi gas at finite imbalance.

It has been known for some time that simple “optically bound” chains of dielectric microparticles can form in a counter propagating Gaussian beam optical trap. Here we report experimental observations of more complex trapped states, which do not reflect the underlying symmetry of the optical beam trap they are confined in. We discuss both stationary off-axis trapping and dynamic motion. We confirm the results using a rigorous Mie scattering model and also give a physical explanation for these static and dynamic off-axis trapped states.

The goal of comparison is to reveal the difference of compared objects as fast and reliably as possible. In this paper we formulate and investigate the unambiguous comparison of unknown quantum measurements represented by nondegenerate sharp positive operator valued measures. We distinguish between measurement devices with a priori labeled and unlabeled outcomes. In both cases we can unambiguously conclude only that the measurements are different. For the labeled case it is sufficient to use each unknown measurement only once and the average conditional success probability decreases with the Hilbert space dimension as $1/d$. If the outcomes of the apparatuses are not labeled, then the problem is more complicated. We analyze the case of two-dimensional Hilbert space. In this case single shot comparison is impossible and each measurement device must be used (at least) twice. The optimal test state in the two-shot scenario gives the average conditional success probability 4/9. Interestingly, the optimal experiment detects unambiguously the difference with nonvanishing probability for any pair of observables.

A generalized time-dependent perturbation theory is derived for superoperators. Instead of using the “standard” breakup of the Hamiltonian into a known zeroth order term and a correction, we use the approximate superpropagator to define the correction superoperator which is then used to obtain a series representation of the exact Liouville operator. The theory reduces to known limits and may be used for a perturbation expansion of classical Wigner and Husimi dynamics as well as for recent phase-space-based semiclassical approximations. The theory is demonstrated for a model quartic potential.

From the local force equation of quantum mechanics and by expanding the interacting wave function in terms of the noninteracting Kohn-Sham wave function, we derive differential equations defining the local Hartree-exchange and the local correlation potential of density functional theory. The derived equations apply to time-dependent as well as to time-independent problems. Approximations to the correlation part of the interacting wave function result in approximations to the effective potential which take the Hartree-exchange forces into account exactly. Under some assumptions, we find explicit expressions for the local effective potential. We analyze the local Hartree-exchange-only approximation for the ground and the first two excited states of an exactly solvable one-dimensional model system of helium and compare the results to an optimized effective potential approach.

We characterize the long-range dipolar scattering in two dimensions. We use the analytic zero energy wave function including the dipolar interaction; this solution yields universal dipolar scattering properties in the threshold regime. We also study the semiclassical dipolar scattering and find universal dipolar scattering for this energy regime. For both energy regimes, we discuss the validity of the universality and give physical examples of the scattering.

We investigate the scattering of intense laser radiation on free electrons using a semiclassical relativistic approach. The laser field is described as an ideal pulse with a finite duration, a fixed direction of propagation, and indefinitely extended in the plane perpendicular to it. This allows the use of Volkov solutions and leads to a transition amplitude which is a product of a three-dimensional delta function with a linear combination of three one-dimensional integrals that we evaluate numerically. We give the general expression of the emitted photon spectrum as a function of frequency and direction valid for any initial geometry of the electron-laser beam scattering and for arbitrary shape, duration, and polarization of the laser pulse averaged over the initial electron spin and summed over the emitted photon and ejected electron polarizations. At a fixed photon scattering angle, one obtains a continuous frequency distribution with a succession of maxima located near the discrete values corresponding to the monochromatic case. We present results for head-on collisions and circularly polarized laser pulses. Our figures illustrate the dependence of the photon spectrum on pulse parameters (duration, shape, and maximum intensity) and the role of the initial electron energy. For a few-cycle linearly polarized pulse we also explore the effect of the carrier-envelope phase.

We study the influence of gain on negative refraction and super-resolution in transparent resonant metal-dielectric photonic band gap structures in the visible and near infrared ranges. We find that while the introduction of gain can compensate for losses caused by the excitation of surface waves, it also improves the resolving characteristics of the lens and leads to gain-tunable super-resolution.

We report the observation of trielectronic recombination with simultaneous excitation of a $K$-shell and an $L$-shell electron, hence involving three active electrons. This process was identified in the x-ray emission spectrum of recombining highly charged Kr ions. An energy resolution three times higher than any reported for this collision energy range around 10 keV resulted in the separation of the associated lines from the stronger dielectronic resonances. For ${\text{Kr}}^{30+}$, intershell trielectronic recombination contributions of nearly 6% to the total resonant photorecombination rate were found.

We propose methods to create fractional vortices in the cyclic state of an $F=2$ spinor Bose-Einstein condensate by manipulating its internal spin structure using pulsed microwave and laser fields. The stability of such vortices is studied as a function of the rotation frequency of the confining harmonic trap both in pancake- and cigar-shaped condensates. We find a range of parameters for which the so-called $\frac{1}{3}$ vortex state is energetically favorable. Such fractional vortices could be created in condensates of ${}^{87}\text{R}\text{b}$ atoms using current experimental techniques facilitating probing of topological defects with non-Abelian statistics.

Quantum fluctuations of an electromagnetic vacuum are investigated in a half-space bounded by a perfectly reflecting plate by introducing a probe described by a charged wave-packet distribution in time direction. The wave-packet distribution of the probe enables one to investigate the smearing effect upon the measured vacuum fluctuations caused by the quantum nature of the probe particle. It is shown that the wave-packet spread of the probe particle significantly influences the measured velocity dispersion of the probe. In particular, the asymptotic late-time behavior of its $z$ component $⟨\Delta v_z^2⟩$ for the wave-packet case is quite different from the test point-particle case ($z$ is the coordinate normal to the plate). The result for the wave packet is $⟨\Delta v_z^2⟩\sim 1/{\tau }^2$ at late time ($\tau$ is the measuring time), instead of the reported late-time behavior $⟨\Delta v_z^2⟩\sim 1/z^2$ for a point-particle probe. This result can be quite significant for further investigations on the measurement of vacuum fluctuations.

We calculate the quantum discord between two free modes of a scalar field, which start in a maximally entangled state and then undergo a relative constant acceleration. In a regime where there is no distillable entanglement due to the Unruh effect, we show that there is a finite amount of quantum discord, which is a measure of purely quantum correlations in a state over and above quantum entanglement. Even in the limit of infinite acceleration of the observer detecting one of the modes, we provide evidence for a nonzero amount of purely quantum correlations. We discuss our result in the context of secure quantum communications involving eavesdroppers in noninertial frames.

The necessary and sufficient conditions for minimization of the generalized rate error for discriminating among $N$ pure qubit states are reformulated in terms of Bloch vectors representing the states. For the direct optimization problem, an algorithmic solution to these conditions is indicated. A solution to the inverse optimization problem is given. General results are widely illustrated by particular cases of equiprobable states and $N=2,3,4$ pure qubit states given with different prior probabilities.

Recently, the $O\left(\alpha \right)$ and $O\left({\alpha }^3\text{ln}\alpha \right)$ radiative corrections to the orthopositronium lifetime have been presented in closed analytical form, in terms of basic irrational numbers that can be evaluated numerically to arbitrary precision [B. A. Kniehl, A. V. Kotikov, and O. L. Veretin, Phys. Rev. Lett. 101, 193401 (2008)]. Here, we present the details of this calculation and reveal the nature of these new constants. We also list explicit transformation formulas for generalized polylogarithms of weight four, which may be useful for other applications.

Target ionization and projectile charge changing were investigated for 20–500 keV/u ${\text{C}}^{q+}$, ${\text{O}}^{q+}+\text{He}$ $\left(q=1–3\right)$ collisions. Double- to single-ionization ratios $R_{21}$ of helium associated with no projectile charge change (direct ionization), single-electron capture, and single-electron loss were measured. The cross-section ratio $R_{21}$ depends strongly on the collision velocity $v$, the projectile charge state $q$, and the outgoing reaction channel. Meanwhile, a model extended from our previous work [J. X. Shao, X. M. Chen, and B. W. Ding, Phys. Rev. A 75, 012701 (2007)] is presented to interpret the above-mentioned dependences. Good agreement is found between the model and the experimental data.