We calculate x-ray line polarization degrees for cases with axial symmetry using a collisional-radiative magnetic-sublevel atomic kinetics model and the properties of multipole radiation fields. This approach is well suited for problems where the alignment is determined by the competition between many atomic processes. We benchmark this method against polarization measurements performed at the Livermore electron beam ion trap, and we study the 3-to-2 cascade effects on the polarization of 2-to-1 lines in He-like Fe.

The energy loss of swift $\mathrm{C}_n{}^{+}$ $(n=2–60)$ clusters moving with velocity $1\lesssim v\lesssim 4\mathrm{a.u.}$ $(0.3\lesssim E\lesssim 6\mathrm{MeV}∕\text{atom})$ through carbon, aluminum, and silicon thin foils has been calculated. We have considered that the carbon atomic ions resulting from the dissociation of these clusters feel Coulomb explosion, stopping, and wake forces due to the target polarization, as well as nuclear scattering with the target nuclei; the three former interactions depend on the ion charge state, which can change during its travel through the foil, due to electron-capture and -loss processes. Our calculation predicts an enhancement of the average energy loss of each dissociated atomic ion in comparison with the case of the same, but isolated, carbon atomic ion, which is small for velocities $v\sim 1\mathrm{a.u.}$ and becomes more important for higher velocities $(v\sim 4\mathrm{a.u.})$. The energy loss of the dissociated atomic ions generally increases with the size and packing level of the cluster, although in some cases it tends to a saturation value (when the number of constituents of the cluster increases) or it could even decrease with cluster size for certain situations (for projectiles with $1\lesssim v\lesssim 2\mathrm{a.u.}$ in aluminum or silicon targets). The vicinage effects in the energy loss also depend on the target nature, being more important for silicon and aluminum foils than for amorphous carbon foils. Our results show that in most cases the highest enhancement in energy loss should be expected for large clusters with high projectile velocities in aluminum or silicon targets. The experimental energy loss measured in carbon targets is well reproduced by our calculations.

A quantum-mechanical approach is employed to study the binding of two bare nuclei of equal charge in strong laser fields beyond the dipole approximation [Smirnova et al., Phys. Rev. Lett. 90, 243001 (2003)]. The role of nondipole effects in the binding mechanism is investigated, and it is found that, in spite of a significant contribution to the dynamics, the nondipole effects do not alter the characteristic lifetime of the system. The results are supported by classical calculations addressing the question of decoupling of the center-of-mass and relative motions.

We derive an effective nonpolynomial Schrödinger equation (NPSE) for self-repulsive or attractive BEC in the nearly one-dimensional cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. In addition to the usual linear cigar-shaped trap, where the periodic modulation emulates the action of an optical lattice (OL), the model may be also relevant to toroidal traps, where an ordinary OL cannot be created. For either sign of the nonlinearity, extended and localized states are found, in the numerical form [using both the effective NPSE and the full three-dimensional (3D) Gross-Pitaevskii equation] and by means of the variational approximation (VA). The latter is applied to construct ground-state solitons and predict the collapse threshold in the case of self-attraction. It is shown that numerical solutions provided by the one-dimensional NPSE are always very close to full 3D solutions, and the VA yields quite reasonable results too. The transition from delocalized states to gap solitons, in the first finite bandgap of the linear spectrum, is examined in detail, for the repulsive and attractive nonlinearities alike.

Through investigating the laser beam patterns at various wavelengths of the filamentation supercontinuum, abnormal wavelength dependence of the beam profile self-cleaning phenomenon is reported. It is founded that only the Stokes light has a nice spatial profile, while the patterns at the anti-Stokes side and the fundamental wavelength are not smooth and regular. Furthermore, by numerical simulations, we propose that the intensity perturbation of the initial beam can be considered as high order spatial modes superpositioning on a fundamental mode. The fundamental mode self-focuses, first producing a single mode profile on the axis. The higher order modes undergo strong diffraction constituting the energy reservoir. That gives rise to the overall “bad” spatial properties at the fundamental wavelength. On the other hand, the distortion of the beam patterns at the anti-Stokes side is due mainly to the interaction of the back part of the pulse with the plasma, which gives rise to anti-Stokes shifts. Finally, a possible application of our results to high beam quality tunable Ti: sapphire laser amplification is suggested.

We study tunneling between period-2 states of a parametrically modulated oscillator. The tunneling matrix element is shown to oscillate with the varying frequency of the modulating field. The effect is due to spatial oscillations of the wave function and the related interference in the classically forbidden region. The oscillations emerge already in the ground state of the oscillator Hamiltonian in the rotating frame.

Two distinct lasers are shown to permit controlled cooling of a three-level atomic system to a regime particularly useful for group-II atoms. Alkaline-earth-metal atoms are difficult to laser cool to the micro- or nanokelvin regime, but this technique exhibits encouraging potential to circumvent current roadblocks. Introduction of a sparse-matrix technique permits efficient solution of the master equation for the stationary density matrix, including the quantized atomic momentum. This overcomes long-standing inefficiencies of exact solution methods, and it sidesteps inaccuracies of frequently implemented semiclassical approximations. The realistic theoretical limiting temperatures are optimized over the full parameter space of detunings and intensities. A qualitative interpretation based on the phenomenon of electromagnetically induced transparency reveals dynamical effects due to photon-atom dressing interactions that generate non-Lorentzian line shapes. Through coherent engineering of an asymmetric Fano-type profile, the temperature can be lowered down to the recoil limit range.

Quantum trajectories in complex space in the framework of the quantum Hamilton-Jacobi formalism are investigated. For time-dependent problems, the complex quantum trajectories determined from the exact analytical wave function for the free Gaussian wave packet and the coherent state in the harmonic potential are used to demonstrate that the information transported by the particles in the complex space can be used to synthesize the time-dependent wave function on the real axis. For time-independent problems, the exact complex quantum trajectories for the Eckart potential are obtained by numerically integrating the equations of motion. The unusual structure of the total potential (the sum of the classical and the quantum potentials) for the stationary states for the Eckart potential is pointed out. The variations of the complex-valued kinetic energy, classical potential, and quantum potential along the complex quantum trajectories are analyzed. This paper not only analyzes complex quantum trajectories for time-dependent and time-independent systems but also provides a unified description for complex quantum trajectories for one-dimensional problems in the quantum Hamilton-Jacobi formalism.

We report the forbidden $6s^2{}^{1}S_0\to 6s5d{}^{3}D_1$ magnetic-dipole transition amplitude computed using multireference Fock-space coupled-cluster theory. Our computed transition matrix element $(1.34\times {10}^{-4}){\mu }_B$ is in excellent agreement with the experimental value $(1.33\times {10}^{-4}){\mu }_B$. This value in combination with other known quantities will be helpful in determining the parity-nonconserving amplitude for the $6s^2{}^{1}S_0\to 6s5d{}^{3}D_1$ transition in atomic Yb. To our knowledge, this calculation is the most accurate to date, and can be very important in the search for physics beyond the standard model. We further report the $6s6p{}^{3}P_0\to 6s6p{}^{1}P_1$ and $6s5d{}^{3}D_1\to 6s6p{}^{3}P_0$ transition matrix elements, which are also in good agreement with the earlier theoretical estimates.

We present a relativistic calculation of the hyperfine structure in pionic and kaonic atoms. A perturbation method has been applied to the Klein-Gordon equation to take into account the relativistic corrections. The perturbation operator has been obtained via a multipole expansion of the nuclear electromagnetic potential. The hyperfine structure of pionic and kaonic atoms provides an additional term in the quantum electrodynamics calculation of the energy transition of these systems. Such a correction is required for a recent measurement of the pion mass.

The behavior of the partial photoionization amplitudes with a given orbital angular momentum $l$ in the complex plane in resonances is studied. In the autoionization resonances the trajectory of the amplitude in the complex plane corresponds to a circle. With increasing photoelectron energy the amplitude moves about a circle in the counterclockwise direction. The new expressions for the partial amplitudes in the resonance are proposed which are similar to the Fano form but contain the “partial” profile parameters which are connected with the Fano parameter $q$ by a simple relation. In the giant dipole resonances the amplitudes in the complex plane also move about a circle in the counterclockwise direction provided the Coulomb phase is excluded from the amplitude. In the correlational resonances created by channel interactions with the giant dipole resonance the trajectories of the amplitudes acquire a loop about which the amplitudes move in the counterclockwise direction. Very similar behavior of partial photoionization amplitudes in the complex plane is demonstrated also for the dipole transitions from the $K$ shells of the ${\mathrm{N}}_2$ molecule in the ${\sigma }^{*}$ shape resonance.

We develop a theoretical approach for the dynamics of Rydberg excitations in ultracold gases,with a realistically large number of atoms. We rely on the reduction of the single-atom Bloch equations to rate equations, which is possible under various experimentally relevant conditions. Here, we explicitly refer to a two-step excitation scheme. We discuss the conditions under which our approach is valid by comparing the results with the solution of the exact quantum master equation for two interacting atoms. Concerning the emergence of an excitation blockade in a Rydberg gas, our results are in qualitative agreement with experiment. Possible sources of quantitative discrepancy are carefully examined. Based on the two-step excitation scheme, we predict the occurrence of an antiblockade effect and propose possible ways to detect this excitation enhancement experimentally in an optical lattice, as well as in the gas phase.

We report theoretical investigations of the tomographic procedure suggested by Itatani et al. [Nature (London) 432, 867 (2004)] for reconstructing highest occupied molecular orbitals (HOMOs) using high-order harmonic generation (HHG). Due to the limited range of harmonics from the plateau region, we found that even under the most favorable assumptions, it is still very difficult to obtain accurate HOMO wave functions using the tomographic procedure, but the symmetry of the HOMOs and the internuclear separation between the atoms can be accurately extracted, especially when lasers of longer wavelengths are used to generate the HHG. Since the tomographic procedure relies on approximating the continuum wave functions in the recombination process by plane waves, the method can no longer be applied upon the improvement of the theory. For future chemical imaging with lasers, we suggest that one may want to focus on how to extract the positions of atoms in molecules instead, by developing an iterative method such that the theoretically calculated macroscopic HHG spectra can best fit the experimental HHG data.

We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation and vibrational modes of localized particles. We show that for a small number of particles the localization is similar for bosons and fermions. Moreover, independent of the range of the interaction, the quantum mechanical spectrum at large internal angular momenta can be understood by vibrational modes of localized particles.

Ionization phenomena are shown to modify the soliton propagation dynamics of high-peak-power laser pulses in hollow-core photonic-crystal fibers (PCFs). Based on the numerical solution of the pulse-evolution equation for a high-peak-power laser field in an ionizing gas medium in a hollow PCF, we demonstrate that hollow PCFs filled with gases having high ionization potentials $I_p$ can support soliton transmission regimes for gigawatt femtosecond laser pulses. In hollow PCFs filled with low-$I_p$ gases, on the other hand, the ionization-induced change in the refractive index of the gas leads to a blueshifting of soliton transients, pushing their spectrum beyond the point of zero group-velocity dispersion, thus preventing the formation of stable high-peak-power solitons.

A broadband squeezed vacuum photon field is characterized by a complex squeezing function. We show that by controlling the wavelength dependence of its phase it is possible to change the dynamics of the atomic polarization interacting with the squeezed vacuum. Such a phase modulation effectively produces a finite range temporal interaction kernel between the two quadratures of the atomic polarization yielding the change in the decay rates as well as the appearance of additional oscillation frequencies. We show that decay rates slower than the spontaneous decay rate can be achieved even for a squeezed bath in the classical regime. For “piecewise linear” and quadratic phase modulations the power spectrum of the scattered light exhibits narrowing of the central peak due to the modified decay rates. For strong phase modulations, side lobes appear symmetrically around the central peak reflecting additional oscillation frequencies.

We study the appearance of resonantly coupled optical modes, optical necklaces, in Anderson-localized one-dimensional random systems with resonant layers. It has been stated that the increasingly low probability of their appearance in thick samples should reduce the theoretically predicted number of coupled resonances, leading to the formation of optimal-order necklaces (OONs). Here we examine through transmission phase studies how the optimal order $m^{*}$, the number of resonances in a necklace, shifts gradually toward higher orders with increasing sample size. We present a model for OON formation in random samples with resonant layers and derive an empirical formula that predicts $m^{*}$. We discuss the situation when in a sample length $L$ the number of resonances degenerate in energy exceeds the optimal one, and show how the extra resonances are pushed out to the miniband edges of the necklace, reducing the order of the latter always by multiples of two.

A perturbation theoretic approach is proposed as an efficient characterization tool for a tapered fiber coupled ultrahigh-quality factor $\left(Q\right)$ toroidal microcavity with a small inverse aspect ratio. The Helmholtz equation with an assumption of quasi-TE/TM modes in local toroidal coordinates is solved via a power series expansion in terms of the inverse aspect ratio and the expanded eigenmode solutions are further manipulated iteratively to generate various characteristic metrics of the ultrahigh-$Q$ toroidal microcavity coupled to a tapered fiber waveguide. Resonance wavelengths, free spectral ranges, cavity mode volumes, phase-matching conditions, and radiative $Q$ factors are derived along with a mode characterization given by a characteristic equation. Calculated results are in excellent agreement with full vectorial finite-element simulations. The results are useful as a shortcut to avoid full numerical simulation, and also render intuitive insight into the modal properties of toroidal microcavities.

We show that with an appropriate surface modification, a slab of photonic crystal can be made to allow wave transmission within the photonic band gap. Furthermore, negative refraction and all-angle negative refraction (AANR) can be achieved by this surface modification in frequency windows that were not realized before in two-dimensional photonic crystals [C. Luo et al., Phys. Rev. B 65, 201104 (2002)]. This approach to AANR leads to different applications in flat lens imaging. Previous flat lens using photonic crystals requires object-image distance $u+v$ less than or equal to the lens thickness $d$, $u+v\sim d$. Our approach can be used to design a flat lens with $u+v=\sigma d$ with $\sigma \gg 1$, thus being able to image large and/or far away objects. Our results are confirmed by finite-difference time-domain simulations.

We have studied the space-time entangled Stokes-anti-Stokes photons generated from a three-level system. In the presence of counterpropagating pump and control lasers, paired Stokes and anti-Stokes fields are spontaneously emitted into opposite directions. The two-photon wave packet is generally a convolution of the phase matching and the third-order nonlinear susceptibility and the feature of the joint temporal correlation is determined by either of them. When the phase matching plays a major role in determining the spectral width of biphotons, the two-photon interference exhibits as conventional type-II spontaneous parametric down-conversion (SPDC). However, if the spectral width of paired photons is determined by the third-order nonlinear susceptibility, two types of four-wave mixings (FWMs) destructively interfere and contribute to the two-photon coincidences. In such a case, the coincidence counting rate appears as a damped Rabi oscillation and exhibits the photon antibunching. The oscillation frequency is equal to the effective Rabi frequency. We have also discussed polarization-entanglement generation in a three-state case. It is found that if the phase matching is crucial in determining the properties of paired Stokes and anti-Stokes photons, the generated state is the same as the degenerate type-II SPDC. However, if the spectral width is mainly controlled by the resonant linewidths in the third-order nonlinearity, one can select one FWM to produce polarization-entangled biphotons, but paired photons from the other FWM process is nonpolarization entangled.