We have studied the quantum dissipative problem of a Gaussian wave packet under the influence of a harmonic potential. A phenomenological approach to dissipation is adopted in the light of the well-known model in which the environment is composed of a bath of noninteracting harmonic oscillators. As one of the effects of the coupling to the bath is the evolution of an initially pure wave packet into a statistical mixture, we estimate the characteristic time elapsed for this to occur for different regimes of temperature, damping, and also different initial states.

We systematically study the influence of laser intensities on the dissociation of $\mathrm{H}{}_2^{+}$ in strong laser fields by numerically solving the time-dependent Schrödinger equation. In Ti:sapphire infrared (IR) laser fields, $\mathrm{H}{}_2^{+}$ mainly dissociates along $1s{\sigma }_g$ and $2p{\sigma }_u$ states. The mixture of these dissociative states results in the laser-intensity-dependent electron asymmetric localization. When the dissociation process is dressed by a laser field with a very long wavelength, the potential surfaces $1s{\sigma }_g$ and $2p{\sigma }_u$ degenerate due to the Stark effect, hence the kinetic energy release is changed. When $\mathrm{H}{}_2^{+}$ is exposed to a strong ultraviolet (UV) pulse, $\mathrm{H}{}_2^{+}$ is pumped to several excited states by absorbing a few energetic photons, resulting in the molecular dissociation ending with several kinetic energy peaks. The discrepancy of simulation results from the numerical models with and without Born-Oppenheimer approximation are analyzed.

At the core of attosecond science lies the ability to generate laser pulses of subfemtosecond duration. In tabletop devices the process relies on high-harmonic generation, where a major challenge is to obtain high yields and high cutoff energies required for the generation of attosecond pulses. We develop a computational method that can simultaneously resolve these issues by optimizing the driving pulses using quantum optimal control theory. Our target functional, an integral over the harmonic yield over a desired energy range, leads to a remarkable cutoff extension and yield enhancement for a one-dimensional model H atom. The physical enhancement process is shown to be twofold: the cutoff extension is of classical origin, whereas the yield enhancement arises from increased tunneling probability. The scheme is directly applicable to more realistic models and, within straightforward refinements, also to experimental verification.

A multiphoton ionization process of He in intense extreme ultraviolet free-electron laser fields is investigated in a photon energy range of $h\mathit{v}=20.1-20.8\mathrm{eV}$ using shot-by-shot photoelectron spectroscopy. A photoelectron peak resulting from sequential double ionization of He due to five-photon absorption is observed around $h\mathit{v}=20.4$. Shot-by-shot analysis of photoelectron spectra shows that two-photon resonance to the $\mathrm{H}{\mathrm{e}}^{+}\left(2s{}^{2}S\right)$ state from the ${\mathrm{He}}^{+}$ ground state is responsible for the substantial enhancement of five-photon double ionization. Effective cross sections for two-photon absorption between the $1s$ and $2s$ states of ${\mathrm{He}}^{+}$ and for one-photon absorption from the ${\mathrm{He}}^{+}$ $2s$ state are obtained.

Particles with repulsive power-law interactions undergo a transition from a single to a double chain (zigzag) by decreasing the confinement in the transverse direction. We theoretically characterize this transition when the particles are classical dipoles, polarized perpendicularly to the plane in which the motion occurs, and argue that this transition is of first order, even though weakly. The nature of the transition is determined by the coupling between transverse and axial modes of the chain and contrasts with the behavior found in Coulomb systems, where the linear-zigzag transition is continuous and belongs to the universality class of the ferromagnetic transition. Our results hold for classical systems with power-law interactions $1/r^{\alpha }$ when $\alpha >2$ and show that structural transitions in dipolar systems and Rydberg atoms can offer a test bed for simulating the critical behavior of magnets with lattice coupling.

Thermalization in closed quantum systems can be understood either by means of the eigenstate thermalization hypothesis or the concept of canonical typicality. Both concepts are based on quantum-mechanical formalism, such as spectral properties of the eigenstates or entanglement between subsystems, respectively. Here we study instead the onset of thermalization of Bose particles in a two-band double-well potential using the truncated Wigner approximation. This allows us to use the familiar classical formalism to understand quantum thermalization in this system. In particular, we demonstrate that sampling of an initial quantum state mimics a statistical mechanical ensemble, while subsequent chaotic classical evolution turns the initial quantum state into the thermal state.

We consider an infinite periodic array of dielectric rods in vacuum with the aim to demonstrate three types of Bloch bound states in the continuum (BSCs): symmetry protected with a zero Bloch vector, embedded in one diffraction channel with nonzero Bloch vector, and embedded in two and three diffraction channels. The first and second types of the BSC exist for a wide range of material parameters of the rods, while the third occurs only at a specific value of the radius of the rods. We show that the second type supports the power flux along the array. In order to find BSCs we put forward an approach based on the expansion over the Hankel functions. We show how the BSC reveals itself in the scattering function when the singular BSC point is approached along a specific path in the parametric space.

The complexity of modeling light propagation in turbid media can be significantly simplified if one assumes it to be diffusive. This is, however, only valid after the light has traveled a sufficient distance so that the diffusion equation can be employed. So far, there has been no reliable way to determine this distance, despite the fact that the assumption is often applied in optics. The discrete nature of scattering events plays an important role in modeling propagation of weakly scattered light, so a continuum equation such as the diffusion equation cannot be used to describe this process. Electric field autocorrelation functions $g_1\left(\tau \right)$ of light transmitted through turbid colloidal samples are measured using diffusing wave spectroscopy and compared to Monte Carlo simulations in order to obtain a better estimation of the continuum limit. The two methods to calculate $g_1\left(\tau \right)$ from the simulated photon trajectories are compared; the first assumes the continuum limit by using the path-length distributions of photon trajectories, while the second considers the square momentum transfers and therefore accurately calculates $g_1\left(\tau \right)$ even if the detected signal is composed of weakly scattered light. The results of the two methods are used to determine the lengths of the shortest diffuse photon trajectories; they grow with the sample thickness and scattering anisotropy.

In this work we use geometrical optics to study the global behavior of the morphology of the wave fronts and their respective caustic associated with the refraction of a circular wave propagating between two given optical media with constant refraction indexes, which are separated by an arbitrary curve. For this purpose, we construct an expression for Stavroudis's general solution to the eikonal equation and obtain analytical equations for the wave fronts and caustic associated with a circular wave refracted by an arbitrary curve after being emitted by a point light source located at an arbitrary position immersed in a two-dimensional homogeneous optical medium. The caustic is computed by using the definitions of the critical and caustic sets of a two-dimensional (2D) map that describes the evolution of an arbitrary wave front associated with Stavroudis's general solution. We find that the caustics have only one branch. Our general results are applied to a conical refracting singular curve of the v-wedge type, which is called the 2D axicon. We find that when the point light source is lying on the optical axis of the axicon curve and near the apex, the virtual caustic locally has singularities of the cusp type, while the singularities associated with the reversion of the refracted wave fronts in the virtual caustic region are of the cusp and double-cusp with self-intersections types. We conclude that the caustic is associated with a local property of nonparallel light rays when the refracting curve is smooth locally and that the multiple-image formation process is associated with a global behavior between nonlocal light rays emanating from disjoint regions of the refracting curve, such that they intersect in the disjuncaustic region. In particular, we remark that caustic fields of the needle type do not exist in a 2D geometry and are limited to surfaces with a symmetry of infinitesimal rotations about the same axis in three dimensions.

We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. The method allows us to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments.

We study the collective spontaneous emission of a linear atomic chain excited by a single photon. The interaction between the atoms and the common vacuum field can significantly change the eigenenergy and the spontaneous emission rate of the system. Due to the dipole-dipole interactions, the system prepared in a single-photon timed Dicke state is the superposition of superradiant and subradiant eigenstates that can have a nonexponential decay dynamics. We can tune the frequency and linewidth of the superradiant and subradiant emission from a timed Dicke state by changing the direction of the atomic dipole moment or the atomic separation. In addition, the emission direction of the superradiant and subradiant photons also depends on the polarization of the atoms.

We propose a scheme for realizing a quantum nondemolition (QND) measurement of a small number of optical photons. Our scheme has two stages: First, we couple a propagating light pulse with fixed photon number to a trapped cold atomic gas within a cavity, such that the pulse is stored within a collective polariton mode. Second, a small-photon-number measurement is engineered by monitoring the cavity-transmission spectrum. Since the polariton mode profile is preserved during the process of detecting the spectrum, photon-number QND measurements could be achieved by retrieving the light pulse from the polariton mode. We also discuss a method which uses QND measurements to generate small-photon Fock states.

Long-range interactions between cold Rydberg atoms, which are used in many important applications, can be enhanced using Förster resonances between collective many-body states controlled by an external electric field. Here we report on the first experimental observation of highly resolved radio-frequency-assisted Förster resonances in a few cold Rb Rydberg atoms. We also observed radio-frequency-induced Förster resonances which cannot be tuned by a dc electric field. They imply an efficient transition from van der Waals to resonant dipole-dipole interaction due to Floquet sidebands of Rydberg levels appearing in the rf field. This method can be applied to enhance the interactions of almost arbitrary Rydberg atoms with large principal quantum numbers.

The striped phase exhibited by a spin-$1/2$ Bose-Einstein condensate with spin-orbit coupling is characterized by the spontaneous breaking of two continuous symmetries: gauge and translational symmetry. This is a peculiar feature of supersolids and is the consequence of interaction effects. We propose an approach to produce striped configurations with high-contrast fringes, making their experimental detection in atomic gases a realistic perspective. Our approach, whose efficiency is directly confirmed by three-dimensional Gross-Pitaevskii simulations, is based on the space separation of the two spin components into a two-dimensional bilayer configuration, causing the reduction of the effective interspecies interaction and the increase of the stability of the striped phase. We also explore the effect of a $\pi /2$ Bragg pulse, causing the increase of the fringe wavelength, and of a $\pi /2$ rf pulse, revealing the coherent nature of the order parameter in the spin channel.

We derive a class of time-dependent Bell inequalities in Wigner form under the assumption of locality in the framework of Kolmogorov's probability theory. We consider violation of the obtained inequalities for three cases: spin correlations in an external magnetic field, oscillations of neutral pseudoscalar mesons, and decays of a pseudoscalar into a fermion-antifermion pair.

We carried out a detailed high-precision study of Ag-like ${\mathrm{Nd}}^{13+}$ and ${\mathrm{Sm}}^{15+}$ and In-like ${\mathrm{Ce}}^{9+}$, ${\mathrm{Pr}}^{10+}$, ${\mathrm{Nd}}^{11+}$, ${\mathrm{Sm}}^{13+}$, and ${\mathrm{Eu}}^{14+}$ highly charged ions. These ions were identified to be of particular interest for the development of ultra-accurate atomic clocks, the search for variation of the fine-structure constant $\alpha$, and quantum information [Safronova et al., Phys. Rev. Lett. 113, 030801 (2014)]. The relativistic linearized coupled-cluster method was used for Ag-like ion calculations, and a hybrid approach that combines configuration interaction and a variant of the coupled-cluster method was used for the In-like ion calculations. Breit and QED corrections were included. Energies, transition wavelengths, electric-dipole, electric-quadrupole, electric-octupole, magnetic-dipole, magnetic-quadrupole, and magnetic-octupole reduced matrix elements, lifetimes, and sensitivity coefficients to $\alpha$ variation were calculated. A detailed study of various contributions was carried out to evaluate uncertainties of the final results. Energies for several similar “reference” ions where the experimental values are available were calculated and compared with experiment for further tests of the accuracy.

We present relativistic many-body calculations of the fine-structure splittings of the $n{}^{2}F$ Rydberg states of Rb $(n=4$–16) using both order-by-order relativistic many-body perturbation theory (RMBPT), up to a subset of fourth-order corrections, and relativistic equation-of-motion coupled-cluster methods, including singles, doubles, and an approximate treatment of valence triples. Good overall agreement is found with the measurements of Brandenberger et al. [Phys. Rev. A 65, 042510 (2002); Phys. Rev. A 81, 032515 (2010)] to better than the 1% level, which is our expected level of theoretical uncertainty due to omitted higher-order correlation effects. It is shown that the RMBPT of the fine-structure splittings is complex and slowly convergent, and that relativistic effects are enhanced compared with the RMBPT of the ionization energy of the ${}^2\mathrm{F}$ states. We also analyze smaller field-theoretic contributions to the fine-structure splittings from retardation and the radiative self-energy and vacuum polarization, finding them to enter at the 0.1% level.