We develop a Floquet based formalism which describes a process of the generation harmonics of in an atom driven by a laser field. Using this formalism, we show that several harmonics are strongly enhanced in the spectrum when the laser frequency is such that a multiphoton resonance occurs between the initial state and a quasienergy state. We illustrate these findings by a numerical calculation of the harmonics generation in the potassium and rubidium atoms driven by a laser in the near-infrared energy range. The present formalism is also applicable when the initial state is a coherent superposition of several field-free atomic states.

We numerically obtain stationary rings of vortices in pancake-shaped Bose-Einstein condensates confined in a three-dimensional nonrotating trap. For this purpose we use a static axisymmetric trapping potential that can sustain locally stable off-axis vortices. We analyze the maximum number of vortices the system can host as a function of the number of particles. We also show that this system provides a very suitable scenario for predicting vortex dynamics in inhomogeneous media. Specifically, on the one hand, we derive an exact and simple analytical expression for the velocity field in a particular vortex position due to the presence of the other vortices of the array. On the other hand, using the fact that in stationary conditions this field should balance all other contributions to the velocity, we investigate the applicability of approximated expressions for the precession velocity obtained in previous works for condensates with a single vortex.

High-precision calculations of the energy levels of the superheavy element $Z=120$ are presented. The relativistic Hartree-Fock and configuration-interaction techniques are employed. The correlations between core and valence electrons are treated by means of the correlation potential method and many-body perturbation theory. Similar calculations for barium and radium are used to gauge the accuracy of the calculations and to improve the ab initio results.

We investigate the entanglement dynamics of two modes in a common squeezed thermal environment by means of the characteristic function method and the logarithmic negativity. When the two modes are prepared initially in separable squeezed states, we find that the external environment can not only induce but also enhance the two-mode entanglement if their initial squeezing parameters are suitably chosen. When the two modes are initially in a two-mode squeezed vacuum state, we find that whether the initial entanglement is degraded or increased depends strongly on the difference between the squeezing parameters of the considered bath and of a quantum state. Finally, we give a condition of all two-mode entangled Gaussian states to be the decoherence-free state in a given squeezed bath.

We show a mechanism that projects a pair of neutral two-level atoms from an initially uncorrelated state to a maximally entangled state while they remain spacelike separated. The atoms begin both excited in a common electromagnetic vacuum, and the radiation is collected with a partial Bell-state analyzer. If the interaction time is short enough and a certain two-photon Bell state is detected after the interaction, a high degree of entanglement, even maximal, can be generated while one atom is outside the light cone of the other, for arbitrary large interatomic distances.

We exactly construct one- and two-qubit holonomic quantum gates in terms of isospectral deformations of an Ising model Hamiltonian. A single logical qubit is constructed out of two spin-$\frac{1}{2}$ particles; the qubit is a dimer. We find that the holonomic gates obtained are discrete but dense in the unitary group. Therefore an approximate gate for a desired one can be constructed with arbitrary accuracy.

Augmenting the unitary transformation which generates a quantum walk by a generalized phase gate $G$ is a symmetry for both noisy and noiseless quantum walk on a line, in the sense that it leaves the position probability distribution invariant. However, this symmetry breaks down in the case of a quantum walk on an $n$ cycle, and hence can be regarded as a probe of the walk topology. Noise, modeled here as phase flip and generalized amplitude damping channels, tends to restore the symmetry because it classicalizes the walk. However, symmetry restoration happens even in the regime where the walker is not entirely classical, because noise also has the effect of desensitizing the operation $G$ to the walk topology. We discuss methods for physical implementation, and talk about the wider implications to condensed matter systems.

Energies and electric dipole rates of x rays from doubly ionized $K$ shells of atoms in the range $Z=12$ to 56 have been calculated in the active space approximation using multiconfiguration Dirac-Fock wave functions with the inclusion of higher order relativistic corrections. Using a scaling procedure on the already available relativistic radial matrix elements for a single vacancy in the $K$ shell, the Auger rates have been calculated for the empty $K$ shell. The present investigation shows that though the contribution from relativistic correlation to the $K\alpha$ x-ray hypersatellite energies is not significant, the strength of correlation on the x-ray rates is appreciable, especially for low $Z$ elements. It is observed that the contribution to single configuration $K{\alpha }_2^h$ rate of low $Z$ ions is essentially from electron-electron correlation whereas Breit interaction contributes significantly to the $K{\alpha }_2^h$ rate of high $Z$ elements. The $K{\alpha }_1^h$ rate is affected both by correlation and higher order relativistic corrections. The computed results for the x-ray and Auger transitions as well the fluorescence yields of double hole $K$ shell of various ions are reported and compared with other available values.

Static dipole polarizabilities for the ${}^{3}P_0$ ground state of the neutral group-14 elements C, Si, Ge, Sn, Pb and element $Z=114$ were obtained from all-electron relativistic coupled cluster theory, and compared to molecular beam electric field deflection experiments for Sn and Pb. The isotropic and anisotropic components of the polarizability increase monotonically with the nuclear charge $Z$, except for the spin-orbit coupled $J=0$ states, which start to decrease from Sn to Pb and even further to element $Z=114$. Hence, spin-orbit coupling leads to a significant reduction of the polarizability of element $Z=114$, i.e., from $47.9\mathrm{a.u.}$ at the scalar-relativistic Douglas-Kroll level to $31.5\mathrm{a.u.}$ at the Dirac-Coulomb level of theory, which is below the value of Si $\left(37.3\mathrm{a.u.}\right)$. The calculations further demonstrate that relativistic and electron correlation effects are nonadditive. The measured dipole polarizabilities of Sn and Pb are in reasonable agreement with the theoretical values.

Closed form analytical expressions are obtained for the Wigner transform of the Bloch density matrix and for the Wigner phase-space density of a two-dimensional harmonically trapped charged quantum gas in a uniform magnetic field of arbitrary strength, at zero and nonzero temperatures. An exact analytic expression is also obtained for the autocorrelation function. The strong magnetic field case, where only few Landau levels are occupied, is also examined, and useful approximate expressions for the spatial and momentum densities are given.

Within the classical field model, we find that the phase of a uniform Bose-Einstein condensate at nonzero temperature undergoes a true diffusive motion in the microcanonical ensemble, the variance of the condensate phase change between time zero and time $t$ growing linearly in $t$. The phase diffusion coefficient obeys a simple scaling law in the double thermodynamic and Bogoliubov limit. We construct an approximate calculation of the diffusion coefficient, in fair agreement with the numerical results over the considered temperature range, and we extend this approximate calculation to the quantum field.

We analyze the propagation regime of an amplitude-modulated $1536\mathrm{nm}$ signal when traveling along a highly doped erbium fiber pumped at $977\mathrm{nm}$ as a function of the fiber length. A propagation-induced transition from superluminal to subluminal propagation takes place along the fiber length which allows a change in regime solely based upon increasing the signal modulation frequency. This peculiar behavior is due to the interplay between pump absorption and pump-power broadening of the spectral hole induced by coherent population oscillations. The effect of ion density on this frequency-dependent regime change has been investigated.

The statistics of photons emitted by single multilevel systems is investigated with emphasis on the nonrenewal characteristics of the photon-arrival times. We consider the correlation between consecutive interphoton times and present closed-form expressions for the corresponding multiple-moment analysis. Based on the moments, a memory measure is proposed which provides an easy way of gauging the nonrenewal statistics. Monte Carlo simulations demonstrate that the experimental verification of nonrenewal statistics is feasible.

We consider a three-level model of a one-atom laser, and show that there are two limiting regimes of parameter space, one in which the system behaves like a conventional laser and one in which the system exhibits novel quantum properties. We show that in the first limiting regime, the model can be approximated by semiclassical laser theory, and in the second limiting regime the model can be approximated as an effective two-level atom. We also perform numerical simulations that confirm the limiting behaviors predicted by these approximate descriptions.

The generation and propagation of an asymptotic parabolic pulse in an optical fiber amplifier with the gain dispersion effect and gain saturation effect is studied. It is found that initial input pulses with small amplitudes and widths can evolve into self-similar pulses at the asymptotic limit. The central region of the self-similar pulse is described by the invert parabola, and its width and power increase linearly, but with its peak amplitude and the width of its spectrum, remain constant. The parameter region for the existence of the parabolic pulse is given.

Quasiprobability measures on a canonical phase space give rise through the action of Weyl’s quantization map to operator-valued measures and, in particular, to region operators. Spectral properties, transformations, and general construction methods of such operators are investigated. Geometric trace-increasing maps of density operators are introduced for the construction of region operators associated with one-dimensional domains, as well as with two-dimensional shapes (segments, canonical polygons, lattices, etc.). Operational methods are developed that implement such maps in terms of unitary operations by introducing extensions of the original quantum system with ancillary spaces (qubits). Tomographic methods of reconstruction of the Wigner function based on the radon transform technique are derived by the construction methods for region operators. A Hamiltonian realization of the region operator associated with the radon transform is provided, together with physical interpretations.

The mechanism of pairwise scattering of photons with cold atoms is investigated. We show that considerable motional correlation can be established between atoms during the scattering process, which can effectively squeeze the scattering spectrum and can be utilized to produce highly entangled atomic wave packet. Under certain conditions, the atomic momentum entanglement can be efficiently enhanced beyond the 1 entanglement bit limit (known as $1\mathrm{ebit}$, e.g., a Bell singlet state) with only single-photon scattering and detection.

We show that it is possible to construct closed quantum systems governed by a bilinear Hamiltonian depending on an arbitrary input signal. This is achieved by coupling the system to a quantum input field and performing a feedback of the output field back into the system to cancel out the stochastic effects, with the signal being added to the field between these events and later subtracted. Here we assume the zero time-delay limit between the various connections and operations.

The fidelity of a quantum transformation is strongly linked with the prior partial information of the state to be transformed. We illustrate this interesting point by proposing and demonstrating the superior cloning of coherent states with prior partial information. More specifically, we propose two simple transformations that under the Gaussian assumption optimally clone symmetric Gaussian distributions of coherent states as well as coherent states with known phases. Furthermore, we implement for the first time near-optimal state-dependent cloning schemes relying on simple linear optics and feedforward.

The rovibrational electric dipole transitions in the ground electronic state of the HD molecule are studied. A simple, yet rigorous formula is derived for the transition rates in terms of the electric dipole moment function $D\left(R\right)$, which is calculated in a wide range of $R$. Our numerical results for transition rates are in moderate agreement with experiments and previous calculations, but are at least an order of magnitude more accurate.