Abstract:
Radar studies of the plasma irregularities produced by meteoroid ablation provide a powerful diagnostic probe of the Earth's atmosphere. This role is especially important as an inexpensive route for studying several atmospheric processes in comparison with other remote sensing techniques or satellite measurements. Ozone concentration has been indirectly measured in the upper mesosphere/lower thermosphere region by the BLM (Bologna-Lecce-Modra) Forward Scatter (FS) meteor radar by the detection of meteoroids interacting with the Earth's atmosphere. Results of variations of mesospheric ozone concentration at different height levels and time scales were deduced in 1992-2000 from the cumulative duration distributions of overdense echoes. Data of the BLM radar obtained in the last millennium decade confi rm the existence of a secondary ozone layer at atmospheric heights of 85-90 km and show a gradual yearly depletion of the ozone content, similarly to the decrease measured in the eighties by the Solar Mesosphere Explorer (SME) satellite throughout consecutive years (Rusch et al., 1990). Radio observations show in addition large seasonal variations at middle latitudes where the abundance at a secondary ozone maximum at 85-90 km is found to be as much as a factor of two higher in spring months than that in summer months.

Abstract:
We study one dimensional fermionic and bosonic gases with repulsive power-law interactions $1/|x|^{\beta}$, with $\beta>1$, in the framework of Tomonaga-Luttinger liquid (LL) theory. We obtain an accurate analytical expression linking the LL parameter to the microscopic Hamiltonian, for arbitrary $\beta$ and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the LL unstable towards the formation of a cascade of lattice solids with fractional filling, thus forming a "Luttinger staircase". Several of these quantum phases and phase transitions are realized with groundstate polar molecules and weakly-bound magnetic Feshbach molecules.

Abstract:
We investigate the existence of quantum {\it quasi} phase transitions for an ensemble of ultracold bosons in a one-dimensional optical lattice, performing exact diagonalizations of the Bose-Hubbard Hamiltonian. When an external parabolic potential is added to the system {\it quasi} phase transitions are induced by the competition of on-site mean-field energy, hopping energy, and energy offset among lattice sites due to the external potential and lead to the coexistence of regions of particle localization and delocalization in the lattice. We clarify the microscopic mechanisms responsible for these {\it quasi} phase transitions as a function of the depth of the external potential when the on-site mean-field energy is large compared to the hopping energy. In particular, we show that a model Hamiltonian involving a few Fock states can describe the behavior of energy gap, mean particle numbers per site, and number fluctuations per site almost quantitatively. The role of symmetry on the gap as a function of the depth of the external trapping potential is elucidated. We discuss possible experimental signatures of {\it quasi} phase transitions studying the single particle density matrix and explain microscopically the occurrence of local maxima in the momentum distribution. The role of a thermal population of the excited states on the momentum distribution is discussed.

Abstract:
We investigate the pairing and crystalline instabilities of bosonic and fermionic polar molecules confined to a ladder geometry. By means of analytical and quasi-exact numerical techniques, we show that gases of composite molecular dimers as well as trimers can be stabilized as a function of the density difference between the wires. A shallow optical lattice can pin both liquids, realizing crystals of composite bosons or fermions. We show that these exotic quantum phases should be realizable under current experimental conditions in finite-size confining potentials.

Abstract:
In this review chapter we focus on the many-body dynamics of cold polar molecules in the strongly interacting regime. In particular, we discuss a toolbox for engineering many-body Hamiltonians based on the manipulation of the electric dipole moments of the molecules, and thus of molecular interactions, using external static and microwave fields. This forms the basis for the realization of novel quantum phases in these systems.

Abstract:
We discuss the realization of mesoscopic phases of dipolar gases relevant to current experiments with cold polar molecules and Rydberg atoms confined to two dimensions. We predict the existence of superfluid clusters, mesoscopic supersolids, and crystals for a small number of trapped particles, with no counterpart in the homogeneous situation. For certain strengths of the dipole-dipole interactions, the stabilization of purely {\it non-classical crystals} by quantum fluctuations is possible. We propose a magnification scheme to detect the spatial structure of these crystalline phases.

Abstract:
We discuss techniques to generate long-range interactions in a gas of groundstate alkali atoms, by weakly admixing excited Rydberg states with laser light. This provides a tool to engineer strongly correlated phases with reduced decoherence from inelastic collisions and spontaneous emission. As an illustration, we discuss the quantum phases of dressed atoms with dipole-dipole interactions confined in a harmonic potential, as relevant to experiments. We show that residual spontaneous emission from the Rydberg state acts as a heating mechanism, leading to a quantum-classical crossover.

Abstract:
We discuss how adiabatic potentials can be used to create addressable lattices on a subwavelength scale, which can be used as a tool for local operations and readout within a lattice substructure, while taking advantage of the faster timescales and higher energy and temperature scales determined by the shorter lattice spacing. For alkaline-earth-like atoms with non-zero nuclear spin, these potentials can be made state dependent, for which we give specific examples with $^{171}$Yb atoms. We discuss in detail the limitations in generating the lattice potentials, in particular non-adiabatic losses, and show that the loss rates can always be made exponentially small by increasing the laser power.

Abstract:
We study Bragg spectroscopy of strongly interacting one dimensional bosons loaded in an optical lattice plus an additional parabolic potential. We calculate the dynamic structure factor by using Monte Carlo simulations for the Bose-Hubbard Hamiltonian, exact diagonalizations and the results of a recently introduced effective fermionization (EF) model. We find that, due to the system's inhomogeneity, the excitation spectrum exhibits a multi-branched structure, whose origin is related to the presence of superfluid regions with different densities in the atomic distribution. We thus suggest that Bragg spectroscopy in the linear regime can be used as an experimental tool to unveil the shell structure of alternating Mott insulator and superfluid phases characteristic of trapped bosons.

Abstract:
We study rotating quasi-two-dimensional Bose-Einstein-condensates, in which atoms are dressed to a highly excited Rydberg state. This leads to weak effective interactions that induce a transition to a mesoscopic supersolid state. Considering slow rotation, we determine its superfluidity using Quantum Monte-Carlo simulations as well as mean field calculations. For rapid rotation, the latter reveal an interesting competition between the supersolid crystal structure and the rotation-induced vortex lattice that gives rise to new phases, including arrays of mesoscopic vortex crystals.