We present a general scheme to realize a cold-atom quantum simulator of bidimensional atomic crystals. Our model is based on the use of two independently trapped atomic species: the first one, subject to a strong in-plane confinement, constitutes a two-dimensional matter wave which interacts only with atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach we show that the system Green function can be exactly determined, allowing for the investigation of the matter-wave transport properties. We propose some illustrative applications to both Bravais (square, triangular) and non-Bravais (graphene, kagomé) lattices, studying both ideal periodic systems and experimental-size and disordered ones. Some remarkable spectral properties of these atomic artificial lattices are pointed out, such as the emergence of single and multiple gaps, flat bands, and Dirac cones. All these features can be manipulated via the interspecies interaction, which proves to be widely tunable due to the interplay between scattering length and confinements.

We calculate the Casimir-Lifshitz pressure in a system consisting of two different one-dimensional dielectric lamellar gratings having two different temperatures and immersed in an environment having a third temperature. The calculation of the pressure is based on the knowledge of the scattering operators, deduced using the Fourier modal method. The behavior of the pressure is characterized in detail as a function of the three temperatures of the system as well as the geometrical parameters of the two gratings. We show that the interplay between nonequilibrium effects and geometrical periodicity offers a rich scenario for the manipulation of the force. In particular, we find regimes where the force can be strongly reduced for large ranges of temperatures. Moreover, a repulsive pressure can be obtained, whose features can be tuned by controlling the degrees of freedom of the system. Remarkably, the transition distance between attraction and repulsion can be decreased with respect to the case of two slabs, implying an experimental interest for the observation of repulsion.

We present a new model to realize artificial 2D lattices with cold atoms investigating the atomic artificial graphene: a 2D confined matter wave is scattered by atoms of a second species trapped around the nodes of a honeycomb optical lattice. The system allows an exact determination of the Green function, hence of the transport properties. The inter-species interaction can be tuned via the interplay between scattering length and confinements. Band structure and density of states of a periodic lattice are derived for different values of the interaction strength. Emergence and features of Dirac cones are pointed out, together with the appearance of multiple gaps and a non-dispersive and isolated flat band. Robustness against finite-size and vacancies effects is numerically investigated.

We study the optomechanical coupling of a oscillating effective mirror with a Rydberg atomic gas, mediated by the dynamical atom-mirror Casimir-Polder force. This coupling may produce a near-field resonant atomic excitation whose probability scales as $\propto (d^2\;a\;n^4\;t)^2/z_0^8$, where $z_0$ is the average atom-surface distance, $d$ the atomic dipole moment, $a$ the mirror's effective oscillation amplitude, $n$ the initial principal quantum number, and $t$ the time. We propose an experimental configuration to realize this system with a cold atom gas trapped at a distance $\sim 2\cdot10 \, \mu$m from a semiconductor substrate, whose dielectric constant is periodically driven by an external laser pulse, hence realizing en effective mechanical mirror motion due to the periodic change of the substrate from transparent to reflecting. For a parabolic gas shape, this effect is predicted to excite about $\sim 10^2$ atoms of a dilute gas of $10^3$ trapped Rydberg atoms with $n=75$ after about $0.5 \,\mu \mbox{s}$, hence high enough to be detected in typical Rydberg gas experimental conditions.

We study the Casimir-Lifshitz force and the radiative heat transfer in a system consisting of three bodies held at three independent temperatures and immersed in a thermal environment, the whole system being in a stationary configuration out of thermal equilibrium. The theory we develop is valid for arbitrary bodies, i.e., for any set of temperatures, dielectric, and geometrical properties, and describes each body by means of its scattering operators. For the three-body system we provide a closed-form unified expression of the radiative heat transfer and of the Casimir-Lifshitz force (both in and out of thermal equilibrium). This expression is thus first applied to the case of three planar parallel slabs. In this context we discuss the nonadditivity of the force at thermal equilibrium, as well as the equilibrium temperature of the intermediate slab as a function of its position between two external slabs having different temperatures. Finally, we consider the force acting on an atom inside a planar cavity. We show that, differently from the equilibrium configuration, the absence of thermal equilibrium admits one or more positions of minima for the atomic potential. While the corresponding atomic potential depths are very small for typical ground-state atoms, they may become particularly relevant for Rydberg atoms, becoming a promising tool to produce an atomic trap.

A layered waveguide supported hybrid modes between a surface plasmon and a confined guided mode is studied. The condition for the strong coupling regime are described. The Green function is obtained and decomposed along the continuous and discrete spectrum.