Absorption imaging of a quasi 2D gas: a multiple scattering analysis

Absorption imaging with quasi-resonant laser light is a commonly used technique to probe ultra-cold atomic gases in various geometries. Here we investigate some non-trivial aspects of this method when it is applied to in situ diagnosis of a quasi two-dimensional gas. Using Monte Carlo simulations we study the modification of the absorption cross-section of a photon when it undergoes multiple scattering in the gas. We determine the variations of the optical density with various parameters, such as the detuning of the light from the atomic resonance and the thickness of the gas. We compare our results to the known three-dimensional result (Beer-Lambert law) and outline the specific features of the two-dimensional case.Comment: 22 pages, 5 figure

Aging, jamming, and the limits of stability of amorphous solids

Apart from not having crystallized, supercooled liquids can be considered as being properly equilibrated and thus can be described by a few thermodynamic control variables. In contrast, glasses and other amorphous solids can be arbitrarily far away from equilibrium and require a description of the history of the conditions under which they formed. In this paper we describe how the locality of interactions intrinsic to finite-dimensional systems affects the stability of amorphous solids far off equilibrium. Our analysis encompasses both structural glasses formed by cooling and colloidal assemblies formed by compression. A diagram outlining regions of marginal stability can be adduced which bears some resemblance to the quasi-equilibrium replica meanfield theory phase diagram of hard sphere glasses in high dimensions but is distinct from that construct in that the diagram describes not true phase transitions but kinetic transitions that depend on the preparation protocol. The diagram exhibits two distinct sectors. One sector corresponds to amorphous states with relatively open structures, the other to high density, more closely-packed ones. The former transform rapidly owing to there being motions with no free energy barriers; these motions are string-like locally. In the dense region, amorphous systems age via compact activated reconfigurations. The two regimes correspond, in equilibrium, to the collisional or uniform liquid and the so called landscape regime, respectively. These are separated by a spinodal line of dynamical crossovers. Owing to the rigidity of the surrounding matrix in the landscape, high-density part of the diagram, a sufficiently rapid pressure quench adds compressive energy which also leads to an instability toward string-like motions with near vanishing barriers. (SEE REST OF ABSTRACT IN THE ARTICLE.)Comment: submitted to J Phys Chem

Engineering spectral properties of non-interacting lattice Hamiltonians

We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.Comment: 19 pages, 4 figure