Several small Josephson junctions in a Resonant Cavity: Deviation from the Dicke Model

We have studied quantum-mechanically a system of several small identical Josephson junctions in a lossless single-mode cavity for different initial states, under conditions such that the system is at resonance. This system is analogous to a collection of identical atoms in a cavity, which is described under appropriate conditions by the Dicke model. We find that our system can be well approximated by a reduced Hamiltonian consisting of two levels per junction. The reduced Hamiltonian is similar to the Dicke Hamiltonian, but contains an additional term resembling a dipole-dipole interaction between the junctions. This extra term arises when states outside the degenerate group are included via degenerate second-order (L\"{o}wdin) perturbation theory. As in the Dicke model, we find that, when N junctions are present in the cavity, the oscillation frequency due to the junction-cavity interaction is enhanced by $\sqrt{N}$. The corresponding decrease in the Rabi oscillation period may cause it to be smaller than the decoherence time due to dissipation, making these oscillations observable. Finally, we find that the frequency enhancement survives even if the junctions differ slightly from one another, as expected in a realistic system.Comment: 11 pages. To be published in Phys. Rev.

Cryptic species within the cosmopolitan desiccation-tolerant moss Grimmia laevigata

The common cushion moss Grimmia laevigata (Bridel) Bridel grows on bare rock in a broad range of environments on every continent except Antarctica. As such, it must harbor adaptations to a remarkably broad set of environmental stresses, the extremes of which can include very high temperatures, prolonged nearly complete desiccation, and high ultraviolet B (UVB) exposure. Yet, like many mosses, G. laevigata shows very little morphological variability across its cosmopolitan range. This presents an evolutionary puzzle, the solution to which lies in understanding the phylogeographic structure of this morphologically simple organism. Here we report the results of an analysis of amplified fragment length polymorphisms (AFLPs) in G. laevigata, focusing on individuals from the California Floristic Province. We found evidence that populations within California constitute two distinct geographically overlapping cryptic species. Each clade harbors multiple private alleles, indicating they have been genetically isolated for some time. We suggest that the existence of cryptic species within G. laevigata, in combination with its life history, growth habits, and extreme desiccation tolerance, makes this moss an ideal research tool and a candidate for a biological indicator of climate change and pollution