Decoherence models for discrete-time quantum walks and their application to neutral atom experiments

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic-instead of diffusive-expansion in position space is not a good indicator of the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

Real-time PCR quantification and diversity analysis of the functional genes aprA and dsrA of sulfate-reducing prokaryotes in marine sediments of the Peru continental margin and the Black Sea

Sulfate-reducing prokaryotes (SRP) are ubiquitous and quantitatively important members in many ecosystems, especially in marine sediments. However their abundance and diversity in subsurface marine sediments is poorly understood. In this study, the abundance and diversity of the functional genes for the enzymes adenosine 5'-phosphosulfate reductase (aprA) and dissimilatory sulfite reductase (dsrA) of SRP in marine sediments of the Peru continental margin and the Black Sea were analyzed, including samples from the deep biosphere (ODP site 1227). For aprA quantification a Q-PCR assay was designed and evaluated. Depth profiles of the aprA and dsrA copy numbers were almost equal for all sites. Gene copy numbers decreased concomitantly with depth from around 10(8)/g sediment close to the sediment surface to less than 10(5)/g sediment at 5 mbsf. The 16S rRNA gene copy numbers of total bacteria were much higher than those of the functional genes at all sediment depths and used to calculate the proportion of SRP to the total Bacteria. The aprA and dsrA copy numbers comprised in average 0.5-1% of the 16S rRNA gene copy numbers of total bacteria in the sediments up to a depth of ca. 40 mbsf. In the zone without detectable sulfate in the pore water from about 40-121 mbsf (Peru margin ODP site 1227), only dsrA (but not aprA) was detected with copy numbers of less than 10(4)/g sediment, comprising ca. 14% of the 16S rRNA gene copy numbers of total bacteria. In this zone, sulfate might be provided for SRP by anaerobic sulfide oxidation. Clone libraries of aprA showed that all isolated sequences originate from SRP showing a close relationship to aprA of characterized species or form a new cluster with only distant relation to aprA of isolated SRP. For dsrA a high diversity was detected, even up to 121 m sediment depth in the deep biosphere.