Parameter estimation in a memory-assisted noisy quantum interferometry

We demonstrate that memory in an $N$-qubit system subjected to decoherence, is a potential resource for the slow-down of the entanglement decay. We show that this effect can be used to retain the sub shot-noise sensitivity of the parameter estimation in quantum interferometry. We calculate quantum Fisher information, which sets the ultimate bound for the precision of the estimation. We also derive the sensitivity of such a noisy interferometer, when the phase is either estimated from the measurements of the population imbalance or from the one-body density.Comment: 10 pages, 5 figure

Entanglement-based signature of nonlocal dispersion cancellation

We derive an inequality bounding the strength of temporal correlations for a pair of light beams prepared in a separable state and propagating through dispersive media with opposite signs of group velocity dispersion. The presented inequality can be violated by entangled states of light, such as photon pairs produced in spontaneous parametric down-conversion. Because the class of separable states covers the entire category of classical fields as a particular case, this result provides an unambiguously quantum feature of nonlocal dispersion cancellation that cannot be reproduced within the classical theory of electromagnetic radiation.Comment: 5 pages, 2 figur

Four-wave mixing in spin-orbit coupled Bose-Einstein condensates

We describe possibilities of spontaneous, degenerate four-wave mixing (FWM) processes in spin-orbit coupled Bose-Einstein condensates. Phase matching conditions (i.e., energy and momentum conservation laws) in such systems allow one to identify four different configurations characterized by involvement of distinct spinor states in which such a process can take place. We derived these conditions from first principles and then illustrated dynamics with direct numerical simulations. We found, among others, the unique configuration, where both probe waves have smaller group velocity than pump wave and proved numerically that it can be observed experimentally under proper choice of the parameters. We also reported the case when two different FWM processes can occur simultaneously. The described resonant interactions of matter waves is expected to play important role in the experiments of BEC with artificial gauge fields. Beams created by FWM processes are important source of correlated particles and can be used the experiments testing quantum properties of atomic ensembles.Comment: 18 pages, 8 figure

Bogoliubov theory for atom scattering into separate regions

We review the Bogoliubov theory in the context of recent experiments, where atoms are scattered from a Bose-Einstein Condensate into two well-separated regions. We find the full dynamics of the pair-production process, calculate the first and second order correlation functions and show that the system is ideally number-squeezed. We calculate the Fisher information to show how the entanglement between the atoms from the two regions changes in time. We also provide a simple expression for the lower bound of the useful entanglement in the system in terms of the average number of scattered atoms and the number of modes they occupy. We then apply our theory to a recent "twin-beam" experiment [R. B\"ucker {\it et al.}, Nat. Phys. {\bf 7}, 608 (2011)]. The only numerical step of our semi-analytical description can be easily solved and does not require implementation of any stochastic methods.Comment: 11 pages, 6 figure

Genericity of Fr\'echet smooth spaces

If a separable Banach space contains an isometric copy of every separable reflexive Fr\'echet smooth Banach space, then it contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach spaces with Fr\'echet smooth dual space. This improves a result of G. Godefroy and N. J. Kalton.Comment: 34 page

RNA-Mediated Gene Silencing Signals Are Not Graft Transmissible from the Rootstock to the Scion in Greenhouse-Grown Apple Plants Malus sp.

RNA silencing describes the sequence specific degradation of RNA targets. Silencing is a non-cell autonomous event that is graft transmissible in different plant species. The present study is the first report on systemic acquired dsRNA-mediated gene silencing of transgenic and endogenous gene sequences in a woody plant like apple. Transgenic apple plants overexpressing a hairpin gene construct of the gusA reporter gene were produced. These plants were used as rootstocks and grafted with scions of the gusA overexpressing transgenic apple clone T355. After grafting, we observed a reduction of the gusA gene expression in T355 scions in vitro, but not in T355 scions grown in the greenhouse. Similar results were obtained after silencing of the endogenous Mdans gene in apple that is responsible for anthocyanin biosynthesis. Subsequently, we performed grafting experiments with Mdans silenced rootstocks and red leaf scions of TNR31-35 in order to evaluate graft transmitted silencing of the endogenous Mdans. The results obtained suggested a graft transmission of silencing signals in in vitro shoots. In contrast, no graft transmission of dsRNA-mediated gene silencing signals was detectable in greenhouse-grown plants and in plants grown in an insect protection tent

Approximation properties for noncommutative Lp-spaces associated with lattices in Lie groups

In 2010, Lafforgue and de la Salle gave examples of noncommutative Lp-spaces without the operator space approximation property (OAP) and, hence, without the completely bounded approximation property (CBAP). To this purpose, they introduced the property of completely bounded approximation by Schur multipliers on Sp and proved that for p 4 the groups SL(n,Z), with n \geq 3, do not have it. Since for 1 < p < \infty the property of completely bounded approximation by Schur multipliers on Sp is weaker than the approximation property of Haagerup and Kraus (AP), these groups were also the first examples of exact groups without the AP. Recently, Haagerup and the author proved that also the group Sp(2,R) does not have the AP, without using the property of completely bounded approximation by Schur multipliers on Sp. In this paper, we prove that Sp(2,R) does not have the property of completely bounded approximation by Schur multipliers on Sp for p 12. It follows that a large class of noncommutative Lp-spaces does not have the OAP or CBAP.Comment: Version 2, 20 pages. Minor corrections, builds on results from arXiv:1201.125

Highly scab-resistant transgenic apple lines achieved by introgression of HcrVf2 controlled by different native promoter lengths

Apple scab, caused by the ascomycete Venturia inaequalis, is the most damaging fungal disease of commercial apple orchards. Functional scab resistance genes are present in some wild Malus species. The HcrVf2 gene, derived from the Vf-region of the wild apple Malus floribunda 821 and encoding a receptor-like protein, has proved to confer scab resistance in a transgenic susceptible cultivar. In order to minimize nonplant DNA in genetically modified apple and to go a step toward the development of cisgenic apples, we have studied the capability of the HcrVf2 gene to confer apple scab resistance when it is controlled by its own promoter. Three promoter deletion constructs containing 115, 288, and 779bp of the 5′ untranslated region and the HcrVf2 gene were used to transform the scab susceptible apple cvs. ‘Gala' and ‘Elstar.' The influence of the promoter length on both the HcrVf2 expression level and the response to V. inaequalis was analyzed in different transgenic lines. Promoter length was found to influence both the constitutive transcription levels of HcrVf2 in transgenic lines and the resistance level. Highly scab resistant ‘Elstar' and ‘Gala' plants were obtained, proving that the HcrVf2 gene controlled by its native promoter is effective in conferring resistance to V. inaequalis similarly as Vf introgressed in apple cvs. through classical breedin