Rigid N=2 superconformal hypermultiplets

We discuss superconformally invariant systems of hypermultiplets coupled to gauge fields associated with target-space isometries.Comment: Invited talk given at the International Seminar "Supersymmetries and Quantum Symmetries", July 1997, Dubna. Latex, 9 p

Full characterization of Gaussian bipartite entangled states by a single homodyne detector

We present the full experimental reconstruction of Gaussian entangled states generated by a type--II optical parametric oscillator (OPO) below threshold. Our scheme provides the entire covariance matrix using a single homodyne detector and allows for the complete characterization of bipartite Gaussian states, including the evaluation of purity, entanglement and nonclassical photon correlations, without a priori assumptions on the state under investigation. Our results show that single homodyne schemes are convenient and robust setups for the full characterization of OPO signals and represent a tool for quantum technology based on continuous variable entanglement.Comment: 4 pages, 3 figures, slightly longer version of published PR

Asymptotics of Random Contractions

In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.Comment: 25 page

An effective method to estimate multidimensional Gaussian states

A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix playing the role of the density matrix and homodyne detection providing Stern-Gerlach-like projections. The major difference stems from a different character of relevant noises: while the statistics of Stern-Gerlach-like measurements is governed by binomial statistics, the detection of quadrature variances correspond to chi-square statistics. For Gaussian and near Gaussian states the suggested method provides, compared to standard tomography techniques, more stable and reliable reconstructions. In addition, by putting together reconstruction methods for Gaussian and arbitrary states, we obtain a tool to detect the non-Gaussian character of optical signals.Comment: 8 pages, 5 fis, accepted for publication on PR

More on integrable structures of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds

In this paper we continue the study, initiated in arXiv:1009.3498 and arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum contains non-supercoset worldsheet degrees of freedom corresponding to broken supersymmetries in the bulk. We derive an explicit expression, to all orders in the coset fermions and to second order in the non-coset fermions, which extends the supercoset Lax connection in these backgrounds with terms depending on the non-coset fermions. An important property of the obtained form of the Lax connection is that it is invariant under Z_4-transformations of the superisometry generators and the spectral parameter. This demonstrates that the contribution of the non-coset fermions does not spoil the Z_4-symmetry of the super-coset Lax connection which is of crucial importance for the application of Bethe-ansatz techniques. The expressions describing the AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superstring sigma--models and their Lax connections have a very similar form. This is because their amount of target-space supersymmetries complement each other to 32=24+8, the maximal number of 10d type II supersymmetries. As a byproduct, this similarity has allowed us to obtain the form of the geometry of the complete type IIA AdS(2) x S(2) x T(6) superspace to all orders in the coset fermions and to the second order in the non-coset ones.Comment: 28 pages; v2: References adde

A special road to AdS vacua

We apply the techniques of special Kaehler geometry to investigate AdS_4 vacua of general N=2 gauged supergravities underlying flux compactifications of type II theories. We formulate the scalar potential and its extremization conditions in terms of a triplet of prepotentials P_x and their special Kaehler covariant derivatives only, in a form that recalls the potential and the attractor equations of N=2 black holes. We propose a system of first order equations for the P_x which generalize the supersymmetry conditions and yield non-supersymmetric vacua. Special geometry allows us to recast these equations in algebraic form, and we find an infinite class of new N=0 and N=1 AdS_4 solutions, displaying a rich pattern of non-trivial charges associated with NSNS and RR fluxes. Finally, by explicit evaluation of the entropy function on the solutions, we derive a U-duality invariant expression for the cosmological constant and the central charges of the dual CFT's.Comment: 41 pages; v2, v3: minor improvements, references added, published versio

Optical response of a misaligned and suspended Fabry-Perot cavity

The response to a probe laser beam of a suspended, misaligned and detuned optical cavity is examined. A five degree of freedom model of the fluctuations of the longitudinal and transverse mirror coordinates is presented. Classical and quantum mechanical effects of radiation pressure are studied with the help of the optical stiffness coefficients and the signals provided by an FM sideband technique and a quadrant detector, for generic values of the product $\varpi \tau$ of the fluctuation frequency times the cavity round trip. A simplified version is presented for the case of small misalignments. Mechanical stability, mirror position entanglement and ponderomotive squeezing are accommodated in this model. Numerical plots refer to cavities under test at the so-called Pisa LF facility.Comment: 14 pages (4 figures) submitted to Phys. Rev.

U-dual fluxes and Generalized Geometry

We perform a systematic analysis of generic string flux compactifications, making use of Exceptional Generalized Geometry (EGG) as an organizing principle. In particular, we establish the precise map between fluxes, gaugings of maximal 4d supergravity and EGG, identifying the complete set of gaugings that admit an uplift to 10d heterotic or type IIB supegravity backgrounds. Our results reveal a rich structure, involving new deformations of 10d supergravity backgrounds, such as the RR counterparts of the $\beta$-deformation. These new deformations are expected to provide the natural extension of the $\beta$-deformation to full-fledged F-theory backgrounds. Our analysis also provides some clues on the 10d origin of some of the particularly less understood gaugings of 4d supergravity. Finally, we derive the explicit expression for the effective superpotential in arbitrary N = 1 heterotic or type IIB orientifold compactifications, for all the allowed fluxes.Comment: 58 pages, 6 table

Characterization of bipartite states using a single homodyne detector

We suggest a scheme to reconstruct the covariance matrix of a two-mode state using a single homodyne detector plus a polarizing beam splitter and a polarization rotator. It can be used to fully characterize bipartite Gaussian states and to extract relevant informations on generic states.Comment: 7 pages, 1 figur