Detection of Entanglement in Ultracold Lattice Gases

Probing non trivial magnetic ordering in quantum magnets realized with ultracold lattice gases demands detection methods with some spatial resolution built on it. Here we demonstrate that the Faraday matter-light interface provides an experimentally feasible tool to distinguish indubitably different quantum phases of a given many-body system in a non-demolishing way. We illustrate our approach by focussing on the Heisenberg chain for spin-1 bosons in the presence of a SU(2) symmetry breaking field. We explain how using the light signal obtained via homodyne detection one can reconstruct the phase diagram of the model. Further we show that the very same technique that provides a direct experimentally measurable signal of different order parameters can be extended to detect also the presence of multipartite entanglement in such systems.

ANISOTROPY OF OPTICAL-CONSTANTS OF YBCO

Otto configuration attenuated total reflection (ATR) measurements of the excitation of surface plasmons in the infrared have been carried out on YBCO films deposited on MgO (100) substrates. The dielectric constants for YBCO at 3.392 mu m are determined to be -10 + 15i for c-axis material. The anisotropic nature of the cuprate is seen from films with other orientations: nearly a-axis material has constants of 4.0 + 7.0i. It is thus not metallic in its optical response along the c-axis which lies parallel to the substrate plane. Ellipsometric measurements in the visible on c-axis material point to a maximum surface plasmon energy of 1 eV.

Case study of the uniaxial anisotropic spin-1 bilinear-biquadratic Heisenberg model on a triangular lattice

We study the spin-1 model on a triangular lattice in the presence of a uniaxial anisotropy field using a cluster mean-field (CMF) approach. The interplay among antiferromagnetic exchange, lattice geometry, and anisotropy forces Gutzwiller mean-field approaches to fail in a certain region of the phase diagram. There, the CMF method yields two supersolid phases compatible with those present in the spin-1/2 XXZ model onto which the spin-1 system maps. Between these two supersolid phases, the three-sublattice order is broken and the results of the CMF approach depend heavily on the geometry and size of the cluster. We discuss the possible presence of a spin liquid in this region.

Low-energy behavior of strongly interacting bosons on a flat-band lattice above the critical filling factor

Bosons interacting repulsively on a lattice with a flat lowest band energy dispersion may, at sufficiently small filling factors, enter into a Wigner-crystal-like phase. This phase is a consequence of the dispersionless nature of the system, which in turn implies the occurrence of single-particle localized eigenstates. We investigate one of these systems-the sawtooth lattice-filled with strongly repulsive bosons at filling factors infinitesimally above the critical point where the crystal phase is no longer the ground state. We find, in the hard-core limit, that the crystal retains its structure in all but one of its cells, where it is broken. The broken cell corresponds to an exotic kind of repulsively bound state, which becomes delocalized. We investigate the excitation spectrum of the system analytically and find that the bound state behaves as a single particle hopping on an effective lattice with reduced periodicity, and is therefore gapless. Thus, the addition of a single particle to a flat-band system at critical filling is found to be enough to make kinetic behavior manifest.

Thermometry precision in strongly correlated ultracold lattice gases

The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated
system is a question of both fundamental and technological importance. Here, we address such
question by combining tools from quantum metrology together with the study of the quantum
correlations embedded in the system at finite temperatures. Within this frame we examine the spin-
1 2 XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable
bound on the temperature precision. We then address the estimation of the temperature of the sample
from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method.
Remarkably, our results show that the collective quantum correlations can become optimal
observables to accurately estimate the temperature of our model in a given range of temperatures.

Structural and electrical anisotropy of (001)-, (116)-, and (103)-oriented epitaxial SrBi2Ta2O9 thin films on SrTiO3 substrates grown by pulsed laser deposition

Epitaxial SrBi2Ta2O9 (SBT) thin films with well-defined (001), (116), and (103) orientations have been grown by pulsed laser deposition on (001)-, (011)-, and (111)-oriented Nb-doped SrTiO3 substrates. X-ray diffraction pole figure and phi -scan measurements revealed that the three-dimensional epitaxial orientation relation SBT(001)parallel to SrTiO3(001), and SBT[1(1) over bar 0]parallel to SrTiO3[100] is valid for all cases of SET thin films on SrTiO3 substrates, irrespective of their orientations. Atomic force microscopy images of the c-axis-oriented SET revealed polyhedron-shaped grains showing spiral growth around screw dislocations. The terrace steps of the c-axis-oriented SET films were integral multiples of a quarter of the lattice parameter c of SBT (similar to 0.6 nm). The grains of (103)-oriented SET films were arranged in a triple-domain configuration consistent with the symmetry of the SrTiO3(111) substrate. The measured remanent polarization (2P(r)) and coercive field (2E(c)) of (116)-oriented SBT films were 9.6 muC/cm(2) and 168 kV/cm, respectively, for a maximum applied electric field of 320 kV/cm. Higher remanent polarization (2P(r)=10.4 muC/cm(2)) and lower coercive field (2E(c)=104 kV/cm) than those of SBT(116) films were observed in (103)-oriented SET thin films, and (001)-oriented SET revealed no ferroelectricity along the [001] axis. The dielectric constants of (001)-, (116)-, and (103)-oriented SBT were 133, 155, and 189, respectively. (C) 2000 American Institute of Physics.

Practical Lattice-Based Digital Signature Schemes

Digital signatures are an important primitive for building secure systems and are used in most real-world security protocols. However, almost all popular signature schemes are either based on the factoring assumption (RSA) or the hardness of the discrete logarithm problem (DSA/ECDSA). In the case of classical cryptanalytic advances or progress on the development of quantum computers, the hardness of these closely related problems might be seriously weakened. A potential alternative approach is the construction of signature schemes based on the hardness of certain lattice problems that are assumed to be intractable by quantum computers. Due to significant research advancements in recent years, lattice-based schemes have now become practical and appear to be a very viable alternative to number-theoretic cryptography. In this article, we focus on recent developments and the current state of the art in lattice-based digital signatures and provide a comprehensive survey discussing signature schemes with respect to practicality. Additionally, we discuss future research areas that are essential for the continued development of lattice-based cryptography.

Lattice-based Encryption Over Standard Lattices in Hardware

Lattice-based cryptography has gained credence recently as a replacement for current public-key cryptosystems, due to its quantum-resilience, versatility, and relatively low key sizes. To date, encryption based on the learning with errors (LWE) problem has only been investigated from an ideal lattice standpoint, due to its computation and size efficiencies. However, a thorough investigation of standard lattices in practice has yet to be considered. Standard lattices may be preferred to ideal lattices due to their stronger security assumptions and less restrictive parameter selection process. In this paper, an area-optimised hardware architecture of a standard lattice-based cryptographic scheme is proposed. The design is implemented on a FPGA and it is found that both encryption and decryption fit comfortably on a Spartan-6 FPGA. This is the first hardware architecture for standard lattice-based cryptography reported in the literature to date, and thus is a benchmark for future implementations.
Additionally, a revised discrete Gaussian sampler is proposed which is the fastest of its type to date, and also is the first to investigate the cost savings of implementing with lamda_2-bits of precision. Performance results are promising in comparison to the hardware designs of the equivalent ring-LWE scheme, which in addition to providing a stronger security proof; generate 1272 encryptions per second and 4395 decryptions per second.