On the Correlation Between Polarized BECs

We consider the $2^n$ channels synthesized by the $n$-fold application of Ar\i{}kan's polar transform to a binary erasure channel (BEC). The synthetic channels are BECs themselves, and we show that, asymptotically for almost all these channels, the pairwise correlations between their erasure events are extremely small: the correlation coefficients vanish faster than any exponential in $n$. Such a fast decay of correlations allows us to conclude that the union bound on the block error probability of polar codes is very tight.Comment: 9 pages, Extended version of a paper submitted to ISIT 201

Split spin-squeezed Bose-Einstein Condensates

We investigate and model the behaviour of split spin-squeezed Bose-Einstein condensates (BECs) system. In such a system, a spin-polarized BEC is first squeezed using a $(S^z)^2$ interaction, then are split into two separate clouds. After the split, we consider that the particle number in each cloud collapses to a fixed number. We show that this procedure is equivalent to applying an interaction corresponding to squeezing each cloud individually plus an entangling operation. We analyse the system's entanglement properties and show that it can be detected using correlation-based entanglement criteria. The nature of the states are illustrated by Wigner functions and have the form of a correlated squeezed state. The conditional Wigner function shows high degrees of non-classicality for dimensionless squeezing times beyond $1/\sqrt{N}$, where $N$ is the number of particles per BEC.Comment: 11 pages, 7 figure

Correlation-based entanglement criterion in bipartite multiboson systems

We describe a criterion for the detection of entanglement between two multi-boson systems. The criterion is based on calculating correlations of Gell-Mann matrices with a fixed boson number on each subsystem. This applies naturally to systems such as two entangled spinor Bose-Einstein condensates. We apply our criterion to several experimentally motivated examples, such as an $S^z S^z$ entangled BECs, ac Stark shift induced two-mode squeezed BECs, and photons under parametric down conversion. We find that entanglement can be detected for all parameter regions for the most general criterion. Alternative criteria based on a similar formalism are also discussed together with their merits.Comment: 8 pages, 4 figures, journal versio

Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle

We present a detailed analysis of the 1D expansion of a coherent interacting matterwave (a Bose-Einstein condensate) in the presence of disorder. A 1D random potential is created via laser speckle patterns. It is carefully calibrated and the self-averaging properties of our experimental system are discussed. We observe the suppression of the transport of the BEC in the random potential. We discuss the scenario of disorder-induced trapping taking into account the radial extension in our experimental 3D BEC and we compare our experimental results with the theoretical predictions

Spinor Bose-Einstein condensates

An overview on the physics of spinor and dipolar Bose-Einstein condensates (BECs) is given. Mean-field ground states, Bogoliubov spectra, and many-body ground and excited states of spinor BECs are discussed. Properties of spin-polarized dipolar BECs and those of spinor-dipolar BECs are reviewed. Some of the unique features of the vortices in spinor BECs such as fractional vortices and non-Abelian vortices are delineated. The symmetry of the order parameter is classified using group theory, and various topological excitations are investigated based on homotopy theory. Some of the more recent developments in a spinor BEC are discussed.Comment: To appear in Physics Reports. The PDF file with high resolution figures is available from the following website: http://cat.phys.s.u-tokyo.ac.jp/publication/review_of_spinorBEC.pd

Bose-Einstein correlations in hadron-pairs from lepto-production on nuclei ranging from hydrogen to xenon

Bose-Einstein correlations of like-sign charged hadrons produced in deep-inelastic electron and positron scattering are studied in the HERMES experiment using nuclear targets of $^1$H, $^2$H, $^3$He, $^4$He, N, Ne, Kr, and Xe. A Gaussian approach is used to parametrize a two-particle correlation function determined from events with at least two charged hadrons of the same sign charge. This correlation function is compared to two different empirical distributions that do not include the Bose-Einstein correlations. One distribution is derived from unlike-sign hadron pairs, and the second is derived from mixing like-sign pairs from different events. The extraction procedure used simulations incorporating the experimental setup in order to correct the results for spectrometer acceptance effects, and was tested using the distribution of unlike-sign hadron pairs. Clear signals of Bose-Einstein correlations for all target nuclei without a significant variation with the nuclear target mass are found. Also, no evidence for a dependence on the invariant mass W of the photon-nucleon system is found when the results are compared to those of previous experiments

Holographic storage of multiple coherence gratings in a Bose-Einstein condensate

We demonstrate superradiant conversion between a two-mode collective atomic state and a single-mode light field in an elongated cloud of Bose-condensed atoms. Two off-resonant write beams induce superradiant Raman scattering, producing two independent coherence gratings with a different wave vector in the cloud. By applying phase-matched read beams after a controllable delay, the gratings can be selectively converted into the light field also in a superradiant way. Due to the large cooperativity parameter and the small velocity width of the condensate, a high conversion efficiency of $> 70$ % and a long storage time of $> 120$ $\mu$s were achieved.Comment: 5 pages, 4 figure

Magnetoelectric Properties of Pb Free Bi2FeTiO6: A Theoretical Investigation

The structural, electronic, magnetic and ferroelectric properties of Pb free double perovskite multiferroic Bi2FeTiO6 are investigated using density functional theory within the general gradient approximation (GGA) method. Our structural optimization using total energy calculations for different potential structures show a minimum energy for a non-centrosymmetric rhombohedral structure with R3 space group. Bi2FeTiO6 is found to be an antiferromagnetic insulator with C-type magnetic ordering with bandgap value of 0.3 eV. The calculated magnetic moment of 3.52 \mu_B at Fe site shows the high spin arrangement of 3d electrons which is also confirmed by our orbital projected density of states analysis. We have analyzed the characteristics of bonding present between the constituents of Bi2FeTiO6 with the help of calculated partial density of states and Born effective charges. The ground state of the nearest centrosymmetric structure is found to be a G-type antiferromagnet with half metallicity showing that by the application of external electric field we can not only get a polarized state but also change the magnetic ordering and electronic structure in the present compound indicating strong magnetoelectric coupling. The cation sites the coexistence of Bi 6s lone pair (bring disproportionate charge distribution) and Ti4+ d0 ions which brings covalency produces off-center displacement and favors a non-centrosymmetric ground state and thus ferroelectricity. Our Berry phase calculation gives a polarization of 48 \muCcm-2 for Bi2FeTiO6.Comment: 4 pages, 5 picture

Quantized vortices in superfluid helium and atomic Bose-Einstein condensates

This article reviews recent developments in the physics of quantized vortices in superfluid helium and atomic Bose-Einstein condensates. Quantized vortices appear in low-temperature quantum condensed systems as the direct product of Bose-Einstein condensation. Quantized vortices were first discovered in superfluid 4He in the 1950s, and have since been studied with a primary focus on the quantum hydrodynamics of this system. Since the discovery of superfluid 3He in 1972, quantized vortices characteristic of the anisotropic superfluid have been studied theoretically and observed experimentally using rotating cryostats. The realization of atomic Bose-Einstein condensation in 1995 has opened new possibilities, because it became possible to control and directly visualize condensates and quantized vortices. Historically, many ideas developed in superfluid 4He and 3He have been imported to the field of cold atoms and utilized effectively. Here, we review and summarize our current understanding of quantized vortices, bridging superfluid helium and atomic Bose-Einstein condensates. This review article begins with a basic introduction, which is followed by discussion of modern topics such as quantum turbulence and vortices in unusual cold atom condensates.Comment: 99 pages, 20 figures, Review articl