The bisymplectomorphism group of a bounded symmetric domain

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also endowed with two natural symplectic forms: the Fubini-Study form and the flat form. It has been shown in arXiv:math.DG/0603141 that there exists a diffeomorphism from the domain to the ambient vector space which puts in correspondence the above pair of forms. This phenomenon is called symplectic duality for Hermitian non compact symmetric spaces. In this article, we first give a different and simpler proof of this fact. Then, in order to measure the non uniqueness of this symplectic duality map, we determine the group of bisymplectomorphisms of a bounded symmetric domain, that is, the group of diffeomorphisms which preserve simultaneously the hyperbolic and the flat symplectic form. This group is the direct product of the compact Lie group of linear automorphisms with an infinite-dimensional Abelian group. This result appears as a kind of Schwarz lemma.Comment: 19 pages. Version 2: minor correction

Entanglement growth in quench dynamics with variable range interactions

Studying entanglement growth in quantum dynamics provides both insight into the underlying microscopic processes and information about the complexity of the quantum states, which is related to the efficiency of simulations on classical computers. Recently, experiments with trapped ions, polar molecules, and Rydberg excitations have provided new opportunities to observe dynamics with long-range interactions. We explore nonequilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spin-spin interactions in a transverse Ising chain is varied. Computing the build-up of bipartite entanglement as well as mutual information between distant spins, we identify linear growth of entanglement entropy corresponding to propagation of quasiparticles for shorter range interactions, with the maximum rate of growth occurring when the Hamiltonian parameters match those for the quantum phase transition. Counter-intuitively, the growth of bipartite entanglement for long-range interactions is only logarithmic for most regimes, i.e., substantially slower than for shorter range interactions. Experiments with trapped ions allow for the realization of this system with a tunable interaction range, and we show that the different phenomena are robust for finite system sizes and in the presence of noise. These results can act as a direct guide for the generation of large-scale entanglement in such experiments, towards a regime where the entanglement growth can render existing classical simulations inefficient.Comment: 17 pages, 7 figure

^25Mg NMR study of the MgB_2 superconductor

^25Mg NMR spectra and nuclear spin-lattice relaxation time, T_1, have been measured in polycrystalline ^25MgB_2 with a superconducting transition temperature T_c = 39.0 K in zero magnetic field. From the first order and second order quadrupole perturbed NMR spectrum a quadrupole coupling frequency nu_Q = 222(1.5) kHz is obtained. T_1T = 1090(50) sK and Knight shift K_c = 242(4) ppm are temperature independent in the normal conducting phase. The ^25Mg Korringa ratio equals to 0.95 which is very close to the ideal value of unity for s-electrons. The comparison of the experimental nu_Q, T_1T, and K_c with the corresponding values obtained by LDA calculations shows an excellent agreement for all three quantities.Comment: 4 pages including 4 eps-figures, revtex

Deterministic entanglement of ions in thermal states of motion

We give a detailed description of the implementation of a Molmer-Sorensen gate entangling two Ca+ ions using a bichromatic laser beam near-resonant with a quadrupole transition. By amplitude pulse shaping and compensation of AC-Stark shifts we achieve a fast gate operation without compromising the error rate. Subjecting different input states to concatenations of up to 21 individual gate operations reveals Bell state fidelities above 0.80. In principle, the entangling gate does not require ground state cooling of the ions as long as the Lamb-Dicke criterion is fulfilled. We present the first experimental evidence for this claim and create Bell states with a fidelity of 0.974(1) for ions in a thermal state of motion with a mean phonon number of =20(2) in the mode coupling to the ions' internal states.Comment: 18 pages, 9 figures (author name spelling corrected

Weighted Bergman kernels and virtual Bergman kernels

We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.Comment: 12 pages. One-hour lecture for graduate students, SCV 2004, August 2004, Beijing, P.R. China. V2: typo correcte

Automated operation of a home made torque magnetometer using LabVIEW

In order to simplify and optimize the operation of our home made torque magnetometer we created a new software system. The architecture is based on parallel, independently running instrument handlers communicating with a main control program. All programs are designed as command driven state machines which greatly simplifies their maintenance and expansion. Moreover, as the main program may receive commands not only from the user interface, but also from other parallel running programs, an easy way of automation is achieved. A program working through a text file containing a sequence of commands and sending them to the main program suffices to automatically have the system conduct a complex set of measurements. In this paper we describe the system's architecture and its implementation in LabVIEW.Comment: 6 pages, 7 figures, submitted to Rev. Sci. Inst

Loading of a cold atomic beam into a magnetic guide

We demonstrate experimentally the continuous and pulsed loading of a slow and cold atomic beam into a magnetic guide. The slow beam is produced using a vapor loaded laser trap, which ensures two-dimensional magneto-optical trapping, as well as cooling by a moving molasses along the third direction. It provides a continuous flux larger than $10^9$ atoms/s with an adjustable mean velocity ranging from 0.3 to 3 m/s, and with longitudinal and transverse temperatures smaller than $100 \mu$K. Up to $3 10^8$ atoms/s are injected into the magnetic guide and subsequently guided over a distance of 40 cm.Comment: 10 pages, 10 figures, accepted for publication to EPJ