We show that the Haldane phase of S=1 antiferromagnetic chain is closely related to breaking a hidden ${\mathit{Z}}_{2}$\ifmmode\times\else\texttimes\fi{}${\mathit{Z}}_{2}$ symmetry. When in phase, this symmetry fully broken, but when massive other than e.g., Ising or dimerized broken only partially not at all. The revealed by introducing nonlocal unitary transformation chain. This also leads simple variational calculation which qualitatively reproduces diagram

The author numerically computes the two lowest eigenvalues of finite length spin-1 chains with Hamiltonian H= Sigma i(Si.Si+1- beta (Si.Si+1)2) and open boundary conditions. For a range , including value 0, he finds that difference decays exponentially chain. This exponential decay provides further evidence these spin are in massive phase as first predicted by Haldane (1982). correlation xi chain can be estimated using this decay. He estimates for Heisenberg ( =0) from 6.7 to 7.8 depending...

We investigate the dynamics of dark-state polaritons in an atomic ensemble with ground-state degeneracy. A signal light pulse may be stored and retrieved from sample by adiabatic variation amplitude a control field. During storage process, magnetic field causes rotation hyperfine coherences, leading to collapses revivals polariton number. These should observable measurements field, as function time orientation.

Differential Stark shift compensation for ground-state $^{87}\mathrm{Rb}$ atoms trapped in an elliptically polarized optical lattice and ``magic'' magnetic field was recently proposed demonstrated experimentally by N. Lundblad et al. [e-print arXiv:0912.1528] analyzed theoretically A. Derevianko arXiv:0912.3233]. Here we demonstrate enhanced hyperfine coherence times using the magic technique. We observe coherent light storage with a $0.32$-s lifetime atomic Rb gas confined one-dimensional field.

The conjecture that the scaling limit of two-dimensional self-avoiding walk (SAW) in a half plane is given by stochastic Loewner evolution (SLE) with $\kappa=8/3$ leads to explicit predictions about SAW. A remarkable feature these they yield not just critical exponents, but probability distributions for certain random variables associated walk. We test two Monte Carlo simulations and find excellent agreement, thus providing numerical support SAW SLE$_{8/3}$.

We consider the quantization of slowly varying optical fields in a dispersive nonlinear medium and application phase-space methods to resulting quantum field equations. A pragmatic approach electromagnetic is adopted whereby we apply canonical Hamiltonian expressed terms electric envelope, all approximations (quasimonochromatic paraxial) having been made at classical level. This allows us include material dispersion, diffraction, nonlinearity. Using then develop c-number functional...

The pivot algorithm is a Markov Chain Monte Carlo for simulating the self-avoiding walk. At each iteration which produces global change in walk proposed. If resulting self-avoiding, new accepted; otherwise, it rejected. Past implementations of required time O(N) per accepted pivot, where N number steps We show how to implement so that O(N^q) with q<1. estimate q less than 0.57 two dimensions, and 0.85 three dimensions. Corrections make an accurate impossible. They also imply asymptotic...

With the use of a quantum theory optical propagation, set nonlinear stochastic partial differential equations may be derived which describes quantum-statistical properties traveling waves due to self-phase modulation in medium. We calculate exact moments for field, exhibit classical short-interaction limit and periodic evolution through field-superposition states long-interaction limit. Reversible irreversible behaviors description are reviewed. The relation present work corresponding...

Quantum mechanics provides a mechanism for absolutely secure communication between remote parties. For distances greater than 100 km, direct quantum via optical fiber is not viable, owing to losses, and intermediate storage of the information along transmission channel necessary. This leads concept repeater, proposed by Briegel et al. [Phys. Rev. Lett. 81, 169 (1998)]. Duan [Nature 414, 413 (2001)] have use atomic ensembles as basic memory elements repeater. We provide an overview our...