Hall response of interacting bosonic atoms in strong gauge fields: from condensed to FQH states

Interacting bosonic atoms under strong gauge fields undergo a series of phase transitions that take the cloud from a simple Bose-Einstein condensate all the way to a family of fractional-quantum-Hall-type states [M. Popp, B. Paredes, and J. I. Cirac, Phys. Rev. A 70, 053612 (2004)]. In this work we demonstrate that the Hall response of the atoms can be used to locate the phase transitions and characterize the ground state of the many-body state. Moreover, the same response function reveals within some regions of the parameter space, the structure of the spectrum and the allowed transitions to excited states. We verify numerically these ideas using exact diagonalization for a small number of atoms, and provide an experimental protocol to implement the gauge fields and probe the linear response using a periodically driven optical lattice. Finally, we discuss our theoretical results in relation to recent experiments with condensates in artificial magnetic fields [ L. J. LeBlanc, K. Jimenez-Garcia, R. A. Williams, M. C. Beeler, A. R. Perry, W. D. Phillips, and I. B. Spielman, Proc. Natl. Acad. Sci. USA 109, 10811 (2012)] and we analyze the role played by vortex states in the Hall response.Comment: 10 pages, 7 figure

Dipole-Mode Vector Solitons

We find a new type of optical vector soliton that originates from trapping of a dipole mode by a soliton-induced waveguide. These solitons, which appear as a consequence of the vector nature of the two component system, are more stable than the previously found optical vortex-mode solitons and represent a new type of extremely robust nonlinear vector structure.Comment: Four pages with five eps figure

Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric

On Rank Problems for Planar Webs and Projective Structures

We present old and recent results on rank problems and linearizability of geodesic planar webs.Comment: 31 pages; LaTeX; corrected the abstract and Introduction; added reference

Construction of exact solutions by spatial traslations in inhomogeneous Nonlinear Schrodinger equations. Applications to Bose-Einstein condensation

In this paper we study a general nonlinear Schr\"odinger equation with a time dependent harmonic potential. Despite the lack of traslational invariance we find a symmetry trasformation which, up from any solution, produces infinitely many others which are centered on classical trajectories. The results presented here imply that, not only the center of mass of the wave-packet satisfies the Ehrenfest theorem and is decoupled from the dynamics of the wave-packet, but also the shape of the solution is independent of the behaviour of the center of the wave. Our findings have implications on the dynamics of Bose-Einstein condensates in magnetic trapsComment: Submitted to Phys. Re

Matrix Product Density Operators: Simulation of finite-T and dissipative systems

We show how to simulate numerically both the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems and it is based on two ideas: (a) a representation for density operators which extends that of matrix product states to mixed states; (b) an algorithm to approximate the evolution (in real or imaginary time) of such states which is variational (and thus optimal) in nature.Comment: See also M. Zwolak et al. cond-mat/040644

Rosemary distillation residues reduce lipid oxidation, increase alpha-tocopherol content and improve fatty acid profile of lamb meat

The experiment studied the effects of rosemary distillation residues (RR) intake on lamb meat quality, oxidative stability and fatty acid (FA) profile. Barbarine lambs of Control group were fed 600 g of hay, which was substituted by 600 g of pellets containing 60 and 87% of RR for RR60 and RR87 groups; all animals received 600 g of concentrate. Meat protein and fat content was similar for 3 treatments. Lipid oxidation was strongly reduced with RR diets. Both RR diets resulted in a higher a- tocopherol content in muscle. The metmyoglobin and deoxymyoglobin percentages were similar for all groups; however oxymyoglobin was higher for RR groups. The saturated (SFA) and unsaturated FAs (UFA) were unaffected by the diets. However, the PUFA, n-6 and n-3 were higher for RR groups. In conclusion, rosemary residues resulted in higher vitamin E content, so it enhanced the oxidative status and improved the fatty acid profile of lamb meat

Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field

We consider the combined effects of large spin-orbit couplings and a perpendicular magnetic field in a 2D honeycomb fermionic lattice. This system provides an elegant setup to generate versatile spin textures propagating along the edge of a sample. The spin-orbit coupling is shown to induce topological phase transitions between a helical quantum spin Hall phase and a chiral spin-imbalanced quantum Hall state. Besides, we find that the spin orientation of a single topological edge state can be tuned by a Rashba spin-orbit coupling, opening an interesting route towards quantum spin manipulation. We discuss the possible realization of our results using cold atoms trapped in optical lattices, where large synthetic magnetic fields and spin-orbit couplings can be engineered and finely tuned. In particular, this system would lead to the observation of a time-reversal-symmetry-broken quantum spin Hall phase.Comment: 8 pages, 3 figures, Accepted in Europhys. Lett. (Dec 2011

Molecular Dynamics Simulation of Solvent-Polymer Interdiffusion. I. Fickian diffusion

The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a function of time. The weight gain is found to scale as t^{1/2}, which is expected for Fickian type of diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity. The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self diffusion constant in the dilute solvent limit. We separately calculated the diffusivity as a function of concentration using the Darken equation and found that the diffusivity is essentially constant for the concentration range relevant for interdiffusion.Comment: 17 pages and 7 figure

Fast high fidelity quantum non-demolition qubit readout via a non-perturbative cross-Kerr coupling

Qubit readout is an indispensable element of any quantum information processor. In this work, we experimentally demonstrate a non-perturbative cross-Kerr coupling between a transmon and a polariton mode which enables an improved quantum non-demolition (QND) readout for superconducting qubits. The new mechanism uses the same experimental techniques as the standard QND qubit readout in the dispersive approximation, but due to its non-perturbative nature, it maximizes the speed, the single-shot fidelity and the QND properties of the readout. In addition, it minimizes the effect of unwanted decay channels such as the Purcell effect. We observed a single-shot readout fidelity of 97.4% for short 50 ns pulses, and we quantified a QND-ness of 99% for long measurement pulses with repeated single-shot readouts