[show abstract][hide abstract] ABSTRACT: We present a systematic study of the generation of the array of optical or matter-wave kinks (dark solitons) in the ground state (GS) of binary systems. We consider quasi-one-dimensional systems described by a pair of nonlinear Schrödinger (NLSE’s) or Gross-Pitaevskii equations (GPE’s), which are coupled by the linear mixing, with local strength Ω, and by nonlinear interactions. We assume the self-repulsive nonlinearity in both components, and include the effects of a harmonic trapping potential, while the nonlinear interaction between the components may be both repulsive and attractive. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics and also in Bose-Einstein condensates. Depending on the sign and strengths of the linear and nonlinear couplings between the components, the ground states in such binary systems may be symmetric, antisymmetric, or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making Ω an odd or even function of the coordinate (x). The sign flips of Ω(x) strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of Ω. Using a systematic numerical analysis and an analytic approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. The final results are presented in the form of maps showing the number of kinks in the GS as a function of the system’s parameters, with the odd (even) modulation function giving rise to the odd (even) number of the kinks. The modulation of Ω(x) also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.
Physical Review A 10/2010; 82(4). · 3.04 Impact Factor
[show abstract][hide abstract] ABSTRACT: We observe signatures of disorder-induced order in one-dimensional XY spin chains with an external site-dependent uniaxial random field within the XY plane. We numerically investigate signatures of a quantum phase transition at T=0, in particular, an upsurge of the magnetization in the direction orthogonal to the external magnetic field and the scaling of the block entropy with the amplitude of this field. Also, we discuss possible realizations of this effect in ultracold atomic experiments.
Physical Review A 07/2010; 82(1). · 3.04 Impact Factor
[show abstract][hide abstract] ABSTRACT: We consider a mixture of a superfluid Fermi gas of ultracold atoms and a Bose-Einstein condensate of molecules possessing a continuous U(1) (relative phase) symmetry. We study the effects of a spatially random photo-associative–dissociative symmetry-breaking coupling of the systems. Such coupling allows one to control the relative phase between a superfluid order parameter of the Fermi system and the condensate wave function of molecules for temperatures below the Bardeen-Cooper-Schriefer critical temperature. The presented mechanism of phase control belongs to the general class of phenomena in which disorder interacts with continuous symmetry. Our results show the robustness and wide range of applicability of disorder-induced order and are valid for both disordered and regular couplings. Here, the effect is studied in the case of interacting fermionic and bosonic gases in the superfluid phase.
[show abstract][hide abstract] ABSTRACT: We propose and analyze a general mechanism of disorder-induced order in two-component Bose-Einstein condensates, analogous to corresponding effects established for XY spin models. We show that a random Raman coupling induces a relative phase of pi/2 between the two BECs and that the effect is robust. We demonstrate it in one, two, and three dimensions at T=0 and present evidence that it persists at small T>0. Applications to phase control in ultracold spinor condensates are discussed.
[show abstract][hide abstract] ABSTRACT: We propose a general mechanism of random-field-induced order (RFIO), in which long-range order is induced by a random field that breaks the continuous symmetry of the model. We particularly focus on the case of the classical ferromagnetic XY model on a two-dimensional lattice, in a uniaxial random field. We prove rigorously that the system has spontaneous magnetization at temperature T=0, and we present strong evidence that this is also the case for small T>0. We discuss generalizations of this mechanism to various classical and quantum systems. In addition, we propose possible realizations of the RFIO mechanism, using ultracold atoms in an optical lattice. Our results shed new light on controversies in existing literature, and open a way to realize RFIO with ultracold atomic systems.
Physical Review B 05/2006; 74(22). · 3.77 Impact Factor