Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States

The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability associated with such an arrangement allows for the study of the competition and interplay between these two, and gives rise to a whole range of interesting and rich nonlinear effects. This review covers the basic idea and overview of such nonlinear phenomena, especially those corresponding to extended states. This includes "swallowtail" loop structures of the energy band, Bloch states with multiple periodicity, and those in "nonlinear lattices", i.e., systems with the nonlinear interaction term itself being a periodic function in space.Comment: 39 pages, 21 figures; review article to be published in a Special Issue of Entropy on "Non-Linear Lattice

Stability of the Breached Pair State for a Two-species Fermionic System in the Presence of Feshbach Resonance

We investigate the phenomenon of fermionic pairing with mismatched Fermi surfaces in a two-species system in the presence of Feshbach resonance, where the resonantly-paired fermions combine to form bosonic molecules. We observe that the Feshbach parameters control the critical temperature of the gapped BCS superfluid state, and also determine the range over which a gapless breached pair state may exist. Demanding the positivity of the superfluid density, it is shown that although a breached pair state with two Fermi surfaces is always unstable, its single Fermi-surface counterpart can be stable if the chemical potentials of the two pairing species have opposite signs. This condition is satisfied only over a narrow region in the BEC side, characterized by an upper and a lower limit for the magnetic field. We estimate these limits for a mixture of two hyperfine states of $^6$Li using recent experimental data.Comment: 14 pages,5 figure

Exotic pairing structures in population-imbalanced fermionic systems: dynamics as a probe

We investigate a population-imbalanced two-species fermionic system where the resonantly paired fermions combine to form bosonic molecules via Feshbach interaction. We study the dynamics of the intrinsic quantum fluctuations of the system. It is shown that the natural fluctuations of the condensate fraction consist of a fixed number of periodic components: indicating that these oscillations do not die out, and are sustained in the mean field dynamics of the system. These frequency components bear distinct signatures of the nature of pairing present in the system. We describe how a time-dependent external magnetic field can be used to locate these oscillation frequencies, and thus to explore the momentum space structure of the population imbalanced system. We propose that this method can be used as an indirect experimental probe for detecting exotic phases like the breached-pair state, FFLO state, and a phase-separated state comprising of BCS and normal regions

Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States

The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability associated with such an arrangement allows for the study of the competition and interplay between these two, and gives rise to a whole range of interesting and rich nonlinear effects. This review covers the basic idea and overview of such nonlinear phenomena, especially those corresponding to extended states. This includes “swallowtail” loop structures of the energy band, Bloch states with multiple periodicity, and those in “nonlinear lattices”, i.e., systems with the nonlinear interaction term itself being a periodic function in space. c 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).1661sciescopu

Attraction-induced dynamical stability of a Bose-Einstein condensate in a nonlinear lattice

We study multiple-period Bloch states of a Bose-Einstein condensate with spatially periodic interatomic interaction. Solving the Gross-Pitaevskii equation for the continuum model, and also using a simplified discrete version of it, we investigate the energy-band structures and the corresponding stability properties. We observe an “attraction-induced dynamical stability” mechanism caused by the localization of the density distribution in the attractive domains of the system and the isolation of these higher-density regions. This makes the superfluid stable near the zone boundary and also enhances the stability of higher-periodic states if the nonlinear interaction strength is sufficiently high. ©2016 American Physical Society1111sciescopu

The grey zone: the 'ordinary' violence of extraordinary times

The article analyses the 'ordinary' violence of revolutionary politics, particularly acts of gendered and sexual violence that tend to be neglected in the face of the 'extraordinariness' of political terror. Focusing on the extreme left Naxalbari movement of West Bengal, it points to those morally ambiguous 'grey zones' that confound the rigid distinctions between victim and victimizer in insurrectionary politics. Public and private recollections of sexual and gender-based injuries by women activists point to the complex intermeshing of different forms of violence (everyday, political, structural, symbolic) across 'safe' and 'unsafe' spaces, 'public' and 'private' worlds, and communities of trust and those of betrayal. In making sense of these memories and their largely secret or 'untellable' nature, the article places sexual violence on a continuum of multiple and interrelated forces that are both overt and symbolic, and include a society's ways of mourning some forms of violence and silencing others. The idea of a continuum explores the 'greyness' of violence as the very object of anthropological inquiry