Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States
arXiv:1603.08818 · doi:10.3390/e18040118
Abstract
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.
arXiv comment39 pages, 21 figures; review article to be published in a Special Issue of Entropy on "Non-Linear Lattice"
References in corpus (62)
- Many-Body Physics with Ultracold Gases
- Theory of Bose-Einstein condensation in trapped gases
- Feshbach Resonances in Ultracold Gases
- Theory of ultracold Fermi gases
- Formation and Propagation of Matter Wave Soliton Trains
- Formation of a Matter-Wave Bright Soliton
- Dark Solitons in Bose-Einstein Condensates
- Solitons in nonlinear lattices
- Vortices and Superfluidity in a Strongly Interacting Fermi Gas
- Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
- Shortcuts to adiabaticity
- Influence of nearly resonant light on the scattering length in low-temperature atomic gases
- Landau and Dynamical Instabilities of the Superflow of Bose-Einstein Condensates in Optical Lattices
- Hysteresis in a quantized, superfluid atomtronic circuit
- Driving phase slips in a superfluid atom circuit with a rotating weak link
- Superfluid and Dissipative Dynamics of a Bose-Einstein Condensate in a Periodic Optical Potential
- Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential
- Dynamical Superfluid-Insulator Transition in a Chain of Weakly Coupled Bose-Einstein Condensates
- Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice
- Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
- Cold Bosons in Optical Lattices
- Nanometer-scale spatial modulation of an inter-atomic interaction in a Bose-Einstein condensate
- Band structure, elementary excitations, and stability of a Bose-Einstein condensate in a periodic potential
- Superfluid current disruption in a chain of weakly coupled Bose-Einstein Condensates
- Spin-orbit coupled Bose-Einstein condensates in a one-dimensional optical lattice
- Critical velocity for superfluid flow across the BEC-BCS crossover
- Inducing Transport in a Dissipation-Free Lattice with Super Bloch Oscillations
- Many-body Landau-Zener dynamics in coupled 1D Bose liquids
- Phase diagram for a Bose-Einstein condensate moving in an optical lattice
- Superfluidity and Swallowtails; Hysteretic Behavior in Bose Condensates
- Bloch Waves and Bloch Bands of Bose-Einstein Condensates in Optical Lattices
- Loop structure of the lowest Bloch band for a Bose-Einstein condensate
- Period-doubling Instability of Bose-Einstein Condensates Induced in Periodically Translated Optical Lattices
- Unstable regimes for a Bose-Einstein condensate in an optical lattice
- Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices
- Spatial period-doubling in Bose-Einstein condensates in an optical lattice
- Role of transverse excitations in the instability of Bose-Einstein condensates moving in optical lattices
- Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations
- Nonlinear Band Structure in Bose Einstein Condensates: The Nonlinear Schrödinger Equation with a Kronig-Penney Potential
- Critical velocity of superfluid flow through single barrier and periodic potentials
- Bose-Einstein Condensate in a Honeycomb Optical Lattice: Fingerprint of Superfluidity at the Dirac Point
- Period doubling, two-color lattices, and the growth of swallowtails in Bose-Einstein condensates
- Stability of Bose-Einstein condensates in a Kronig-Penney potential
- Bose-Einstein condensates in toroidal traps: instabilities, swallow-tail loops, and self-trapping
- Stable periodic density waves in dipolar Bose-Einstein condensates trapped in optical lattices
- Nonlinear Krönig-Penney model
- Dynamical instabilities of Bose-Einstein condensates at the band-edge in one-dimensional optical lattices
- Mean field loops versus quantum anti-crossing nets in trapped Bose-Einstein condensates
- Superfluidity and Stabilities of a Bose-Einstein condensate with periodically modulated interatomic interaction
- Band structure loops and multistability in cavity-QED
- Impurity in a bosonic Josephson junction: swallowtail loops, chaos, self-trapping and the poor man's Dicke model
- Swallowtail Band Structure of the Superfluid Fermi Gas in an Optical Lattice
- Loss and revival of phase coherence in a Bose-Einstein condensate moving through an optical lattice
- Loop Structure Stability of a Double-Well-Lattice BEC
- Molecular Dynamics for Dense Matter
- Superfluidity of Bose-Einstein condensates in ultracold atomic gases
- Dynamical instability and dispersion management of an attractive condensate in an optical lattice
- Expansion of a Bose-Einstein condensate formed on a joint harmonic and one-dimensional optical-lattice potentials
- Attraction-induced dynamical stability of a Bose-Einstein condensate in a nonlinear lattice
- Swallowtail Structure in Fermi Superfluids with Periodically Modulated Interactions
- Aspects of Superfluid Cold Atomic Gases in Optical Lattices
- Multiple period states of the superfluid Fermi gas in an optical lattice
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- Vortex solitons: Old results and new perspectives
- Nonlinearity induced topological physics in momentum space and real space
- Nonlinear Dirac Cones
- Non-exponential tunneling due to mean-field induced swallowtails
- Breakdown of quantization in nonlinear Thouless pumping
- Floquet eigenspectra of a nonlinear two-mode system under periodic driving: the emergence of "ring" structures
- Thermally activated phase slips of one-dimensional Bose gases in shallow optical lattices
- Attraction-induced dynamical stability of a Bose-Einstein condensate in a nonlinear lattice
- Instabilities of a Bose-Einstein condensate with mixed nonlinear and linear lattices
- Stabilization of Nonlinear Lattices: A Route to Superfluidity and Hysteresis
- Topological characteristics of gap closing points in nonlinear Weyl semimetals
- Stabilizing period-doubled density waves by spin-orbit coupling in Bose-Einstein condensates in optical lattices
- Nonreciprocity Induced Fractional Nonlinear Thouless Pumping