Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential
arXiv:cond-mat/0007174 · doi:10.1103/PhysRevLett.86.1402
Abstract
We present a new family of stationary solutions to the cubic nonlinear Schroedinger equation with a Jacobian elliptic function potential. In the limit of a sinusoidal potential our solutions model a dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided the ratio of the height of the variations of the condensate to its DC offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Numerical simulations suggest such stationary states are experimentally observable.
4 pages, 4 figures
References in corpus (3)
Cited by in corpus (98)
- Transition from a strongly interacting 1D superfluid to a Mott insulator
- Solitons in nonlinear lattices
- Landau and Dynamical Instabilities of the Superflow of Bose-Einstein Condensates in Optical Lattices
- A Bose-Einstein condensate in an optical lattice
- Modulational instability in cigar shaped Bose-Einstein condensates in optical lattices
- Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
- Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
- Bose-Einstein Condensates in Optical Lattices: Band-Gap Structure and Solitons
- 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
- Adiabatic dynamics of periodic waves in Bose-Einstein condensate with time dependent atomic scattering length
- Quantized Quasi-Two Dimensional Bose-Einstein Condensates with Spatially Modulated Nonlinearity
- Nonlinear localized waves in a periodic medium
- 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
- Superfluid to Mott insulator transition in one, two, and three dimensions
- Spatial period-doubling in Bose-Einstein condensates in an optical lattice
- Linearly Coupled Bose-Einstein Condensates: From Rabi Oscillations and Quasi-Periodic Solutions to Oscillating Domain Walls and Spiral Waves
- Quantum Entangled Dark Solitons Formed by Ultracold Atoms in Optical Lattices
- Fractional Integrable Nonlinear Soliton Equations
- Nonlinear Band Structure in Bose Einstein Condensates: The Nonlinear Schrödinger Equation with a Kronig-Penney Potential
- Creation of solitons and vortices by Bragg reflection of Bose-Einstein condensates in an optical lattice
- Band-gap solitons in nonlinear optically-induced lattices
- Quantum Many-Body Dynamics of Dark Solitons in Optical Lattices
- Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth
- Matter-wave solutions in the Bose-Einstein condensates with the harmonic and Gaussian potentials
- Nonlinear Lattice Dynamics of Bose-Einstein Condensates
- Phase diagram of two-species Bose-Einstein condensates in an optical lattice
- Period doubling, two-color lattices, and the growth of swallowtails in Bose-Einstein condensates
- Nonautonomous solitons of Bose-Einstein condensation in a linear potential with an arbitrary time-dependence
- Manipulating localized matter waves in multi-component Bose-Einstein condensates
- Dynamics of a Bose-Einstein condensate at finite temperature in an atomoptical coherence filter
- Hirota method for the nonlinear Schrődinger equation with an arbitrary linear time-dependent potential
- Dark-in-Bright Solitons in Bose-Einstein Condensates with Attractive Interactions
- Stability of exact solutions of the defocusing nonlinear Schrodinger equation with periodic potential in two dimensions
- Sound speed of a Bose-Einstein condensate in an optical lattice
- Resonant and Non-Resonant Modulated Amplitude Waves for Binary Bose-Einstein Condensates in Optical Lattices
- Nonautonomous Bright and Dark Solitons of Bose-Einstein Condensates with Feshbach-Managed Time-Dependent Scattering Length
- Modulated Amplitude Waves in Bose-Einstein Condensates
- Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials
- Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with a spatially modulated nonlinearity
- Nonlinear waves of Bose-Einstein condensates in rotating ring lattice potentials
- The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions
- Swallowtail Band Structure of the Superfluid Fermi Gas in an Optical Lattice
- Nonlinear Bloch-waves and current states of exciton-polariton condensates
- Bulk vortices and half-vortex surface modes in parity-time-symmetric media
- Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism
- Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States
- Spatially modulated two- and three-component Rabi-coupled Gross-Pitaevskii systems
- Modulated amplitude waves with nonzero phases in Bose-Einstein condensates
- Singular instability of exact stationary solutions of the nonlocal Gross-Pitaevskii equation
- Bose-Einstein Condensates in Superlattices
- Bound States and Band Structure - a Unified Treatment through the Quantum Hamilton - Jacobi Approach
- Exact Floquet states of a driven condensate and their stabilities
- A Perturbative Analysis of Modulated Amplitude Waves in Bose-Einstein Condensates
- Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
- Smoothing and parameter estimation by soft-adherence to governing equations
- Effects of a rotating periodic lattice on coherent quantum states in a ring topology: The case of positive nonlinearity
- Uniform semiclassical approximations of the nonlinear Schroedinger equation by a Painleve mapping
- Ultracold Atoms in 1D Optical Lattices: Mean Field, Quantum Field, Computation, and Soliton Formation
- Dynamics of a period-three pattern loaded Bose-Einstein condensate in an optical lattice
- Stable multicolor periodic-wave arrays
- Analytical results for the superflow of spin-orbit-coupled Bose-Einstein condensates in optical lattices
- Self-trapping of Bose-Einstein condensates expanding into shallow optical lattices
- Balancing long-range interactions and quantum pressure: solitons in the HMF model
- Exact Dynamics of Multicomponent Bose-Einstein Condensates in Optical Lattices in One, Two and Three Dimensions
- Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm
- Stability of persistent currents in a Bose-Einstein condensate confined in a toroidal trap
- Regular and chaotic Bose-Einstein condensate in an accelerated Wannier-Stark lattice
- Controlled Generation of Nonlinear Resonances through Sinusoidal Lattice Modes in Bose-Einstein Condensate
- Attraction-induced dynamical stability of a Bose-Einstein condensate in a nonlinear lattice
- Loss of superfluidity in the Bose-Einstein condensate in an optical lattice with cubic and quintic nonlinearity
- Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice
- Spatiotemporal Bloch states of a spin-orbit coupled Bose-Einstein condensate in an optical lattice
- Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
- Nonlinear Bloch-Zener oscillations for Bose-Einstein condensates in a Lieb optical lattice
- Controllable Persistent Atom Current of Bose-Einstein Condensates in an Optical Lattice Ring
- Tunneling and Revival of Anderson Localization in Bose-Einstein Condensate
- Aspects of Superfluid Cold Atomic Gases in Optical Lattices
- Stabilities of one-dimensional stationary states of Bose-Einstein condensates
- Symmetry breaking and superfluid currents in a split-ring spinor polariton condensate
- Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged
- Kinetic Thomas-Fermi solutions of the Gross-Pitaevskii equation
- Exact nonlinear Bloch-state solutions for Bose-Einstein condensates in a periodic array of quantum wells
- Period-doubled Bloch states in a Bose-Einstein condensate
- Stability and Dynamics of Microring Combs: Elliptic function solutions of the Lugiato-Lefever equation
- Exact solutions for periodic and solitary matter waves in nonlinear lattices
- A Jacobian generalization of the pseudo Nambu-Goldstone bosons potential
- A coupled focusing-defocusing complex short pulse equation: multisoliton, breather, and rogue wave
- Solitary waves in a stochastic parametrically forced nonlinear Schrödinger equation
- Krylov integrators for Hamiltonian systems
- Dynamics and Stability of Bose-Einstein Condensates: the Nonlinear Schrodinger Equation with Periodic Potential
- Energy Band Engineering of Periodic Scatterers by Quasi-1D Confinement
- Construction of modulated amplitude waves via averaging in collisionally inhomogeneous Bose-Einstein condensates
- Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices
- Cold Atoms in Driven Optical Lattices
- Variable coefficient complex Ginzburg-Landau equation