Exact Floquet states of a driven condensate and their stabilities
arXiv:0705.0058 · doi:10.1088/0953-4075/41/9/095301
Abstract
We investigate the Gross-Pitaevskii equation for a classically chaotic system, which describes an atomic Bose-Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continuing region and a phase-jumping one. In the latter region, the Floquet states are spatiotemporal vortices of nontrivial phase structures and zero-density cores. Due to the velocity singularities of vortex cores and the blowing-up of perturbed solutions, the spatiotemporal vortices are unstable periodic states embedded in chaos. The stability and instability of these Floquet states are numerically explored by the time evolution of fidelity between the exact and numerical solutions. It is numerically illustrated that the stable Floquet states could be prepared from the uniformly initial states by slow growth of the external potential.
arXiv comment14 pages, 3 eps figures, final version accepted for publication in J. Phys. B
References in corpus (21)
- Vortex formation in a stirred Bose-Einstein condensate
- Dynamics of Loschmidt echoes and fidelity decay
- Spatial quantum noise interferometry in expanding ultracold atom clouds
- Superfluid-insulator transition in a periodically driven optical lattice
- Landau and Dynamical Instabilities of the Superflow of Bose-Einstein Condensates in Optical Lattices
- Vortex Nucleation in a Stirred Bose-Einstein Condensate
- Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential
- Observation of dynamical instability for a Bose-Einstein condensate in a moving 1D optical lattice
- Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential
- Quantum Computation with a One-Dimensional Optical Lattice
- Matter-wave gap vortices in optical lattices
- On collapse in the nonlinear Schrodinger equation with time dependent nonlinearity. Application to Bose-Einstein condensates
- Dynamics of bright matter wave solitons in a quasi 1D Bose-Einstein condensate with a rapidly varying trap
- Nonlinear Bloch modes in two-dimensional photonic lattices
- Quantum Computation with Diatomic Bits in Optical Lattices
- Melting of Discrete Vortices via Quantum Fluctuations
- Quantum information processing in bosonic lattices
- Resonance in Bose-Einstein condensate oscillation from a periodic variation in scattering length
- Bose-Einstein Condensation of Particle-Hole Pairs in Ultracold Fermionic Atoms Trapped within Optical Lattices
- Exact nonstationary solutions to the mean-field equations of motion for two-component Bose-Einstein condensates in periodic potentials
- Quantum dynamics of two-dimensional vortex pairs with arbitrary total vorticity
Cited by in corpus (8)
- Fractional photon-assisted tunneling for Bose-Einstein condensates in a double well
- Discrete chaotic states of a Bose-Einstein condensate
- Exact control of parity-time symmetry in periodically modulated nonlinear optical couplers
- Reproducible mesoscopic superpositions of Bose-Einstein condensates and mean-field chaos
- Regular and chaotic Bose-Einstein condensate in an accelerated Wannier-Stark lattice
- Solvable model of a generic driven mixture of trapped Bose-Einstein condensates and properties of a many-boson Floquet state at the limit of an infinite number of particles
- Dynamic renormalization group theory for open Floquet systems
- Faraday Waves in strongly interacting superfluids