251 research outputs found
Effect of spatial resolution on apparent sensitivity to initial conditions of a decaying flow as it becomes turbulent
Grids with 32(exp 3), 64(exp 3), and 128(exp 3) points are used in numerical solutions for a decaying flow. The sensitivity of initially neighboring solutions to small changes in initial conditions increases as the spatial resolution improves. A fourth-order finite-difference method is used for the solutions with 32(exp 3) and 64(exp 3) grid points, and a pseudospectral method is used for 128(exp 3) grid points. The latter solutions appear to be rather well-resolved, in spite of the formation of steep velocity gradients in the flow
Confinement effects in a guided-wave interferometer with millimeter-scale arm separation
Guided-wave atom interferometers measure interference effects using atoms
held in a confining potential. In one common implementation, the confinement is
primarily two-dimensional, and the atoms move along the nearly free dimension
under the influence of an off-resonant standing wave laser beam. In this
configuration, residual confinement along the nominally free axis can introduce
a phase gradient to the atoms that limits the arm separation of the
interferometer. We experimentally investigate this effect in detail, and show
that it can be alleviated by having the atoms undergo a more symmetric motion
in the guide. This can be achieved by either using additional laser pulses or
by allowing the atoms to freely oscillate in the potential. Using these
techniques, we demonstrate interferometer measurement times up to 72 ms and arm
separations up to 0.42 mm with a well controlled phase, or times of 0.91 s and
separations of 1.7 mm with an uncontrolled phase.Comment: 14 pages, 6 figure
A Bose-Einstein condensate interferometer with macroscopic arm separation
A Michelson interferometer using Bose-Einstein condensates is demonstrated
with coherence times of up to 44 ms and arm separations up to 0.18 mm. This arm
separation is larger than that observed for any previous atom interferometer.
The device uses atoms weakly confined in a magnetic guide and the atomic motion
is controlled using Bragg interactions with an off-resonant standing wave laser
beam.Comment: 4 pages, 3 figure
A Time-Orbiting Potential Trap for Bose-Einstein Condensate Interferometry
We describe a novel atom trap for Bose-Einstein condensates of 87Rb to be
used in atom interferometry experiments. The trap is based on a time-orbiting
potential waveguide. It supports the atoms against gravity while providing weak
confinement to minimize interaction effects. We observe harmonic oscillation
frequencies omega_x, omega_y, omega_z as low as 2 pi times (6.0,1.2,3.3) Hz. Up
to 2 times 10^4 condensate atoms have been loaded into the trap, at estimated
temperatures as low as 850 pK. We anticipate that interferometer measurement
times of 1 s or more should be achievable in this device.Comment: 9 pages, 3 figure
N-tree approximation for the largest Lyapunov exponent of a coupled-map lattice
The N-tree approximation scheme, introduced in the context of random directed
polymers, is here applied to the computation of the maximum Lyapunov exponent
in a coupled map lattice. We discuss both an exact implementation for small
tree-depth and a numerical implementation for larger s. We find that the
phase-transition predicted by the mean field approach shifts towards larger
values of the coupling parameter when the depth is increased. We conjecture
that the transition eventually disappears.Comment: RevTeX, 15 pages,5 figure
Measurement of the ac Stark shift with a guided matter-wave interferometer
We demonstrate the effectiveness of a guided-wave Bose-Einstein condensate
interferometer for practical measurements. Taking advantage of the large arm
separations obtainable in our interferometer, the energy levels of the 87Rb
atoms in one arm of the interferometer are shifted by a calibrated laser beam.
The resulting phase shifts are used to determine the ac polarizability at a
range of frequencies near and at the atomic resonance. The measured values are
in good agreement with theoretical expectations. However, we observe a
broadening of the transition near the resonance, an indication of collective
light scattering effects. This nonlinearity may prove useful for the production
and control of squeezed quantum states.Comment: 5 pages, three figure
Observation of subdiffusion of a disordered interacting system
We study the transport dynamics of matter-waves in the presence of disorder
and nonlinearity. An atomic Bose-Einstein condensate that is localized in a
quasiperiodic lattice in the absence of atom-atom interaction shows instead a
slow expansion with a subdiffusive behavior when a controlled repulsive
interaction is added. The measured features of the subdiffusion are compared to
numerical simulations and a heuristic model. The observations confirm the
nature of subdiffusion as interaction-assisted hopping between localized states
and highlight a role of the spatial correlation of the disorder.Comment: 8 pages, to be published on Physical Review Letter
Quantum diffusion with disorder, noise and interaction
Disorder, noise and interaction play a crucial role in the transport
properties of real systems, but they are typically hard to control and study
both theoretically and experimentally, especially in the quantum case. Here we
explore a paradigmatic problem, the diffusion of a wavepacket, by employing
ultra-cold atoms in a disordered lattice with controlled noise and tunable
interaction. The presence of disorder leads to Anderson localization, while
both interaction and noise tend to suppress localization and restore transport,
although with completely different mechanisms. When only noise or interaction
are present we observe a diffusion dynamics that can be explained by existing
microscopic models. When noise and interaction are combined, we observe instead
a complex anomalous diffusion. By combining experimental measurements with
numerical simulations, we show that such anomalous behavior can be modeled with
a generalized diffusion equation, in which the noise- and interaction-induced
diffusions enter in an additive manner. Our study reveals also a more complex
interplay between the two diffusion mechanisms in regimes of strong interaction
or narrowband noise.Comment: 11 pages, 10 figure
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