358 research outputs found
Making, probing and understanding Bose-Einstein condensates
Contribution to the proceedings of the 1998 Enrico Fermi summer school on
Bose-Einstein condensation in Varenna, Italy.Comment: Long review paper with ~90 pages, ~20 figures. 2 GIF figures in
separate files (4/5/99 fixed figure
Use of Markov Chains to Design an Agent Bidding Strategy for Continuous Double Auctions
As computational agents are developed for increasingly complicated e-commerce
applications, the complexity of the decisions they face demands advances in
artificial intelligence techniques. For example, an agent representing a seller
in an auction should try to maximize the seller's profit by reasoning about a
variety of possibly uncertain pieces of information, such as the maximum prices
various buyers might be willing to pay, the possible prices being offered by
competing sellers, the rules by which the auction operates, the dynamic arrival
and matching of offers to buy and sell, and so on. A naive application of
multiagent reasoning techniques would require the seller's agent to explicitly
model all of the other agents through an extended time horizon, rendering the
problem intractable for many realistically-sized problems. We have instead
devised a new strategy that an agent can use to determine its bid price based
on a more tractable Markov chain model of the auction process. We have
experimentally identified the conditions under which our new strategy works
well, as well as how well it works in comparison to the optimal performance the
agent could have achieved had it known the future. Our results show that our
new strategy in general performs well, outperforming other tractable heuristic
strategies in a majority of experiments, and is particularly effective in a
'seller?s market', where many buy offers are available
Chen-Ruan cohomology of ADE singularities
We study Ruan's \textit{cohomological crepant resolution conjecture} for
orbifolds with transversal ADE singularities. In the -case we compute both
the Chen-Ruan cohomology ring and the quantum corrected
cohomology ring . The former is achieved in general, the
later up to some additional, technical assumptions. We construct an explicit
isomorphism between and in the -case,
verifying Ruan's conjecture. In the -case, the family
is not defined for . This implies that
the conjecture should be slightly modified. We propose a new conjecture in the
-case which we prove in the -case by constructing an explicit
isomorphism.Comment: This is a short version of my Ph.D. Thesis math.AG/0510528. Version
2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a
link with the classical McKay correpondence is given. International Journal
of Mathematics (to appear
Atomic wave packet dynamics in finite time-dependent optical lattices
Atomic wave packets in optical lattices which are both spatially finite and
time-dependent exhibit many striking similarities with light pulses in photonic
crystals. We analytically characterize the transmission properties of such a
potential geometry for an ideal gas in terms of a position-dependent band
structure. In particular, we find that at specific energies, wave packets at
the center of the finite lattice may be enclosed by pairs of band gaps. These
act as mirrors between which the atomic wave packet is reflected, thereby
effectively yielding a matter wave cavity. We show that long trapping times may
be obtained in such a resonator and investigate the collapse and revival
dynamics of the atomic wave packet by numerical evaluation of the Schr\"odinger
equation
Long-Term Stability of an Area-Reversible Atom-Interferometer Sagnac Gyroscope
We report on a study of the long-term stability and absolute accuracy of an
atom interferometer gyroscope. This study included the implementation of an
electro-optical technique to reverse the vector area of the interferometer for
reduced systematics and a careful study of systematic phase shifts. Our data
strongly suggests that drifts less than 96 deg/hr are possible after
empirically removing shifts due to measured changes in temperature, laser
intensity, and several other experimental parameters.Comment: 4 pages, 4 figures, submitted to PR
Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates
Squeezed states, a special kind of entangled states, are known as a useful
resource for quantum metrology. In interferometric sensors they allow to
overcome the "classical" projection noise limit stemming from the independent
nature of the individual photons or atoms within the interferometer. Motivated
by the potential impact on metrology as wells as by fundamental questions in
the context of entanglement, a lot of theoretical and experimental effort has
been made to study squeezed states. The first squeezed states useful for
quantum enhanced metrology have been proposed and generated in quantum optics,
where the squeezed variables are the coherences of the light field. In this
tutorial we focus on spin squeezing in atomic systems. We give an introduction
to its concepts and discuss its generation in Bose-Einstein condensates. We
discuss in detail the experimental requirements necessary for the generation
and direct detection of coherent spin squeezing. Two exemplary experiments
demonstrating adiabatically prepared spin squeezing based on motional degrees
of freedom and diabatically realized spin squeezing based on internal hyperfine
degrees of freedom are discussed.Comment: Phd tutorial, 23 pages, 17 figure
Self-interference of a single Bose-Einstein condensate due to boundary effects
A simple model wavefunction, consisting of a linear combination of two
free-particle Gaussians, describes many of the observed features seen in the
interactions of two isolated Bose-Einstein condensates as they expand, overlap,
and interfere. We show that a simple extension of this idea can be used to
predict the qualitative time-development of a single expanding BEC condensate
produced near an infinite wall boundary, giving similar interference phenomena.
We also briefly discuss other possible time-dependent behaviors of single BEC
condensates in restricted geometries,such as wave packet revivals.Comment: 8 pages, no figures, to appear in Physica Script
Calorimetry of Bose-Einstein condensates
We outline a practical scheme for measuring the thermodynamic properties of a
Bose-Einstein condensate as a function of internal energy. We propose using
Bragg scattering and controlled trap manipulations to impart a precise amount
of energy to a near zero temperature condensate. After thermalisation the
temperature can be measured using standard techniques to determine the state
equation . Our analysis accounts for interaction effects and the
excitation of constants of motion which restrict the energy available for
thermalisation.Comment: 6 pages, 1 figure. Updated to published versio
Extracting density-density correlations from in situ images of atomic quantum gases
We present a complete recipe to extract the density-density correlations and
the static structure factor of a two-dimensional (2D) atomic quantum gas from
in situ imaging. Using images of non-interacting thermal gases, we characterize
and remove the systematic contributions of imaging aberrations to the measured
density-density correlations of atomic samples. We determine the static
structure factor and report results on weakly interacting 2D Bose gases, as
well as strongly interacting gases in a 2D optical lattice. In the strongly
interacting regime, we observe a strong suppression of the static structure
factor at long wavelengths.Comment: 15 pages, 5 figure
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