15,151 research outputs found
Anharmonicity Induced Resonances for Ultracold Atoms and their Detection
When two atoms interact in the presence of an anharmonic potential, such as
an optical lattice, the center of mass motion cannot be separated from the
relative motion. In addition to generating a confinement-induced resonance (or
shifting the position of an existing Feshbach resonance), the external
potential changes the resonance picture qualitatively by introducing new
resonances where molecular excited center of mass states cross the scattering
threshold. We demonstrate the existence of these resonances, give their
quantitative characterization in an optical superlattice, and propose an
experimental scheme to detect them through controlled sweeping of the magnetic
field.Comment: 6 pages, 5 figures; expanded presentatio
Comment on "Quantum Phase Slips and Transport in Ultrathin Superconducting Wires"
In a recent Letter (Phys. Rev. Lett.78, 1552 (1997) ), Zaikin, Golubev, van
Otterlo, and Zimanyi criticized the phenomenological time-dependent
Ginzburg-Laudau model which I used to study the quantum phase-slippage rate for
superconducting wires. They claimed that they developed a "microscopic" model,
made qualitative improvement on my overestimate of the tunnelling barrier due
to electromagnetic field. In this comment, I want to point out that, i), ZGVZ's
result on EM barrier is expected in my paper; ii), their work is also
phenomenological; iii), their renormalization scheme is fundamentally flawed;
iv), they underestimated the barrier for ultrathin wires; v), their comparison
with experiments is incorrect.Comment: Substantial changes made. Zaikin et al's main result was expected
from my work. They underestimated tunneling barrier for ultrathin wires by
one order of magnitude in the exponen
Three-dimensional theory for interaction between atomic ensembles and free-space light
Atomic ensembles have shown to be a promising candidate for implementations
of quantum information processing by many recently-discovered schemes. All
these schemes are based on the interaction between optical beams and atomic
ensembles. For description of these interactions, one assumed either a
cavity-QED model or a one-dimensional light propagation model, which is still
inadequate for a full prediction and understanding of most of the current
experimental efforts which are actually taken in the three-dimensional free
space. Here, we propose a perturbative theory to describe the three-dimensional
effects in interaction between atomic ensembles and free-space light with a
level configuration important for several applications. The calculations reveal
some significant effects which are not known before from the other approaches,
such as the inherent mode-mismatching noise and the optimal mode-matching
conditions. The three-dimensional theory confirms the collective enhancement of
the signal-to-noise ratio which is believed to be one of the main advantage of
the ensemble-based quantum information processing schemes, however, it also
shows that this enhancement need to be understood in a more subtle way with an
appropriate mode matching method.Comment: 16 pages, 9 figure
A dynamical approximation for stochastic partial differential equations
Random invariant manifolds often provide geometric structures for
understanding stochastic dynamics. In this paper, a dynamical approximation
estimate is derived for a class of stochastic partial differential equations,
by showing that the random invariant manifold is almost surely asymptotically
complete. The asymptotic dynamical behavior is thus described by a stochastic
ordinary differential system on the random invariant manifold, under suitable
conditions. As an application, stationary states (invariant measures) is
considered for one example of stochastic partial differential equations.Comment: 28 pages, no figure
Optimal time decay of the non cut-off Boltzmann equation in the whole space
In this paper we study the large-time behavior of perturbative classical
solutions to the hard and soft potential Boltzmann equation without the angular
cut-off assumption in the whole space \threed_x with \DgE. We use the
existence theory of global in time nearby Maxwellian solutions from
\cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to
determine the large time decay rates for the soft potential Boltzmann equation
in the whole space, with or without the angular cut-off assumption
\cite{MR677262,MR2847536}. For perturbative initial data, we prove that
solutions converge to the global Maxwellian with the optimal large-time decay
rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the
L^2_\vel(L^r_x)-norm for any .Comment: 31 pages, final version to appear in KR
A heralded quantum gate between remote quantum memories
We demonstrate a probabilistic entangling quantum gate between two distant
trapped ytterbium ions. The gate is implemented between the hyperfine "clock"
state atomic qubits and mediated by the interference of two emitted photons
carrying frequency encoded qubits. Heralded by the coincidence detection of
these two photons, the gate has an average fidelity of 90+-2%. This entangling
gate together with single qubit operations is sufficient to generate large
entangled cluster states for scalable quantum computing
Inseparability criterion for continuous variable systems
An inseparability criterion based on the total variance of a pair of
Einstein-Podolsky-Rosen type operators is proposed for continuous variable
systems. The criterion provides a sufficient condition for entanglement of any
two-party continuous variable states. Furthermore, for all the Gaussian states,
this criterion turns out to be a necessary and sufficient condition for
inseparability.Comment: minor changes in the introduction and ref
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