444 research outputs found
Localization of Chaotic Resonance States due to a Partial Transport Barrier
Chaotic eigenstates of quantum systems are known to localize on either side
of a classical partial transport barrier if the flux connecting the two sides
is quantum mechanically not resolved due to Heisenberg's uncertainty.
Surprisingly, in open systems with escape chaotic resonance states can localize
even if the flux is quantum mechanically resolved. We explain this using the
concept of conditionally invariant measures from classical dynamical systems by
introducing a new quantum mechanically relevant class of such fractal measures.
We numerically find quantum-to-classical correspondence for localization
transitions depending on the openness of the system and on the decay rate of
resonance states.Comment: 5+1 pages, 4 figure
First-principle calculations of Dark Matter scattering off light nuclei
We study the scattering of Dark Matter particles off various light nuclei
within the framework of chiral effective field theory. We focus on scalar
interactions and include one- and two-nucleon scattering processes whose form
and strength are dictated by chiral symmetry. The nuclear wave functions are
calculated from chiral effective field theory interactions as well and we
investigate the convergence pattern of the chiral expansion in the nuclear
potential and the Dark Matter-nucleus currents. This allows us to provide a
systematic uncertainty estimate of our calculations. We provide results for
H, H, and He nuclei which are theoretically interesting and
the latter is a potential target for experiments. We show that two-nucleon
currents can be systematically included but are generally smaller than
predicted by power counting and suffer from significant theoretical
uncertainties even in light nuclei. We demonstrate that accurate high-order
wave functions are necessary in order to incorporate two-nucleon currents. We
discuss scenarios in which one-nucleon contributions are suppressed such that
higher-order currents become dominant
Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems
In open chaotic systems the number of long-lived resonance states obeys a
fractal Weyl law, which depends on the fractal dimension of the chaotic saddle.
We study the generic case of a mixed phase space with regular and chaotic
dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the
hierarchical decomposition of the chaotic phase-space component. This is based
on our observation of hierarchical resonance states localizing on these
regions. Numerically this is verified for the standard map and a hierarchical
model system.Comment: 5 pages, 3 figure
Measurement of the hyperfine structure of the S1/2-D5/2 transition in 43Ca+
The hyperfine structure of the S1/2-D5/2 quadrupole transition at 729 nm in
43Ca+ has been investigated by laser spectroscopy using a single trapped 43Ca+
ion. We determine the hyperfine structure constants of the metastable level as
A=-3.8931(2) MHz and B=-4.241(4) MHz. The isotope shift of the transition with
respect to 40Ca+ was measured to be 4134.713(5) MHz. We demonstrate the
existence of transitions that become independent of the first-order Zeeman
shift at non-zero low magnetic fields. These transitions might be better suited
for building a frequency standard than the well-known 'clock transitions'
between m=0 levels at zero magnetic field.Comment: corrected for sign errors in the hyperfine constants. No corrections
to were made to the data analysi
Resonance eigenfunction hypothesis for chaotic systems
A hypothesis about the average phase-space distribution of resonance
eigenfunctions in chaotic systems with escape through an opening is proposed.
Eigenfunctions with decay rate are described by a classical measure
that is conditionally invariant with classical decay rate and
is uniformly distributed on sets with the same temporal distance to the
quantum resolved chaotic saddle. This explains the localization of
fast-decaying resonance eigenfunctions classically. It is found to occur in the
phase-space region having the largest distance to the chaotic saddle. We
discuss the dependence on the decay rate and the semiclassical limit.
The hypothesis is numerically demonstrated for the standard map
Process tomography of ion trap quantum gates
A crucial building block for quantum information processing with trapped ions
is a controlled-NOT quantum gate. In this paper, two different sequences of
laser pulses implementing such a gate operation are analyzed using quantum
process tomography. Fidelities of up to 92.6(6)% are achieved for single gate
operations and up to 83.4(8)% for two concatenated gate operations. By process
tomography we assess the performance of the gates for different experimental
realizations and demonstrate the advantage of amplitude--shaped laser pulses
over simple square pulses. We also investigate whether the performance of
concatenated gates can be inferred from the analysis of the single gates
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