6,861 research outputs found
Raman transitions between hyperfine clock states in a magnetic trap
We present our experimental investigation of an optical Raman transition
between the magnetic clock states of Rb in an atom chip magnetic trap.
The transfer of atomic population is induced by a pair of diode lasers which
couple the two clock states off-resonantly to an intermediate state manifold.
This transition is subject to destructive interference of two excitation paths,
which leads to a reduction of the effective two-photon Rabi-frequency.
Furthermore, we find that the transition frequency is highly sensitive to the
intensity ratio of the diode lasers. Our results are well described in terms of
light shifts in the multi-level structure of Rb. The differential light
shifts vanish at an optimal intensity ratio, which we observe as a narrowing of
the transition linewidth. We also observe the temporal dynamics of the
population transfer and find good agreement with a model based on the system's
master equation and a Gaussian laser beam profile. Finally, we identify several
sources of decoherence in our system, and discuss possible improvements.Comment: 10 pages, 7 figure
Domain structure of epitaxial Co films with perpendicular anisotropy
Epitaxial hcp Cobalt films with pronounced c-axis texture have been prepared
by pulsed lased deposition (PLD) either directly onto Al2O3 (0001) single
crystal substrates or with an intermediate Ruthenium buffer layer. The crystal
structure and epitaxial growth relation was studied by XRD, pole figure
measurements and reciprocal space mapping. Detailed VSM analysis shows that the
perpendicular anisotropy of these highly textured Co films reaches the
magnetocrystalline anisotropy of hcp-Co single crystal material. Films were
prepared with thickness t of 20 nm < t < 100 nm to study the crossover from
in-plane magnetization to out-of-plane magnetization in detail. The analysis of
the periodic domain pattern observed by magnetic force microscopy allows to
determine the critical minimum thickness below which the domains adopt a pure
in-plane orientation. Above the critical thickness the width of the stripe
domains is evaluated as a function of the film thickness and compared with
domain theory. Especially the discrepancies at smallest film thicknesses show
that the system is in an intermediate state between in-plane and out-of-plane
domains, which is not described by existing analytical domain models
Phase diagram of magnetic domain walls in spin valve nano-stripes
We investigate numerically the transverse versus vortex phase diagram of
head-to-head domain walls in Co/Cu/Py spin valve nano-stripes (Py: Permalloy),
in which the Co layer is mostly single domain while the Py layer hosts the
domain wall. The range of stability of the transverse wall is shifted towards
larger thickness compared to single Py layers, due to a magnetostatic screening
effect between the two layers. An approached analytical scaling law is derived,
which reproduces faithfully the phase diagram.Comment: 4 page
Surface Roughness Dominated Pinning Mechanism of Magnetic Vortices in Soft Ferromagnetic Films
Although pinning of domain walls in ferromagnets is ubiquitous, the absence
of an appropriate characterization tool has limited the ability to correlate
the physical and magnetic microstructures of ferromagnetic films with specific
pinning mechanisms. Here, we show that the pinning of a magnetic vortex, the
simplest possible domain structure in soft ferromagnets, is strongly correlated
with surface roughness, and we make a quantitative comparison of the pinning
energy and spatial range in films of various thickness. The results demonstrate
that thickness fluctuations on the lateral length scale of the vortex core
diameter, i.e. an effective roughness at a specific length scale, provides the
dominant pinning mechanism. We argue that this mechanism will be important in
virtually any soft ferromagnetic film.Comment: 4 figure
X-ray photoelectron emission microscopy in combination with x-ray magnetic circular dichroism investigation of size effects on field-induced N\'eel-cap reversal
X-ray photoelectron emission microscopy in combination with x-ray magnetic
circular dichroism is used to investigate the influence of an applied magnetic
field on N\'eel caps (i.e., surface terminations of asymmetric Bloch walls).
Self-assembled micron-sized Fe(110) dots displaying a moderate distribution of
size and aspect ratios serve as model objects. Investigations of remanent
states after application of an applied field along the direction of N\'eel-cap
magnetization give clear evidence for the magnetization reversal of the N\'eel
caps around 120 mT, with a 20 mT dispersion. No clear correlation could be
found between the value of the reversal field and geometrical features of the
dots
An Improved Private Mechanism for Small Databases
We study the problem of answering a workload of linear queries ,
on a database of size at most drawn from a universe
under the constraint of (approximate) differential privacy.
Nikolov, Talwar, and Zhang~\cite{NTZ} proposed an efficient mechanism that, for
any given and , answers the queries with average error that is
at most a factor polynomial in and
worse than the best possible. Here we improve on this guarantee and give a
mechanism whose competitiveness ratio is at most polynomial in and
, and has no dependence on . Our mechanism
is based on the projection mechanism of Nikolov, Talwar, and Zhang, but in
place of an ad-hoc noise distribution, we use a distribution which is in a
sense optimal for the projection mechanism, and analyze it using convex duality
and the restricted invertibility principle.Comment: To appear in ICALP 2015, Track
Rational invariants of even ternary forms under the orthogonal group
In this article we determine a generating set of rational invariants of
minimal cardinality for the action of the orthogonal group on
the space of ternary forms of even degree . The
construction relies on two key ingredients: On one hand, the Slice Lemma allows
us to reduce the problem to dermining the invariants for the action on a
subspace of the finite subgroup of signed permutations. On the
other hand, our construction relies in a fundamental way on specific bases of
harmonic polynomials. These bases provide maps with prescribed
-equivariance properties. Our explicit construction of these
bases should be relevant well beyond the scope of this paper. The expression of
the -invariants can then be given in a compact form as the
composition of two equivariant maps. Instead of providing (cumbersome) explicit
expressions for the -invariants, we provide efficient algorithms
for their evaluation and rewriting. We also use the constructed
-invariants to determine the -orbit locus and
provide an algorithm for the inverse problem of finding an element in
with prescribed values for its invariants. These are
the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application,
refinement of Definition 3.1. To appear in "Foundations of Computational
Mathematics
Nearly Optimal Private Convolution
We study computing the convolution of a private input with a public input
, while satisfying the guarantees of -differential
privacy. Convolution is a fundamental operation, intimately related to Fourier
Transforms. In our setting, the private input may represent a time series of
sensitive events or a histogram of a database of confidential personal
information. Convolution then captures important primitives including linear
filtering, which is an essential tool in time series analysis, and aggregation
queries on projections of the data.
We give a nearly optimal algorithm for computing convolutions while
satisfying -differential privacy. Surprisingly, we follow
the simple strategy of adding independent Laplacian noise to each Fourier
coefficient and bounding the privacy loss using the composition theorem of
Dwork, Rothblum, and Vadhan. We derive a closed form expression for the optimal
noise to add to each Fourier coefficient using convex programming duality. Our
algorithm is very efficient -- it is essentially no more computationally
expensive than a Fast Fourier Transform.
To prove near optimality, we use the recent discrepancy lowerbounds of
Muthukrishnan and Nikolov and derive a spectral lower bound using a
characterization of discrepancy in terms of determinants
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