9,251 research outputs found
Complete methods set for scalable ion trap quantum information processing
Large-scale quantum information processors must be able to transport and
maintain quantum information, and repeatedly perform logical operations. Here
we demonstrate a combination of all the fundamental elements required to
perform scalable quantum computing using qubits stored in the internal states
of trapped atomic ions. We quantify the repeatability of a multi-qubit
operation, observing no loss of performance despite qubit transport over
macroscopic distances. Key to these results is the use of different pairs of
beryllium ion hyperfine states for robust qubit storage, readout and gates, and
simultaneous trapping of magnesium re-cooling ions along with the qubit ions.Comment: 9 pages, 4 figures. Accepted to Science, and thus subject to a press
embarg
Representation of Markov chains by random maps: existence and regularity conditions
We systematically investigate the problem of representing Markov chains by
families of random maps, and which regularity of these maps can be achieved
depending on the properties of the probability measures. Our key idea is to use
techniques from optimal transport to select optimal such maps. Optimal
transport theory also tells us how convexity properties of the supports of the
measures translate into regularity properties of the maps via Legendre
transforms. Thus, from this scheme, we cannot only deduce the representation by
measurable random maps, but we can also obtain conditions for the
representation by continuous random maps. Finally, we present conditions for
the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including
extended discussion of many detail
Temporal solitons in optical microresonators
Dissipative solitons can emerge in a wide variety of dissipative nonlinear
systems throughout the fields of optics, medicine or biology. Dissipative
solitons can also exist in Kerr-nonlinear optical resonators and rely on the
double balance between parametric gain and resonator loss on the one hand and
nonlinearity and diffraction or dispersion on the other hand. Mathematically
these solitons are solution to the Lugiato-Lefever equation and exist on top of
a continuous wave (cw) background. Here we report the observation of temporal
dissipative solitons in a high-Q optical microresonator. The solitons are
spontaneously generated when the pump laser is tuned through the effective zero
detuning point of a high-Q resonance, leading to an effective red-detuned
pumping. Red-detuned pumping marks a fundamentally new operating regime in
nonlinear microresonators. While usually unstablethis regime acquires unique
stability in the presence of solitons without any active feedback on the
system. The number of solitons in the resonator can be controlled via the pump
laser detuning and transitions to and between soliton states are associated
with discontinuous steps in the resonator transmission. Beyond enabling to
study soliton physics such as soliton crystals our observations open the route
towards compact, high repetition-rate femto-second sources, where the operating
wavelength is not bound to the availability of broadband laser gain media. The
single soliton states correspond in the frequency domain to low-noise optical
frequency combs with smooth spectral envelopes, critical to applications in
broadband spectroscopy, telecommunications, astronomy and low phase-noise
microwave generation.Comment: Includes Supplementary Informatio
Mode spectrum and temporal soliton formation in optical microresonators
The formation of temporal dissipative solitons in optical microresonators
enables compact, high repetition rate sources of ultra-short pulses as well as
low noise, broadband optical frequency combs with smooth spectral envelopes.
Here we study the influence of the resonator mode spectrum on temporal soliton
formation. Using frequency comb assisted diode laser spectroscopy, the measured
mode structure of crystalline MgF2 resonators are correlated with temporal
soliton formation. While an overal general anomalous dispersion is required, it
is found that higher order dispersion can be tolerated as long as it does not
dominate the resonator's mode structure. Mode coupling induced avoided
crossings in the resonator mode spectrum are found to prevent soliton
formation, when affecting resonator modes close to the pump laser. The
experimental observations are in excellent agreement with numerical simulations
based on the nonlinear coupled mode equations, which reveal the rich interplay
of mode crossings and soliton formation
Spectral plots and the representation and interpretation of biological data
It is basic question in biology and other fields to identify the char-
acteristic properties that on one hand are shared by structures from a
particular realm, like gene regulation, protein-protein interaction or neu- ral
networks or foodwebs, and that on the other hand distinguish them from other
structures. We introduce and apply a general method, based on the spectrum of
the normalized graph Laplacian, that yields repre- sentations, the spectral
plots, that allow us to find and visualize such properties systematically. We
present such visualizations for a wide range of biological networks and compare
them with those for networks derived from theoretical schemes. The differences
that we find are quite striking and suggest that the search for universal
properties of biological networks should be complemented by an understanding of
more specific features of biological organization principles at different
scales.Comment: 15 pages, 7 figure
Radion Induced Spontaneous Baryogenesis
We describe a possible scenario for the baryogenesis arising when matter is
added on the branes of a Randall-Sundrum model with a radion stabilizing
potential. We show that the radion field can naturally induce spontaneous
baryogenesis when the cosmological evolution for the matter on the branes is
taken into account.Comment: LaTeX 2e, 8 pages and no figures, minor corrections to match version
to appear in MPL
Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies
In previous work, empirical evidence indicated that a time-varying network
could propagate sufficient information to allow synchronization of the
sometimes coupled oscillators, despite an instantaneously disconnected
topology. We prove here that if the network of oscillators synchronizes for the
static time-average of the topology, then the network will synchronize with the
time-varying topology if the time-average is achieved sufficiently fast. Fast
switching, fast on the time-scale of the coupled oscillators, overcomes the
descychnronizing decoherence suggested by disconnected instantaneous networks.
This result agrees in spirit with that of where empirical evidence suggested
that a moving averaged graph Laplacian could be used in the master-stability
function analysis. A new fast switching stability criterion here-in gives
sufficiency of a fast-switching network leading to synchronization. Although
this sufficient condition appears to be very conservative, it provides new
insights about the requirements for synchronization when the network topology
is time-varying. In particular, it can be shown that networks of oscillators
can synchronize even if at every point in time the frozen-time network topology
is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD
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