56,608 research outputs found
Deterministic multi-mode photonic device for quantum information processing
We propose the implementation of a light source, which can deterministically
generate a rich variety of multi-mode quantum states. The desired states are
encoded in the collective population of different ground hyperfine states of an
atomic ensemble and converted to multi-mode photonic states by excitation to
optically excited levels followed by cooperative spontaneous emission. Among
our examples of applications, we demonstrate how two-photon entangled states
can be prepared and implemented in a protocol for reference frame free quantum
key distribution and how one-dimensional as well as higher-dimensional cluster
states can be produced.Comment: 5 pages, 4 figure
Atomic spin squeezing in an optical cavity
We consider squeezing of one component of the collective spin vector of an
atomic ensemble inside an optical cavity. The atoms interact with a cavity
mode, and the squeezing is obtained by probing the state of the light field
that is transmitted through the cavity. Starting from the stochastic master
equation, we derive the time evolution of the state of the atoms and the cavity
field, and we compute expectation values and variances of the atomic spin
components and the quadratures of the cavity mode. The performance of the setup
is compared to spin squeezing of atoms by probing of a light field transmitted
only once through the sample.Comment: 8 pages, 2 figure
Model wavefunctions for interfaces between lattice Laughlin states
We study the interfaces between lattice Laughlin states at different
fillings. We propose a class of model wavefunctions for such systems
constructed using conformal field theory. We find a nontrivial form of charge
conservation at the interface, similar to the one encountered in the field
theory works from the literature. Using Monte Carlo methods, we evaluate the
correlation function and entanglement entropy at the border. Furthermore, we
construct the wavefunction for quasihole excitations and evaluate their mutual
statistics with respect to quasiholes originating at the same or the other side
of the interface. We show that some of these excitations lose their anyonic
statistics when crossing the interface, which can be interpreted as
impermeability of the interface to these anyons. Contrary to most of the
previous works on interfaces between topological orders, our approach is
microscopic, allowing for a direct simulation of e.g. an anyon crossing the
interface. Even though we determine the properties of the wavefunction
numerically, the closed-form expressions allow us to study systems too large to
be simulated by exact diagonalization.Comment: A number of changes were made in response to referees' comments:
large parts of the text were rewritten, new results were added, some of the
old results were reinterpreted, the discussion of connection to earlier works
was expande
Chain and ladder models with two-body interactions and analytical ground states
We consider a family of spin-1/2 models with few-body, SU(2) invariant
Hamiltonians and analytical ground states related to the 1D Haldane-Shastry
wavefunction. The spins are placed on the surface of a cylinder, and the
standard 1D Haldane-Shastry model is obtained by placing the spins with equal
spacing in a circle around the cylinder. Here, we show that another interesting
family of models with two-body exchange interactions is obtained if we instead
place the spins along one or two lines parallel to the cylinder axis, giving
rise to chain and ladder models, respectively. We can change the scale along
the cylinder axis without changing the radius of the cylinder. This gives us a
parameter that controls the ratio between the circumference of the cylinder and
all other length scales in the system. We use Monte Carlo simulations and
analytical investigations to study how this ratio affects the properties of the
models. If the ratio is large, we find that the two legs of the ladder decouple
into two chains that are in a critical phase with Haldane-Shastry-like
properties. If the ratio is small, the wavefunction reduces to a product of
singlets. In between, we find that the behavior of the correlations and the
Renyi entropy depends on the distance considered. For small distances the
behavior is critical, and for long distances the correlations decay
exponentially and the entropy shows an area law behavior. The distance up to
which there is critical behavior gets larger and larger as the ratio increases.Comment: 19 pages, 16 figure
Probability measures, L\'{e}vy measures and analyticity in time
We investigate the relation of the semigroup probability density of an
infinite activity L\'{e}vy process to the corresponding L\'{e}vy density. For
subordinators, we provide three methods to compute the former from the latter.
The first method is based on approximating compound Poisson distributions, the
second method uses convolution integrals of the upper tail integral of the
L\'{e}vy measure and the third method uses the analytic continuation of the
L\'{e}vy density to a complex cone and contour integration. As a by-product, we
investigate the smoothness of the semigroup density in time. Several concrete
examples illustrate the three methods and our results.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6114 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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