101 research outputs found
Instability to a heterogeneous oscillatory state in randomly connected recurrent networks with delayed interactions
Oscillatory dynamics are ubiquitous in biological networks. Possible sources
of oscillations are well understood in low-dimensional systems, but have not
been fully explored in high-dimensional networks. Here we study large networks
consisting of randomly coupled rate units. We identify a novel type of
bifurcation in which a continuous part of the eigenvalue spectrum of the linear
stability matrix crosses the instability line at non-zero-frequency. This
bifurcation occurs when the interactions are delayed and partially
anti-symmetric, and leads to a heterogeneous oscillatory state in which
oscillations are apparent in the activity of individual units, but not on the
population-average level
A bridge between the single-photon and squeezed-vacuum state
The two modes of the Einstein-Podolsky-Rosen quadrature entangled state
generated by parametric down-conversion interfere on a beam splitter of
variable splitting ratio. Detection of a photon in one of the beam splitter
output channels heralds preparation of a signal state in the other, which is
characterized using homodyne tomography. By controlling the beam splitting
ratio, the signal state can be chosen anywhere between the single-photon and
squeezed state
Dispersive optical nonlinearities in an EIT-Rydberg medium
We investigate dispersive optical nonlinearities that arise from Rydberg
excitation blockade in cold Rydberg gases. We consider a two-photon transition
scheme and study the non-linear response to a weak optical probe in presence of
a strong control beam. For very low probe fields, the dominant nonlinearities
are of the third order and they can be exactly evaluated in a steady state
regime. In a more general case, the change in average atomic populations and
coherences due to Rydberg interactions can be characterized by properly defined
scaling parameters, which are generally complex numbers but in certain
situations take the usual meaning of the number of atoms in a blockade sphere.
They can be used in a simple "universal scaling" formula to determine the
dispersive optical nonlinearity of the medium. We also develop a novel
technique to account for the Rydberg interaction effects, by simplifying the
treatment of nonlocal interaction terms, the so-called collisional integrals.
We find algebraic relations that only involve two-body correlations, which can
be solved numerically. All average populations and coherences are then obtained
straightforwardly.Comment: 9 pages, 4 figure
Generating non-Gaussian states using collisions between Rydberg polaritons
We investigate theoretically the deterministic generation of quantum states
with negative Wigner functions, by using giant non-linearities due to
collisional interactions between Rydberg polaritons. The state resulting from
the polariton interactions may be transferred with high fidelity into a
photonic state, which can be analyzed using homodyne detection followed by
quantum tomography. Besides generating highly non-classical states of the
light, this method can also provide a very sensitive probe for the physics of
the collisions involving Rydberg states.Comment: 5 pages, 3 figure
Quantum optical non-linearities induced by Rydberg-Rydberg interactions: a perturbative approach
In this article, we theoretically study the quantum statistical properties of
the light transmitted through or reflected from an optical cavity, filled by an
atomic medium with strong optical non-linearity induced by Rydberg-Rydberg van
der Waals interactions. Atoms are driven on a two-photon transition from their
ground state to a Rydberg level via an intermediate state by the combination of
a weak signal field and a strong control beam. By using a perturbative
approach, we get analytic results which remain valid in the regime of weak
feeding fields, even when the intermediate state becomes resonant. Therefore
they allow us to investigate quantitatively new features associated with the
resonant behaviour of the system. We also propose an effective non-linear
three-boson model of the system which, in addition to leading to the same
analytic results as the original problem, sheds light on the physical processes
at work in the system
Rydberg-induced optical nonlinearities from a cold atomic ensemble trapped inside a cavity
We experimentally characterize the optical nonlinear response of a cold
atomic medium placed inside an optical cavity, and excited to Rydberg states.
The excitation to S and D Rydberg levels is carried out via a two-photon
transition in an EIT (electromagnetically induced transparency) configuration,
with a weak (red) probe beam on the lower transition, and a strong (blue)
coupling beam on the upper transition. The observed optical nonlinearities
induced by S states for the probe beam can be explained using a semi-classical
model with van der Waals' interactions. For the D states, it appears necessary
to take into account a dynamical decay of Rydberg excitations into a long-lived
dark state. We show that the measured nonlinearities can be explained by using
a Rydberg bubble model with a dynamical decay.Comment: 8 pages, 6 figure
Instability to a heterogeneous oscillatory state in randomly connected recurrent networks with delayed interactions
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems but have not been fully explored in high-dimensional networks. Here we study large networks consisting of randomly coupled rate units. We identify a type of bifurcation in which a continuous part of the eigenvalue spectrum of the linear stability matrix crosses the instability line at nonzero frequency. This bifurcation occurs when the interactions are delayed and partially antisymmetric and leads to a heterogeneous oscillatory state in which oscillations are apparent in the activity of individual units but not on the population-average level
Controlling the quantum state of a single photon emitted from a single polariton
We investigate in detail the optimal conditions for a high fidelity transfer
from a single-polariton state to a single-photon state and subsequent homodyne
detection of the single photon. We assume that, using various possible
techniques, the single polariton has initially been stored as a spin-wave
grating in a cloud of cold atoms inside a low-finesse cavity. This state is
then transferred to a single-photon optical pulse using an auxiliary beam. We
optimize the retrieval efficiency and determine the mode of the local
oscillator that maximizes the homodyne efficiency of such a photon. We find
that both efficiencies can have values close to one in a large region of
experimental parameters.Comment: 10 pages, 8 figure
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