1,164 research outputs found
Microscopic theory of photonic band gaps in optical lattices
We propose a microscopic model to describe the scattering of light by atoms
in optical lattices. The model is shown to efficiently capture Bragg
scattering, spontaneous emission and photonic band gaps. A connection to the
transfer matrix formalism is established in the limit of a one-dimensional
optical lattice, and we find the two theories to yield results in good
agreement. The advantage of the microscopic model is, however, that it suits
better for studies of finite-size and disorder effects.Comment: 5 pages, 6 figure
Reducing or enhancing chaos using periodic orbits
A method to reduce or enhance chaos in Hamiltonian flows with two degrees of
freedom is discussed. This method is based on finding a suitable perturbation
of the system such that the stability of a set of periodic orbits changes
(local bifurcations). Depending on the values of the residues, reflecting their
linear stability properties, a set of invariant tori is destroyed or created in
the neighborhood of the chosen periodic orbits. An application on a
paradigmatic system, a forced pendulum, illustrates the method
Stabilizing the intensity of a wave amplified by a beam of particles
The intensity of an electromagnetic wave interacting self-consistently with a
beam of charged particles as in a free electron laser, displays large
oscillations due to an aggregate of particles, called the macro-particle. In
this article, we propose a strategy to stabilize the intensity by re-shaping
the macro-particle. This strategy involves the study of the linear stability
(using the residue method) of selected periodic orbits of a mean-field model.
As parameters of an additional perturbation are varied, bifurcations occur in
the system which have drastic effect on the modification of the self-consistent
dynamics, and in particular, of the macro-particle. We show how to obtain an
appropriate tuning of the parameters which is able to strongly decrease the
oscillations of the intensity without reducing its mean-value
Synchronization of Bloch oscillations by a ring cavity
We consider Bloch oscillations of ultracold atoms stored in a one-dimensional
vertical optical lattice and simultaneously interacting with a unidirectionally
pumped optical ring cavity whose vertical arm is collinear with the optical
lattice. We find that the feedback provided by the cavity field on the atomic
motion synchronizes Bloch oscillations via a mode-locking mechanism, steering
the atoms to the lowest Bloch band. It also stabilizes Bloch oscillations
against noise, and even suppresses dephasing due to atom-atom interactions.
Furthermore, it generates periodic bursts of light emitted into the
counter-propagating cavity mode, providing a non-destructive monitor of the
atomic dynamics. All these features may be crucial for future improvements of
the design of atomic gravimeters based on recording Bloch oscillations.Comment: 14 pages, 7 figure
Mode-locked Bloch oscillations in a ring cavity
We present a new technique for stabilizing and monitoring Bloch oscillations
of ultracold atoms in an optical lattice under the action of a constant
external force. In the proposed scheme, the atoms also interact with a
unidirectionally pumped optical ring cavity whose one arm is collinear with the
optical lattice. For weak collective coupling, Bloch oscillations dominate over
the collective atomic recoil lasing instability and develop a synchronized
regime in which the atoms periodically exchange momentum with the cavity field.Comment: 7 pages, 5 figure
The Function of Bachelardian Epistemology in the Post-colonial Project of Mohammed ‘Abed al-Jabri
This paper explores the function of historical epistemology in the thought of Gaston Bachelard (1884–1962) and Mohammed ‘Abed al-Jabri (1935–2010). Attributing thought with a particular function challenges our tendency to explain the development of thought in other socio-historical contexts in terms of mere conceptual influence. Available English-language literature on al-Jabri commonly references Bachelard’s concept of epistemological rupture as a source of inspiration. Though the reference is astute, this term remains poorly understood and has long been overshadowed by Thomas Kuhn’s notion of ‘paradigm shift’. The broader function of Bachelard’s thought as a renegotiation of time, place, subject, and reason in the natural sciences has been largely neglected in historiographies of the philosophy of science outside of France. This paper emphasizes the level of insight and ingenuity with which al-Jabri employs the function of Bachelard’s epistemology by re-interpreting it within the framework of his own socio-historical context. Far from reducing al-Jabri’s thought to a mere programmatic reproduction of French thought, I suggest that al-Jabri was among the most astute interpreters of this long-misunderstood theorist
Cooperative scattering and radiation pressure force in dense atomic clouds
We consider the collective scattering by a cloud of two-level atoms
driven by an uniform radiation field. Dense atomic clouds can be described by a
continuous density and the problem reduces to deriving the spectrum of the
atom-atom coupling operator. For clouds much larger than the optical
wavelength, the spectrum is treated as a continuum, and analytical expressions
for several macroscopic quantities, such as scattered radiation intensity and
radiation pressure force, are derived. The analytical results are then compared
to the exact -body solution and with those obtained assuming a symmetric
timed Dicke state. In contrast with the symmetric timed Dicke state, our
calculations takes account of the back action of the atoms on the driving field
leading to phase shifts due to the finite refraction of the cloud
Targeted mixing in an array of alternating vortices
Transport and mixing properties of passive particles advected by an array of
vortices are investigated. Starting from the integrable case, it is shown that
a special class of perturbations allows one to preserve separatrices which act
as effective transport barriers, while triggering chaotic advection. In this
setting, mixing within the two dynamical barriers is enhanced while long range
transport is prevented. A numerical analysis of mixing properties depending on
parameter values is performed; regions for which optimal mixing is achieved are
proposed. Robustness of the targeted mixing properties regarding errors in the
applied perturbation are considered, as well as slip/no-slip boundary
conditions for the flow
Stabilizing the intensity for a Hamiltonian model of the FEL
The intensity of an electromagnetic wave interacting self-consistently with a
beam of charged particles, as in a Free Electron Laser, displays large
oscillations due to an aggregate of particles, called the macro-particle. In
this article, we propose a strategy to stabilize the intensity by destabilizing
the macro-particle. This strategy involves the study of the linear stability of
a specific periodic orbit of a mean-field model. As a control parameter - the
amplitude of an external wave - is varied, a bifurcation occur in the system
which has drastic effects on the self-consistent dynamics, and in particular,
on the macro-particle. We show how to obtain an appropriate tuning of the
control parameter which is able to strongly decrease the oscillations of the
intensity without reducing its mean-value
Resonances in Mie scattering by an inhomogeneous atomic cloud
Despite the quantum nature of the process, collective scattering by dense
cold samples of two-level atoms can be interpreted classically describing the
sample as a macroscopic object with a complex refractive index. We demonstrate
that resonances in Mie theory can be easily observable in the cooperative
scattering by tuning the frequency of the incident laser field or the atomic
number. The solution of the scattering problem is obtained for spherical atomic
clouds who have the parabolic density characteristic of BECs, and the
cooperative radiation pressure force calculated exhibits resonances in the
cloud displacement for dense clouds. At odds from uniform clouds which show a
complex structure including narrow peaks, these densities show resonances, yet
only under the form of quite regular and contrasted oscillations
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