306 research outputs found

### Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates

We study the dynamical phase diagram of a dilute Bose-Einstein condensate
(BEC) trapped in a periodic potential. The dynamics is governed by a discrete
non-linear Schr\"odinger equation: intrinsically localized excitations,
including discrete solitons and breathers, can be created even if the BEC's
interatomic potential is repulsive. Furthermore, we analyze the
Anderson-Kasevich experiment [Science 282, 1686 (1998)], pointing out that mean
field effects lead to a coherent destruction of the interwell Bloch
oscillations

### On Defect-Mediated Transitions in Bosonic Planar Lattices

We discuss the finite-temperature properties of Bose-Einstein condensates
loaded on a 2D optical lattice. In an experimentally attainable range of
parameters the system is described by the XY model, which undergoes a
Berezinskii-Kosterlitz-Thouless (BKT) transition driven by the vortex pair
unbinding. The interference pattern of the expanding condensates provides the
experimental signature of the BKT transition: near the critical temperature,
the k=0 component of the momentum distribution sharply decreases

### 1D Lieb-Liniger Bose Gas as Non-Relativistic Limit of the Sinh-Gordon Model

The repulsive Lieb-Liniger model can be obtained as the non-relativistic
limit of the Sinh-Gordon model: all physical quantities of the latter model
(S-matrix, Lagrangian and operators) can be put in correspondence with those of
the former. We use this mapping, together with the Thermodynamical Bethe Ansatz
equations and the exact form factors of the Sinh-Gordon model, to set up a
compact and general formalism for computing the expectation values of the
Lieb-Liniger model both at zero and finite temperature. The computation of
one-point correlators is thoroughly detailed and, when possible, compared with
known results in the literature.Comment: published version, 27 pages, 10 figure

### Self-Consistent Mean-Field Theory for Frustrated Josephson Junction Arrays

We review the self-consistent mean-field theory for charge-frustrated
Josephson junction arrays. Using (\phi is the phase of the
superconducting wavefunction) as order parameter and imposing the
self-consistency condition, we compute the phase boundary line between the
superconducting region ( not equal to zero) and the insulating one
( = 0). For a uniform offset charge q=e the superconducting phase
increases with respect to the situation in which q=0. Here, we generalize the
self-consistent mean-field theory to include the effects induced by a random
distribution of offset charges and/or of diagonal self-capacitances. For most
of the phase diagram, our results agree with the outcomes of Quantum Monte
Carlo simulations as well as with previous studies using the path-integral
approach.Comment: Presented by F. P. Mancini at the Conference "Highlights in Condensed
Matter Physics", May 9-11 2003, Salerno, Ital

### Ultracold Bosons with 3-Body Attractive Interactions in an Optical Lattice

We study the effect of an optical lattice (OL) on the ground-state properties
of one-dimensional ultracold bosons with three-body attraction and two-body
repulsion, which are described by a cubic-quintic Gross-Pitaevskii equation
with a periodic potential. Without the OL and with a vanishing two-body
interaction term, soliton solutions of the Townes type are possible only at a
critical value of the three-body interaction strength, at which an infinite
degeneracy of the ground-state occurs; a repulsive two-body interaction makes
such localized solutions unstable. We show that the OL opens a stability window
around the critical point when the strength of the periodic potential is above
a critical threshold. We also consider the effect of an external parabolic
trap, studying how the stability of the solitons depends on matching between
minima of the periodic potential and the minimum of the parabolic trap.Comment: Special issue of European Physical Journal B on the conference
"Theory of Quantum Gases and Quantum Coherence" held in Grenoble, 200

### Quantum measuring processes for trapped ultracold bosonic gases

The standard experimental techniques usually adopted in the study of the
behaviour of ultracold atoms in optical lattices involve extracting the atom
density profile from absorption images of the atomic sample after trap release.
Quantum mechanically this procedure is described by a generalized measure
(POVM); interference patterns found in absorption images suggest a generalized
measure based on fixed-phase, coherent-like states. We show that this leads to
an average atomic density which differs from the usually adopted one, obtained
as the expectation value of the atom density operator in the many-body state.Comment: 11 pages, LaTe

### Avoiding Infrared Catastrophes in Trapped Bose-Einstein Condensates

This paper is concerned with the long wavelength instabilities (infrared
catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the
modulational instability in ``cigar-shaped'' (1D) attractive BECs and the
transverse instability of dark solitons in ``pancake'' (2D) repulsive BECs. We
suggest mechanisms, and give explicit estimates, on how to ``engineer'' the
trapping conditions of the condensate to avoid such instabilities: the main
result being that a tight enough trapping potential suppresses the
instabilities present in the homogeneous limit. We compare the obtained
estimates with numerical results and we highlight the relevant regimes of
dynamical behavior

### Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model

We introduce and study the properties of a periodic model interpolating
between the sine-- and the sinh--Gordon theories in $1+1$ dimensions. This
model shows the peculiarities, due to the preservation of the functional form
of their potential across RG flows, of the two limiting cases: the sine-Gordon,
not having conventional order/magnetization at finite temperature, but
exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the
sinh-Gordon, not having a phase transition, but being integrable. The
considered interpolation, which we term as {\em sn-Gordon} model, is performed
with potentials written in terms of Jacobi functions. The critical properties
of the sn-Gordon theory are discussed by a renormalization-group approach. The
critical points, except the sinh-Gordon one, are found to be of BKT type.
Explicit expressions for the critical coupling as a function of the elliptic
modulus are given.Comment: v2, 10 pages, 8 figures, accepted in J. Phys.

### Pseudo-Periodic Natural Higgs Inflation

Inflationary cosmology represents a well-studied framework to describe the
expansion of space in the early universe, as it explains the origin of the
large-scale structure of the cosmos and the isotropy of the cosmic microwave
background radiation. The recent detection of the Higgs boson renewed research
activities based on the assumption that the inflaton could be identified with
the Higgs field. At the same time, the question whether the inflationary
potential can be be extended to the electroweak scale and whether it should be
necessarily chosen ad hoc in order to be physically acceptable are at the
center of an intense debate. Here, we perform the slow-roll analysis of the
so-called Massive Natural Inflation (MNI) model which has three adjustable
parameters, the explicit mass term, a Fourier amplitude u, and a frequency
parameter $\beta$, in addition to a constant term of the potential. This theory
has the advantage to present a structure of infinite non-degenerate minima and
is amenable to an easy integration of high-energy modes. We show that, using
PLANCK data, one can fix, in the large $\beta$-region, the parameters of the
model in a unique way. We also demonstrate that the value for the parameters
chosen at the cosmological scale does not influence the results at the
electroweak scale. We argue that other models can have similar properties both
at cosmological and electroweak scales, but with the MNI model one can complete
the theory towards low energies and easily perform the integration of modes up
to the electroweak scale, producing the correct order-of-magnitude for the
Higgs mass.Comment: 12 pages, 6 figures, published in Nuclear Physics

### Expectation Values in the Lieb-Liniger Bose Gas

Taking advantage of an exact mapping between a relativistic integrable model
and the Lieb-Liniger model we present a novel method to compute expectation
values in the Lieb-Liniger Bose gas both at zero and finite temperature. These
quantities, relevant in the physics of one-dimensional ultracold Bose gases,
are expressed by a series that has a remarkable behavior of convergence. Among
other results, we show the computation of the three-body expectation value at
finite temperature, a quantity that rules the recombination rate of the Bose
gas.Comment: Published version. Selected for the December 2009 issue of Virtual
Journal of Atomic Quantum Fluid

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