102 research outputs found
Emergent quantum Euler equation and Bose-Einstein condensates
In this paper, proceeding from the recently developed way of deriving the
quantum-mechanical equations from the classical ones, the complete system of
hydrodynamical equations, including the quantum Euler equation, is derived for
a perfect fluid and an imperfect fluid with pairwise interaction between the
particles. For the Bose-Einstein condensate of the latter one the Bogolyubov
spectrum of elementary excitations is easily reproduced in the acoustic
approximation.Comment: 10 page
Disordered vortex arrays in a two-dimensional condensate
We suggest a method to create turbulence in a Bose-Einstein condensate. The
method consists in, firstly, creating an ordered vortex array, and, secondly,
imprinting a phase difference in different regions of the condensate. By
solving numerically the two-dimensional Gross-Pitaevskii equation we show that
the motion of the resulting positive and negative vortices is disordered.Comment: 14 pages, 18 figures, accepted by Geophysical and Astrophysical Fluid
Dynamic
Collapse of a Bose gas: kinetic approach
We have analytically explored temperature dependence of critical number of
particles for the collapse of a harmonically trapped attractively interacting
Bose gas below the condensation point by introducing a kinetic approach within
the Hartree-Fock approximation. The temperature dependence obtained by this
easy approach is consisted with that obtained from the scaling theory.Comment: Brief Report, 4 pages, 1 figure, Accepted in Pramana-Journal of
Physic
Vortex nucleation as a case study of symmetry breaking in quantum systems
Mean-field methods are a very powerful tool for investigating weakly
interacting many-body systems in many branches of physics. In particular, they
describe with excellent accuracy trapped Bose-Einstein condensates. A generic,
but difficult question concerns the relation between the symmetry properties of
the true many-body state and its mean-field approximation. Here, we address
this question by considering, theoretically, vortex nucleation in a rotating
Bose-Einstein condensate. A slow sweep of the rotation frequency changes the
state of the system from being at rest to the one containing one vortex. Within
the mean-field framework, the jump in symmetry occurs through a turbulent phase
around a certain critical frequency. The exact many-body ground state at the
critical frequency exhibits strong correlations and entanglement. We believe
that this constitutes a paradigm example of symmetry breaking in - or change of
the order parameter of - quantum many-body systems in the course of adiabatic
evolution.Comment: Minor change
{\phi}^4 Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics
We explore a {\phi}^4 model with an added external parabolic potential term.
This term dramatically alters the spectral properties of the system. We
identify single and multiple kink solutions and examine their stability
features; importantly, all of the stationary structures turn out to be
unstable. We complement these with a dynamical study of the evolution of a
single kink in the trap, as well as of the scattering of kink and anti-kink
solutions of the model. We see that some of the key characteristics of
kink-antikink collisions, such as the critical velocity and the multi-bounce
windows, are sensitively dependent on the trap strength parameter, as well as
the initial displacement of the kink and antikink
Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices
Orbital physics plays a significant role for a vast number of important
phenomena in complex condensed matter systems such as high-T
superconductivity and unconventional magnetism. In contrast, phenomena in
superfluids -- especially in ultracold quantum gases -- are commonly well
described by the lowest orbital and a real order parameter. Here, we report on
the observation of a novel multi-orbital superfluid phase with a {\it complex}
order parameter in binary spin mixtures. In this unconventional superfluid, the
local phase angle of the complex order parameter is continuously twisted
between neighboring lattice sites. The nature of this twisted superfluid
quantum phase is an interaction-induced admixture of the p-orbital favored by
the graphene-like band structure of the hexagonal optical lattice used in the
experiment. We observe a second-order quantum phase transition between the
normal superfluid (NSF) and the twisted superfluid phase (TSF) which is
accompanied by a symmetry breaking in momentum space. The experimental results
are consistent with calculated phase diagrams and reveal fundamentally new
aspects of orbital superfluidity in quantum gas mixtures. Our studies might
bridge the gap between conventional superfluidity and complex phenomena of
orbital physics.Comment: 5 pages, 4 figure
Quantised Vortices in an Exciton-Polariton Fluid
One of the most striking quantum effects in a low temperature interacting
Bose gas is superfluidity. First observed in liquid 4He, this phenomenon has
been intensively studied in a variety of systems for its amazing features such
as the persistence of superflows and the quantization of the angular momentum
of vortices. The achievement of Bose-Einstein condensation (BEC) in dilute
atomic gases provided an exceptional opportunity to observe and study
superfluidity in an extremely clean and controlled environment. In the solid
state, Bose-Einstein condensation of exciton polaritons has now been reported
several times. Polaritons are strongly interacting light-matter
quasi-particles, naturally occurring in semiconductor microcavities in the
strong coupling regime and constitute a very interesting example of composite
bosons. Even though pioneering experiments have recently addressed the
propagation of a fluid of coherent polaritons, still no conclusive evidence is
yet available of its superfluid nature. In the present Letter, we report the
observation of spontaneous formation of pinned quantised vortices in the
Bose-condensed phase of a polariton fluid by means of phase and amplitude
imaging. Theoretical insight into the possible origin of such vortices is
presented in terms of a generalised Gross-Pitaevskii equation. The implications
of our observations concerning the superfluid nature of the non-equilibrium
polariton fluid are finally discussed.Comment: 14 pages, 4 figure
Construction of non-PT-symmetric complex potentials with all-real spectra
We review recent work on the generalization of PT symmetry. We show that, in
addition to PT-symmetric complex potentials, there are also large classes of
non-PT-symmetric complex potentials which also feature all-real spectra. In
addition, some classes of these non-PT-symmetric potentials allow phase
transitions which do or do not go through exceptional points. These
non-PT-symmetric potentials are constructed by a variety of methods, such as
the symmetry and supersymmetry methods and the soliton theory. A generalization
of PT symmetry in multi-dimensions is also reviewed.Comment: 22 pages, 6 figure
Optical Lattices: Theory
This chapter presents an overview of the properties of a Bose-Einstein
condensate (BEC) trapped in a periodic potential. This system has attracted a
wide interest in the last years, and a few excellent reviews of the field have
already appeared in the literature (see, for instance, [1-3] and references
therein). For this reason, and because of the huge amount of published results,
we do not pretend here to be comprehensive, but we will be content to provide a
flavor of the richness of this subject, together with some useful references.
On the other hand, there are good reasons for our effort. Probably, the most
significant is that BEC in periodic potentials is a truly interdisciplinary
problem, with obvious connections with electrons in crystal lattices, polarons
and photons in optical fibers. Moreover, the BEC experimentalists have reached
such a high level of accuracy to create in the lab, so to speak, paradigmatic
Hamiltonians, which were first introduced as idealized theoretical models to
study, among others, dynamical instabilities or quantum phase transitions.Comment: Chapter 13 in Part VIII: "Optical Lattices" of "Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P.
G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez (Springer
Series on Atomic, Optical, and Plasma Physics, 2007) - pages 247-26
Beyond Gross-Pitaevskii Mean Field Theory
A large number of effects related to the phenomenon of Bose-Einstein
Condensation (BEC) can be understood in terms of lowest order mean field
theory, whereby the entire system is assumed to be condensed, with thermal and
quantum fluctuations completely ignored. Such a treatment leads to the
Gross-Pitaevskii Equation (GPE) used extensively throughout this book. Although
this theory works remarkably well for a broad range of experimental parameters,
a more complete treatment is required for understanding various experiments,
including experiments with solitons and vortices. Such treatments should
include the dynamical coupling of the condensate to the thermal cloud, the
effect of dimensionality, the role of quantum fluctuations, and should also
describe the critical regime, including the process of condensate formation.
The aim of this Chapter is to give a brief but insightful overview of various
recent theories, which extend beyond the GPE. To keep the discussion brief,
only the main notions and conclusions will be presented. This Chapter
generalizes the presentation of Chapter 1, by explicitly maintaining
fluctuations around the condensate order parameter. While the theoretical
arguments outlined here are generic, the emphasis is on approaches suitable for
describing single weakly-interacting atomic Bose gases in harmonic traps.
Interesting effects arising when condensates are trapped in double-well
potentials and optical lattices, as well as the cases of spinor condensates,
and atomic-molecular coupling, along with the modified or alternative theories
needed to describe them, will not be covered here.Comment: Review Article (19 Pages) - To appear in 'Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment', Edited by
P.G. Kevrekidis, D.J. Frantzeskakis and R. Carretero-Gonzalez (Springer
Verlag
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