5 research outputs found
Metastable Quantum Phase Transitions in a Periodic One-dimensional Bose Gas: Mean-Field and Bogoliubov Analyses
We generalize the concept of quantum phase transitions, which is
conventionally defined for a ground state and usually applied in the
thermodynamic limit, to one for \emph{metastable states} in \emph{finite size
systems}. In particular, we treat the one-dimensional Bose gas on a ring in the
presence of both interactions and rotation. To support our study, we bring to
bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear
perturbation or Bogoliubov-de Gennes theory. Both methods give a consistent
result in the weakly interacting regime: there exist \emph{two topologically
distinct quantum phases}. The first is the typical picture of superfluidity in
a Bose-Einstein condensate on a ring: average angular momentum is quantized and
the superflow is uniform. The second is new: one or more dark solitons appear
as stationary states, breaking the symmetry, the average angular momentum
becomes a continuous quantity, and the phase of the condensate can be
continuously wound and unwound
Reflection of a Lieb-Liniger wave packet from the hard-wall potential
Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the
hard-wall potential is studied. We demonstrate that a time-dependent wave
function, which describes quantum dynamics of a Lieb-Liniger wave packet
comprised of N particles, can be found by solving an -dimensional Fourier
transform; this follows from the symmetry properties of the many-body
eigenstates in the presence of the hard-wall potential. The presented formalism
is employed to numerically calculate reflection of a few-body wave packet from
the hard wall for various interaction strengths and incident momenta.Comment: revised version, improved notation, Fig. 5 adde
Theory of Multidimensional Solitons
We review a number of topics germane to higher-dimensional solitons in
Bose-Einstein condensates. For dark solitons, we discuss dark band and planar
solitons; ring dark solitons and spherical shell solitons; solitary waves in
restricted geometries; vortex rings and rarefaction pulses; and multi-component
Bose-Einstein condensates. For bright solitons, we discuss instability,
stability, and metastability; bright soliton engineering, including pulsed atom
lasers; solitons in a thermal bath; soliton-soliton interactions; and bright
ring solitons and quantum vortices. A thorough reference list is included.Comment: review paper, to appear as Chapter 5a 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