4 research outputs found
Dynamics of one-dimensional tight-binding models with arbitrary time-dependent external homogeneous fields
The exact propagators of two one-dimensional systems with time-dependent
external fields are presented by following the path-integral method. It is
shown that the Bloch acceleration theorem can be generalized to the
impulse-momentum theorem in quantum version. We demonstrate that an evolved
Gaussian wave packet always keeps its shape in an arbitrary time-dependent
homogeneous driven field. Moreover, that stopping and accelerating of a wave
packet can be achieved by the pulsed field in a diabatic way.Comment: 8 pages, 6 figure
Faraday and Resonant Waves in Dipolar Cigar-Shaped Bose-Einstein Condensates
Faraday and resonant density waves emerge in Bose-Einstein condensates as a
result of harmonic driving of the system. They represent nonlinear excitations
and are generated due to the interaction-induced coupling of collective
oscillation modes and the existence of parametric resonances. Using a
mean-field variational and a full numerical approach, we studied density waves
in dipolar condensates at zero temperature, where breaking of the symmetry due
to anisotropy of the dipole-dipole interaction (DDI) plays an important role.
We derived variational equations of motion for the dynamics of a driven dipolar
system and identify the most unstable modes that correspond to the Faraday and
resonant waves. Based on this, we derived the analytical expressions for
spatial periods of both types of density waves as functions of the contact and
the DDI strength. We compared the obtained variational results with the results
of extensive numerical simulations that solve the dipolar Gross-Pitaevskii
equation in 3D, and found a very good agreement.Comment: 18 pages, 10 figure
Geometric Resonances in Bose-Einstein Condensates with Two- and Three-Body Interactions
We investigate geometric resonances in Bose-Einstein condensates by solving
the underlying time-dependent Gross-Pitaevskii equation for systems with two-
and three-body interactions in an axially-symmetric harmonic trap. To this end,
we use a recently developed analytical method [Phys. Rev. A 84, 013618 (2011)],
based on both a perturbative expansion and a Poincar\'e-Lindstedt analysis of a
Gaussian variational approach, as well as a detailed numerical study of a set
of ordinary differential equations for variational parameters. By changing the
anisotropy of the confining potential, we numerically observe and analytically
describe strong nonlinear effects: shifts in the frequencies and mode coupling
of collective modes, as well as resonances. Furthermore, we discuss in detail
the stability of a Bose-Einstein condensate in the presence of an attractive
two-body interaction and a repulsive three-body interaction. In particular, we
show that a small repulsive three-body interaction is able to significantly
extend the stability region of the condensate.Comment: 27 pages, 13 figure