15 research outputs found
Excitation spectroscopy of vortex lattices in a rotating Bose-Einstein condensate
Excitation spectroscopy of vortex lattices in rotating Bose-Einstein
condensates is described. We numerically obtain the Bogoliubov-deGenne
quasiparticle excitations for a broad range of energies and analyze them in the
context of the complex dynamics of the system. Our work is carried out in a
regime in which standard hydrodynamic assumptions do not hold, and includes
features not readily contained within existing treatments.Comment: 4 pages, 4 figures. Submitted for publicatio
Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates
The complete low-energy collective-excitation spectrum of vortex lattices is
discussed for rotating Bose-Einstein condensates (BEC) by solving the
Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode
recently observed at JILA. The totally symmetric subset of these modes includes
the transverse shear, common longitudinal, and differential longitudinal modes.
We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate
the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair
of breathing modes. Combining both the BdG and TDGP approaches allows one to
unambiguously identify every observed mode.Comment: 5 pages, 4 figure
Collective Oscillations of Vortex Lattices in Rotating Bose-Einstein Condensates
The complete low-energy collective-excitation spectrum of vortex lattices is
discussed for rotating Bose-Einstein condensates (BEC) by solving the
Bogoliubov-de Gennes (BdG) equation, yielding, e.g., the Tkachenko mode
recently observed at JILA. The totally symmetric subset of these modes includes
the transverse shear, common longitudinal, and differential longitudinal modes.
We also solve the time-dependent Gross-Pitaevskii (TDGP) equation to simulate
the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair
of breathing modes. Combining both the BdG and TDGP approaches allows one to
unambiguously identify every observed mode.Comment: 5 pages, 4 figure
Excitation spectrum of vortex lattices in rotating Bose-Einstein condensates
Using the coarse grain averaged hydrodynamic approach, we calculate the
excitation spectrum of vortex lattices sustained in rotating Bose-Einstein
condensates. The spectrum gives the frequencies of the common-mode longitudinal
waves in the hydrodynamic regime, including those of the higher-order
compressional modes. Reasonable agreement with the measurements taken in a
recent JILA experiment is found, suggesting that one of the longitudinal modes
reported in the experiment is likely to be the , mode.Comment: 2 figures. Submitted to Physical Review A. v2 contains more
references. No change in the main resul
Vortex Synchronization in Bose-Einstein Condensates: A Time-Dependent Gross-Pitaevskii Equation Approach
In this work we consider vortex lattices in rotating Bose-Einstein
Condensates composed of two species of bosons having different masses.
Previously [1] it was claimed that the vortices of the two species form bound
pairs and the two vortex lattices lock. Remarkably, the two condensates and the
external drive all rotate at different speeds due to the disparity of the
masses of the constituent bosons. In this paper we study the system by solving
the full two-component Gross-Pitaevskii equations numerically. Using this
approach we verify the stability of the putative locked state which is found to
exist within a disk centered on the axis of rotation and which depends on the
mass ratio of the two bosons. We also show that an analytic estimate of this
locking radius based on a two-body force calculation agrees well with the
numerical results.Comment: 6.1 pages, 3 figure
Equatorial Waves in Rotating Bubble-Trapped Superfluids
As the Earth rotates, the Coriolis force causes several oceanic and
atmospheric waves to be trapped along the equator, including Kelvin, Yanai,
Rossby, and Poincar\'e modes. It has been demonstrated that the mathematical
origin of these waves is related to the nontrivial topology of the underlying
hydrodynamic equations. Inspired by recent observations of Bose-Einstein
condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas
experiments, we show that equatorial modes are supported by a rapidly rotating
condensate in a spherical geometry. Based on a zero-temperature coarse-grained
hydrodynamic framework, we reformulate the coupled oscillations of the
superfluid and the Abrikosov vortex lattice resulting from rotation by a
Schr\"odinger-like eigenvalue problem. The obtained non-Hermitian Hamiltonian
is topologically nontrivial. Furthermore, we solve the hydrodynamic equations
for a spherical geometry and find that the rotating superfluid hosts Kelvin,
Yanai, and Poincar\'e equatorial modes, but not the Rossby mode. Our
predictions can be tested with state-of-the-art bubble-shaped trapped BEC
experiments.Comment: 11 pages, 5 figure
Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps
We study a rotating Bose-Einstein Condensate in a strongly anharmonic trap
(flat trap with a finite radius) in the framework of 2D Gross-Pitaevskii
theory. We write the coupling constant for the interactions between the gas
atoms as and we are interested in the limit (TF
limit) with the angular velocity depending on . We derive
rigorously the leading asymptotics of the ground state energy and the density
profile when tends to infinity as a power of . If
a ``hole'' (i.e., a region where the
density becomes exponentially small as ) develops for
above a certain critical value. If
the hole essentially exhausts the container and a ``giant vortex'' develops
with the density concentrated in a thin layer at the boundary. While we do not
analyse the detailed vortex structure we prove that rotational symmetry is
broken in the ground state for .Comment: LaTex2e, 28 pages, revised version to be published in Journal of
Mathematical Physic