71 research outputs found
Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
Optical traps and lattices provide a new opportunity to study strongly
correlated high spin systems with cold atoms. In this article, we review the
recent progress on the hidden symmetry properties in the simplest high spin
fermionic systems with hyperfine spin , which may be realized with atoms
of Cs, Be, Ba, Ba, and Hg. A {\it generic}
SO(5) or isomorphically, ) symmetry is proved in such systems with the
s-wave scattering interactions in optical traps, or with the on-site Hubbard
interactions in optical lattices. Various important features from this high
symmetry are studied in the Fermi liquid theory, the mean field phase diagram,
and the sign problem in quantum Monte-Carlo simulations. In the s-wave quintet
Cooper pairing phase, the half-quantum vortex exhibits the global analogue of
the Alice string and non-Abelian Cheshire charge properties in gauge theories.
The existence of the quartetting phase, a four-fermion counterpart of the
Cooper pairing phase, and its competition with other orders are studied in one
dimensional spin-3/2 systems. We also show that counter-intuitively quantum
fluctuations in spin-3/2 magnetic systems are even stronger than those in
spin-1/2 systems
Band structure, elementary excitations, and stability of a Bose-Einstein condensate in a periodic potential
We investigate the band structure of a Bose-Einstein condensate in a
one-dimensional periodic potential by calculating stationary solutions of the
Gross-Pitaevskii equation which have the form of Bloch waves. We demonstrate
that loops ("swallow tails") in the band structure occur both at the Brillouin
zone boundary and at the center of the zone, and they are therefore a generic
feature. A physical interpretation of the swallow tails in terms of periodic
solitons is given. The linear stability of the solutions is investigated as a
function of the strength of the mean-field interaction, the magnitude of the
periodic potential, and the wave vector of the condensate. The regions of
energetic and dynamical stability are identified by considering the behavior of
the Gross-Pitaevskii energy functional for small deviations of the condensate
wave function from a stationary state. It is also shown how for long-wavelength
disturbances the stability criteria may be obtained within a hydrodynamic
approach.Comment: 15 pages, 7 figure
Spatial period-doubling in Bose-Einstein condensates in an optical lattice
We demonstrate that there exist stationary states of Bose-Einstein
condensates in an optical lattice that do not satisfy the usual Bloch
periodicity condition. Using the discrete model appropriate to the
tight-binding limit we determine energy bands for period-doubled states in a
one-dimensional lattice. In a complementary approach we calculate the band
structure from the Gross-Pitaevskii equation, considering both states of the
usual Bloch form and states which have the Bloch form for a period equal to
twice that of the optical lattice. We show that the onset of dynamical
instability of states of the usual Bloch form coincides with the occurrence of
period-doubled states with the same energy. The period-doubled states are shown
to be related to periodic trains of solitons.Comment: 4 pages, 3 figures, change of conten
Loss and revival of phase coherence in a Bose-Einstein condensate moving through an optical lattice
We investigate the phase coherence of a trapped Bose-Einstein condensate that
undergoes a dynamical superfluid-insulator transition in the presence of a
one-dimensional optical lattice. We study the evolution of the condensate after
a sudden displacement of the harmonic trapping potential by solving the
Gross-Pitaevskii equation, and comparing the results with the prediction of two
effective 1D models. We show that, owing to the 3D nature of the system, the
breakdown of the superfluid current above a critical displacement is not
associated to a sharp transition, but there exists a range of displacements for
which the condensate can recover a certain degree of coherence. We also discuss
the implications on the interference pattern after the ballistic expansion as
measured in recent experiments at LENS.Comment: 7 pages, 9 figure
Superfluid Dynamics of a Bose-Einstein Condensate in a Periodic Potential
We investigate the superfluid properties of a Bose-Einstein condensate (BEC)
trapped in a one dimensional periodic potential. We study, both analytically
(in the tight binding limit) and numerically, the Bloch chemical potential, the
Bloch energy and the Bogoliubov dispersion relation, and we introduce {\it two}
different, density dependent, effective masses and group velocities. The
Bogoliubov spectrum predicts the existence of sound waves, and the arising of
energetic and dynamical instabilities at critical values of the BEC
quasi-momentum which dramatically affect its coherence properties. We
investigate the dependence of the dipole and Bloch oscillation frequencies in
terms of an effective mass averaged over the density of the condensate. We
illustrate our results with several animations obtained solving numerically the
time-dependent Gross-Pitaevskii equation.Comment: 13 pages, 7 figures, movies and published paper available at
http://www.iop.org/EJ/abstract/1367-2630/5/1/11
Time-dependent unitary perturbation theory for intense laser driven molecular orientation
We apply a time-dependent perturbation theory based on unitary
transformations combined with averaging techniques, on molecular orientation
dynamics by ultrashort pulses. We test the validity and the accuracy of this
approach on LiCl described within a rigid-rotor model and find that it is more
accurate than other approximations. Furthermore, it is shown that a noticeable
orientation can be achieved for experimentally standard short laser pulses of
zero time average. In this case, we determine the dynamically relevant
parameters by using the perturbative propagator, that is derived from this
scheme, and we investigate the temperature effects on the molecular orientation
dynamics.Comment: 16 pages, 6 figure
Velocity of sound in a Bose-Einstein condensate in the presence of an optical lattice and transverse confinement
We study the effect of the transverse degrees of freedom on the velocity of
sound in a Bose-Einstein condensate immersed in a one-dimensional optical
lattice and radially confined by a harmonic trap. We compare the results of
full three-dimensional calculations with those of an effective 1D model based
on the equation of state of the condensate. The perfect agreement between the
two approaches is demonstrated for several optical lattice depths and
throughout the full crossover from the 1D mean-field to the Thomas Fermi regime
in the radial direction.Comment: final versio
Landau and dynamical instabilities of Bose-Einstein condensates with superfluid flow in a Kronig-Penney potential
We study the elementary excitations of Bose-Einstein condensates in a
one-dimensional periodic potential and discuss the stability of superfluid flow
based on the Kronig-Penney model. We analytically solve the Bogoliubov
equations and calculate the excitation spectrum. The Landau and dynamical
instabilities occur in the first condensate band when the superfluid velocity
exceeds certain critical values, which agrees with the result of condensates in
a sinusoidal potential. It is found that the onset of the Landau instability
coincides with the point where the perfect transmission of low-energy
excitations is forbidden, while the dynamical instability occurs when the
effective mass is negative. It is well known that the condensate band has a
peculiar structure called swallowtail when the periodic potential is shallow
compared to the mean field energy. We find that the upper side of the
swallowtail is dynamically unstable although the excitations have the linear
dispersion reflecting the positive effective mass.Comment: 6 pages, 2 figures, Proceedings of the International Symposium on
Quantum Fluids and Solids (QFS2006
Atomic motion in tilted optical lattices
This paper presents a formalism describing the dynamics of a quantum particle
in a one-dimensional, time-dependent, tilted lattice. The formalism uses the
Wannier-Stark states, which are localized in each site of the lattice, and
provides a simple framework allowing fully-analytical developments. Analytic
solutions describing the particle motion are explicit derived, and the
resulting dynamics is studied.Comment: 6 pages, 2 figs, submitted to EPJD, Springer Verlag styl
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