12 research outputs found
Global and local condensate and superfluid fraction of a few hard core bosons in a cubic optical lattice plus external harmonic confinement
We explore the global and local condensate and superfluid (SF) fractions in a
system of a few hard core (HC) bosons (N=8 and N=40) trapped inside a combined
harmonic optical cubic lattice (CHOCL) at T=0 K. The condensate fraction (CF)
is computed for individual lattice wells by separating the one-body density
matrix (OBDM) of the whole system into components at the various lattice sites.
Then each "lattice-site" component is diagonalized to find its eigenvalues. The
eigenvalues are obtained by a method presented earlier [Dubois and Glyde, Phys.
Rev. A {\bf 63}, 023602 (2001)]. The effects of interference between the
condensates in the lattice wells on the CF in one well is also investigated.
The SF fraction (SFF) is calculated for N=40 by using the diffusion formula of
Pollock and Ceperley [Pollock and Ceperley, Phys. Rev. B {\bf 36}, 8343
(1987)]. Our chief result is an opposing behavior of the global CF and SFF with
increasing lattice wave vector . In addition, the CF in a lattice well is
enhanced by the interference with its neighbor wells beyond the result when the
interference is neglected. The global SF is depleted with a rise of the
repulsion between the bosons, yet at very strong interaction superfluidity is
still present. The global CF remains almost constant with increasing HC
repulsion. A reduction in the lattice dimension, i.e. an increase in the
lattice wave vector, increases the local CF in each lattice well, but reduces
the corresponding local SFF. At large HC repulsion, a coexisting SF-(vacuum)MI
phase is established.Comment: The tables in the previous withdrawn version (v2) have been corrected
and the article updated. This is the final version which has been submitted
to Phys. Rev.
Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space
We investigate numerically conditions for order and chaos in the dynamics of
an interacting Bose- Einstein condensate (BEC) confined by an external trap cut
off by a hard-wall box potential. The BEC is stirred by a laser to induce
excitations manifesting as irregular spatial and energy oscillations of the
trapped cloud. Adding laser stirring to the external trap results in an
effective time-varying trapping frequency in connection with the dynamically
changing combined external+laser potential trap. The resulting dynamics are
analyzed by plotting their trajectories in coordinate phase space and in energy
space. The Lyapunov exponents are computed to confirm the existence of chaos in
the latter space. Quantum effects and trap anharmonicity are demonstrated to
generate chaos in energy space, thus confirming its presence and implicating
either quantum effects or trap anharmonicity as its generator. The presence of
chaos in energy space does not necessarily translate into chaos in coordinate
space. In general, a dynamic trapping frequency is found to promote chaos in a
trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved
by increasing the characteristic scale of the external trap with respect to the
condensate size.Comment: 19 pages, 14 page
Tunneling of a few strongly repulsive hard-sphere bosons in an optical lattice with tight external harmonic confinement: A quantum Monte Carlo investigation in continuous space
The effect of strongly repulsive interactions on the tunneling amplitude of
hard-sphere (HS) bosons confined in a simple cubic (sc) optical lattice plus
tight external harmonic confinement in continuous space is investigated. The
quantum variational Monte Carlo (VMC) and the variational path integral Monte
Carlo (VPI) techniques are used at zero temperature. The effects of the lattice
spacing on the tunneling amplitude is also considered. The occupancies
of the lattice sites as a function of the repulsion between the bosons are
further revealed. Our chief result is, that for a small number of bosons (N=8)
the overlap of the wave functions in neighboring wells does not change with an
increase of the repulsive interactions and changes only minimally for a larger
number of particles (N=40). The tunneling amplitude rises with a reduction in
the lattice spacing. In addition, the occupancy of the center of the trap
decreases in favor of a rise in the occupancy of the lattice sites at the edges
of the trap with increasing HS repulsion. Further, it was found that the energy
per particle at certain optical depths is insensitive to the number of
particles and variations in the HS diameter of the bosons. In order to support
our results, we compare the VMC results with corresponding VPI results.Comment: 16 pages, 24 figures. This is an improvement of the previous version
in which we consider the presence of pair-tunneling in the strongly
interacting regime. The tunneling amplitude is measured in terms of the
overlap of wave functions in neighboring well
Thermodynamic properties of an interacting hard-sphere Bose gas in a trap using the static fluctuation approximation
A hard-sphere (HS) Bose gas in a trap is investigated at finite temperatures
in the weakly-interacting regime and its thermodynamic properties are evaluated
using the static fluctuation approximation (SFA). The energies are calculated
with a second-quantized many-body Hamiltonian and a harmonic oscillator wave
function. The specific heat capacity, internal energy, pressure, entropy and
the Bose-Einstein (BE) occupation number of the system are determined as
functions of temperature and for various values of interaction strength and
number of particles. It is found that the number of particles plays a more
profound role in the determination of the thermodynamic properties of the
system than the HS diameter characterizing the interaction, that the critical
temperature drops with the increase of the repulsion between the bosons, and
that the fluctuations in the energy are much smaller than the energy itself in
the weakly-interacting regime.Comment: 34 pages, 24 Figures. To appear in the International Journal of
Modern Physics
Generalized Bose-Einstein Condensation
Generalized Bose-Einstein condensation (GBEC) involves condensates appearing
simultaneously in multiple states. We review examples of the three types in an
ideal Bose gas with different geometries. In Type I there is a discrete number
of quantum states each having macroscopic occupation; Type II has condensation
into a continuous band of states, with each state having macroscopic
occupation; in Type III each state is microscopically occupied while the entire
condensate band is macroscopically occupied. We begin by discussing Type I or
"normal" BEC into a single state for an isotropic harmonic oscillator
potential. Other geometries and external potentials are then considered: the
{}"channel" potential (harmonic in one dimension and hard-wall in the other),
which displays Type II, the {}"cigar trap" (anisotropic harmonic potential),
and the "Casimir prism" (an elongated box), the latter two having Type III
condensations. General box geometries are considered in an appendix. We
particularly focus on the cigar trap, which Van Druten and Ketterle first
showed had a two-step condensation: a GBEC into a band of states at a
temperature and another "one-dimensional" transition at a lower
temperature into the ground state. In a thermodynamic limit in which
the ratio of the dimensions of the anisotropic harmonic trap is kept fixed,
merges with the upper transition, which then becomes a normal BEC.
However, in the thermodynamic limit of Beau and Zagrebnov, in which the ratio
of the boundary lengths increases exponentially, becomes fixed at the
temperature of a true Type I phase transition. The effects of interactions on
GBEC are discussed and we show that there is evidence that Type III
condensation may have been observed in the cigar trap.Comment: 17 pages; 6 figures. Intended for American Journal of Physic