Stability and vortex states in Bose-Fermi mixture with attraction between bosons and fermions
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Since the first realization of Bose-Einstein condensation (BEC)
in ultracold atomic gas clouds, studies in this direction have
yielded unprecedented insight into the quantum statistical
properties of matter. Besides the studies using the bosonic
atoms, growing interest is focused on the cooling of fermionic
atoms to a temperature regime where quantum effects dominate the
properties of the gas. Because s-wave interactions that
facilitate evaporative cooling of bosons are absent among
spin-polarized fermions due to the exclusion Pauli principle the
fermions are cooled to degeneracy through the mediation of
fermions in another spin state or via a buffer gas of bosons
(sympathetic cooling). The physical properties of Bose-Fermi
mixtures are the subject of intensive investigations including
the analysis of ground state properties, stability, effective
Fermi-Fermi interaction mediated by the bosons, and new quantum
phases in optical lattices.
In this talk we study the instability and collapses of the
trapped boson-fermion mixture due to the boson-fermion
attractive interaction in the presence of the quantized
vortices, using the effective Hamiltonian for the Bose system
which is obtained by integrating out the fermion degrees of
freedom 1-5. Using the effective Hamiltonian, a collapse of the trapped
boson-fermion mixture due to the boson-fermion attractive
interaction without and in the presence of the quantized
vortices is studied in the framework of variational Bose wave
function and Thomas-Fermi approximation. The properties of the
$^87$Rb and $^40$K mixture are analyzed quantitatively. The
critical number of bosons for the collapse transition is
estimated without and in the presence of the vortices as a
function of the fermion number. It is shown that the critical
number of bosons increases in the presence of the vortex. The
vortex critical velocities are calculated as functions of the
numbers of bosons and fermions. We find numerically solutions of
modified Gross- Pitaevskii equation which continuously go from
stable to unstable branch and discuss the relation of the onset
of collapse with macroscopic properties of the system. A
comparison with the case of a Bose condensate of atomic $^7Li$
system with a purely attractive interaction is given.
The work was supported in part by the Russian Foundation for
Basic Research (Grant No 05-02-17280).
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