395 research outputs found
Static and Dynamic Properties of Trapped Fermionic Tonks-Girardeau Gases
We investigate some exact static and dynamic properties of one-dimensional
fermionic Tonks-Girardeau gases in tight de Broglie waveguides with attractive
p-wave interactions induced by a Feshbach resonance. A closed form solution for
the one-body density matrix for harmonic trapping is analyzed in terms of its
natural orbitals, with the surprising result that for odd, but not for even,
numbers of fermions the maximally occupied natural orbital coincides with the
ground harmonic oscillator orbital and has the maximally allowed fermionic
occupancy of unity. The exact dynamics of the trapped gas following turnoff of
the p-wave interactions are explored.Comment: 4 pages, 2 figures, submitted to PR
Fermi-Bose mapping for one-dimensional Bose gases
One-dimensional Bose gases are considered, interacting either through the
hard-core potentials or through the contact delta potentials. Interest in these
gases gained momentum because of the recent experimental realization of
quasi-one-dimensional Bose gases in traps with tightly confined radial motion,
achieving the Tonks-Girardeau (TG) regime of strongly interacting atoms. For
such gases the Fermi-Bose mapping of wavefunctions is applicable. The aim of
the present communication is to give a brief survey of the problem and to
demonstrate the generality of this mapping by emphasizing that: (i) It is valid
for nonequilibrium wavefunctions, described by the time-dependent Schr\"odinger
equation, not merely for stationary wavefunctions. (ii) It gives the whole
spectrum of all excited states, not merely the ground state. (iii) It applies
to the Lieb-Liniger gas with the contact interaction, not merely to the TG gas
of impenetrable bosons.Comment: Brief review, Latex file, 15 page
Bose-Fermi variational theory of the BEC-Tonks crossover
A number-conserving hybrid Bose-Fermi variational theory is developed and
applied to investigation of the BEC-Tonks gas crossover in toroidal and long
cylindrical traps of high aspect ratio, where strong many-body correlations and
condensate depletion occur.Comment: 4 pages RevTeX including 2 figures, uses epsfig. Submitted to Phys.
Rev. Let
Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance
In a recent article [M. Olshanii, Phys. Rev. Lett. {\bf 81}, 938 (1998)], an
analytic solution of atom-atom scattering with a delta-function pseudopotential
interaction in the presence of transverse harmonic confinement yielded an
effective coupling constant that diverged at a `confinement induced resonance.'
In the present work, we report numerical results that corroborate this
resonance for more realistic model potentials. In addition, we extend the
previous theoretical discussion to include two-atom bound states in the
presence of transverse confinement, for which we also report numerical results
hereComment: New version with major revisions. We now provide a detailed physical
interpretation of the confinement-induced resonance in tight atomic
waveguide
Two-boson Correlations in Various One-dimensional Traps
A one-dimensional system of two trapped bosons which interact through a
contact potential is studied using the optimized configuration interaction
method. The rapid convergence of the method is demonstrated for trapping
potentials of convex and non-convex shapes. The energy spectra, as well as
natural orbitals and their occupation numbers are determined in function of the
inter-boson interaction strength. Entanglement characteristics are discussed in
dependence on the shape of the confining potential.Comment: 5 pages, 3 figure
Pfaffian-like ground state for 3-body-hard-core bosons in 1D lattices
We propose a Pfaffian-like Ansatz for the ground state of bosons subject to
3-body infinite repulsive interactions in a 1D lattice. Our Ansatz consists of
the symmetrization over all possible ways of distributing the particles in two
identical Tonks-Girardeau gases. We support the quality of our Ansatz with
numerical calculations and propose an experimental scheme based on mixtures of
bosonic atoms and molecules in 1D optical lattices in which this Pfaffian-like
state could be realized. Our findings may open the way for the creation of
non-abelian anyons in 1D systems
Commensurate-incommensurate transition of cold atoms in an optical lattice
An atomic gas subject to a commensurate periodic potential generated by an
optical lattice undergoes a superfluid--Mott insulator transition. Confining a
strongly interacting gas to one dimension generates an instability where an
arbitrary weak potential is sufficient to pin the atoms into the Mott state;
here, we derive the corresponding phase diagram. The commensurate pinned state
may be detected via its finite excitation gap and the Bragg peaks in the static
structure factor.Comment: 4 pages, 2 figure
Bose-Einstein Condensation in Geometrically Deformed Tubes
We show that Bose-Einstein condensate can be created in quasi-one-dimensional
systems in a purely geometrical way, namely by bending or other suitable
deformation of a tube.Comment: RevTex, 4pages, no figure
Ground-state properties of one-dimensional anyon gases
We investigate the ground state of the one-dimensional interacting anyonic
system based on the exact Bethe ansatz solution for arbitrary coupling constant
() and statistics parameter (). It
is shown that the density of state in quasi-momentum space and the ground
state energy are determined by the renormalized coupling constant . The
effect induced by the statistics parameter exhibits in the momentum
distribution in two aspects: Besides the effect of renormalized coupling, the
anyonic statistics results in the nonsymmetric momentum distribution when the
statistics parameter deviates from 0 (Bose statistics) and
(Fermi statistics) for any coupling constant . The momentum distribution
evolves from a Bose distribution to a Fermi one as varies from 0 to
. The asymmetric momentum distribution comes from the contribution of the
imaginary part of the non-diagonal element of reduced density matrix, which is
an odd function of . The peak at positive momentum will shift to
negative momentum if is negative.Comment: 6 pages, 5 figures, published version in Phys. Rev.
Quasi-one-dimensional Bose gases with large scattering length
Bose gases confined in highly-elongated harmonic traps are investigated over
a wide range of interaction strengths using quantum Monte Carlo techniques. We
find that the properties of a Bose gas under tight transverse confinement are
well reproduced by a 1d model Hamiltonian with contact interactions. We point
out the existence of a unitary regime, where the properties of the quasi-1d
Bose gas become independent of the actual value of the 3d scattering length. In
this unitary regime, the energy of the system is well described by a hard rod
equation of state. We investigate the stability of quasi-1d Bose gases with
positive and negative 3d scattering length.Comment: 5 pages, 3 figure
- …