460 research outputs found
Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
A generalized Fermi-Bose mapping method is used to determine the exact ground
states of several models of mixtures of strongly interacting ultracold gases in
tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D
Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D
spin-aligned Fermi gas with infinitely strong zero-range attractions). We
detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and
boson-fermion (BF) interactions. Exact results are given for density profiles
in a harmonic trap, single-particle density matrices, momentum distributions,
and density-density correlations. Since the ground state is highly degenerate,
we analyze the splitting of the ground manifold for large but finite BB and BF
repulsions.Comment: Revised to discuss splitting of degenerate ground manifold for large
but finite BB and BF repulsions; accepted by PR
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
Bosonization, Pairing, and Superconductivity of the Fermionic Tonks-Girardeau Gas
We determine some exact static and time-dependent properties of the fermionic
Tonks-Girardeau (FTG) gas, a spin-aligned one-dimensional Fermi gas with
infinitely strongly attractive zero-range odd-wave interactions. We show that
the two-particle reduced density matrix exhibits maximal off-diagonal
long-range order, and on a ring an FTG gas with an even number of atoms has a
highly degenerate ground state with quantization of Coriolis rotational flux
and high sensitivity to rotation and to external fields and accelerations. For
a gas initially under harmonic confinement we show that during an expansion the
momentum distribution undergoes a "dynamical bosonization", approaching that of
an ideal Bose gas without violating the Pauli exclusion principle.Comment: v3: 4 pages, 2 figures, revtex4. Section on the fermionic TG gas on a
ring revised, emphasizing degeneracy of ground state for even N and resultant
high sensitivity to external fields. Submitted to PR
Interference of a Tonks-Girardeau Gas on a Ring
We study the quantum dynamics of a one-dimensional gas of impenetrable bosons
on a ring, and investigate the interference that results when an initially
trapped gas localized on one side of the ring is released, split via an
optical-dipole grating, and recombined on the other side of the ring. Large
visibility interference fringes arise when the wavevector of the optical dipole
grating is larger than the effective Fermi wavevector of the initial gas.Comment: 7 pages, 3 figure
Three-dimensional quasi-Tonks gas in a harmonic trap
We analyze the macroscopic dynamics of a Bose gas in a harmonic trap with a
superimposed two-dimensional optical lattice, assuming a weak coupling between
different lattice sites. We consider the situation in which the local chemical
potential at each lattice site can be considered as that provided by the
Lieb-Liniger solution. Due to the weak coupling between sites and the form of
the chemical potential, the three-dimensional ground-state density profile and
the excitation spectrum acquire remarkable properties different from both 1D
and 3D gases. We call this system a quasi-Tonks gas. We discuss the range of
applicability of this regime, as well as realistic experimental situations
where it can be observed.Comment: 4 pages, 3 figures, misprints correcte
Low-density, one-dimensional quantum gases in a split trap
We investigate degenerate quantum gases in one dimension trapped in a
harmonic potential that is split in the centre by a pointlike potential. Since
the single particle eigenfunctions of such a system are known for all strengths
of the central potential, the dynamics for non-interacting fermionic gases and
low-density, strongly interacting bosonic gases can be investigated exactly
using the Fermi-Bose mapping theorem. We calculate the exact many-particle
ground-state wave-functions for both particle species, investigate soliton-like
solutions, and compare the bosonic system to the well-known physics of Bose
gases described by the Gross-Pitaevskii equation. We also address the
experimentally important questions of creation and detection of such states.Comment: 7 pages, 5 figure
Super Tonks-Girardeau state in an attractive one-dimensional dipolar gas
The ground state of a one-dimensional (1D) quantum gas of dipoles oriented
perpendicular to the longitudinal axis, with a strong 1/x^3 repulsive
potential, is studied at low 1D densities . Near contact the dependence of
the many-body wave function on the separation x_{jl} of two particles reduces
to a two-body wave function \Psi_{rel}(x_{jl}). Immediately after a sudden
rotation of the dipoles so that they are parallel to the longitudinal axis,
this wave function will still be that of the repulsive potential, but since the
potential is now that of the attractive potential, it will not be stationary.
It is shown that as nd^2 -> 0 the rate of change of this wave function
approaches zero. It follows that for small values of nd^2, this state is
metastable and is an analog of the super Tonks-Girardeau state of bosons with a
strong zero-range attraction. The dipolar system is equivalent to a spinor
Fermi gas with spin components \sigma_{\uparrow}=\perp (perpendicular to
the longitudinal axis) and \sigma_{\downarrow}=|| (parallel to the longitudinal
axis). A Fermi-Fermi mapping from spinor to spinless Fermi gas followed by the
standard 1960 Fermi-Bose mapping reduces the Fermi system to a Bose gas.
Potential experiments realizing the sudden spin rotation with ultracold dipolar
gases are discussed, and a few salient properties of these states are
accurately evaluated by a Monte Carlo method.Comment: 5 pages, 2 figures, revtex4. Published versio
One-dimensional non-interacting fermions in harmonic confinement: equilibrium and dynamical properties
We consider a system of one-dimensional non-interacting fermions in external
harmonic confinement. Using an efficient Green's function method we evaluate
the exact profiles and the pair correlation function, showing a direct
signature of the Fermi statistics and of the single quantum-level occupancy. We
also study the dynamical properties of the gas, obtaining the spectrum both in
the collisionless and in the collisional regime. Our results apply as well to
describe a one-dimensional Bose gas with point-like hard-core interactions.Comment: 11 pages, 5 figure
Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime
Recent experiments on ultracold atomic alkali gases in a one-dimensional
optical lattice have demonstrated the transition from a gas of soft-core bosons
to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons
behave like fermions in many respects. We have studied the underlying many-body
physics through numerical simulations which accommodate both the soft-core and
hard-core limits in one single framework. We find that the Tonks-Girardeau gas
is reached only at the strongest optical lattice potentials. Results for
slightly higher densities, where the gas develops a Mott-like phase already at
weaker optical lattice potentials, show that these Mott-like short range
correlations do not enhance the convergence to the hard-core limit.Comment: 4 pages, 3 figures, replaced with published versio
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
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