47 research outputs found

### Theory of spinor Fermi and Bose gases in tight atom waveguides

Divergence-free pseudopotentials for spatially even and odd-wave interactions
in spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bose
mapping method is used to relate the effectively one-dimensional fermionic
many-body problem to that of a spinor Bose gas. Depending on the relative
magnitudes of the even and odd-wave interactions, the N-atom ground state may
have total spin S=0, S=N/2, and possibly also intermediate values, the case
S=N/2 applying near a p-wave Feshbach resonance, where the N-fermion ground
state is space-antisymmetric and spin-symmetric. In this case the fermionic
ground state maps to the spinless bosonic Lieb-Liniger gas. An external
magnetic field with a longitudinal gradient causes a Stern-Gerlach spatial
separation of the corresponding trapped Fermi gas with respect to various
values of $S_z$.Comment: 4+ pages, 1 figure, revtex4. Submitted to PRA. Minor corrections of
typos and notatio

### 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

### 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

### Fermi super-Tonks-Girardeau state for attractive Fermi gases in an optical lattice

We demonstrate that a kind of highly excited state of strongly attractive
Hubbard model, named of Fermi super-Tonks-Girardeau state, can be realized in
the spin-1/2 Fermi optical lattice system by a sudden switch of interaction
from the strongly repulsive regime to the strongly attractive regime. In
contrast to the ground state of the attractive Hubbard model, such a state is
the lowest scattering state with no pairing between attractive fermions. With
the aid of Bethe-ansatz method, we calculate energies of both the Fermi
Tonks-Girardeau gas and the Fermi super-Tonks-Girardeau state of spin-1/2
ultracold fermions and show that both energies approach to the same limit as
the strength of the interaction goes to infinity. By exactly solving the quench
dynamics of the Hubbard model, we demonstrate that the Fermi
super-Tonks-Girardeau state can be transferred from the initial repulsive
ground state very efficiently. This allows the experimental study of properties
of Fermi super-Tonks-Girardeau gas in optical lattices.Comment: 7 pages, 7 figure

### Effective interactions, Fermi-Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides

Derivation of effective zero-range one-dimensional (1D) interactions between
atoms in tight waveguides is reviewed, as is the Fermi-Bose mapping method for
determination of exact and strongly-correlated states of ultracold bosonic and
fermionic atomic vapors in such waveguides, including spin degrees of freedom.
Odd-wave 1D interactions derived from 3D p-wave scattering are included as well
as the usual even-wave interactions derived from 3D s-wave scattering, with
emphasis on the role of 3D Feshbach resonances for selectively enhancing s-wave
or p-wave interactions. A duality between 1D fermions and bosons with
zero-range interactions suggested by Cheon and Shigehara is shown to hold for
the effective 1D dynamics of a spinor Fermi gas with both even and odd-wave
interactions and that of a spinor Bose gas with even and odd-wave interactions,
with even(odd)-wave Bose coupling constants inversely related to odd(even)-wave
Fermi coupling constants. Some recent applications of Fermi-Bose mapping to
determination of many-body ground states of Bose gases and of both magnetically
trapped, spin-aligned and optically trapped, spin-free Fermi gases are
described, and a new generalized Fermi-Bose mapping is used to determine the
phase diagram of ground-state total spin of the spinor Fermi gas as a function
of the even and odd-wave coupling constants.Comment: 16 pages, 3 figures. Submitted to Optics Communications for special
issue "Degenerate Quantum Gases

### Violation of self-similarity in the expansion of a 1D Bose gas

The expansion of a 1D Bose gas is investigated employing the Lieb-Liniger
equation of state within the local density approximation. We show that during
the expansion the density profile of the gas does not follow a self-similar
solution, as one would expect from a simple scaling Ansatz. We carry out a
variational calculation, which recovers the numerical results for the
expansion, the equilibrium properties of the density profile, and the frequency
of the lowest compressional mode. The variational approach allows for the
analysis of the expansion in all interaction regimes between the mean field and
the Tonks-Girardeau limits, and in particular shows the range of parameters for
which the expansion violates self-similarity.Comment: 6 pages, 5 eps figure

### Temperature dependence of density profiles for a cloud of non-interacting fermions moving inside a harmonic trap in one dimension

We extend to finite temperature a Green's function method that was previously
proposed to evaluate ground-state properties of mesoscopic clouds of
non-interacting fermions moving under harmonic confinement in one dimension. By
calculations of the particle and kinetic energy density profiles we illustrate
the role of thermal excitations in smoothing out the quantum shell structure of
the cloud and in spreading the particle spill-out from quantum tunnel at the
edges. We also discuss the approach of the exact density profiles to the
predictions of a semiclassical model often used in the theory of confined
atomic gases at finite temperature.Comment: 7 pages, 4 figure

### Momentum flux density, kinetic energy density and their fluctuations for one-dimensional confined gases of non-interacting fermions

We present a Green's function method for the evaluation of the particle
density profile and of the higher moments of the one-body density matrix in a
mesoscopic system of N Fermi particles moving independently in a linear
potential. The usefulness of the method is illustrated by applications to a
Fermi gas confined in a harmonic potential well, for which we evaluate the
momentum flux and kinetic energy densities as well as their quantal mean-square
fluctuations. We also study some properties of the kinetic energy functional
E_{kin}[n(x)] in the same system. Whereas a local approximation to the kinetic
energy density yields a multi-valued function, an exact single-valued
relationship between the density derivative of E_{kin}[n(x)] and the particle
density n(x) is demonstrated and evaluated for various values of the number of
particles in the system.Comment: 10 pages, 5 figure

### The Bogoliubov Theory of a BEC in Particle Representation

In the number-conserving Bogoliubov theory of BEC the Bogoliubov
transformation between quasiparticles and particles is nonlinear. We invert
this nonlinear transformation and give general expression for eigenstates of
the Bogoliubov Hamiltonian in particle representation. The particle
representation unveils structure of a condensate multiparticle wavefunction. We
give several examples to illustrate the general formalism.Comment: 10 pages, 9 figures, version accepted for publication in Phys. Rev.

### Highly anisotropic Bose-Einstein condensates: crossover to lower dimensionality

We develop a simple analytical model based on a variational method to explain
the properties of trapped cylindrically symmetric Bose-Einstein condensates
(BEC) of varying degrees of anisotropy well into regimes of effective one
dimension (1D) and effective two dimension (2D). Our results are accurate in
regimes where the Thomas-Fermi approximation breaks down and they are shown to
be in agreement with recent experimental data.Comment: 4 pages, 2 figures; significantly more new material added; title and
author-list changed due to changes in conten