115 research outputs found
Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
One-dimensional spinor gases with strong delta interaction fermionize and
form a spin chain. The spatial degrees of freedom of this atom chain can be
described by a mapping to spinless noninteracting fermions and the spin degrees
of freedom are described by a spin-chain model with nearest-neighbor
interactions. Here, we compute momentum and occupation-number distributions of
up to 16 strongly interacting spinor fermions and bosons as a function of their
spin imbalance, the strength of an externally applied magnetic field gradient,
the length of their spin, and for different excited states of the multiplet. We
show that the ground-state momentum distributions resemble those of the
corresponding noninteracting systems, apart from flat background distributions,
which extend to high momenta. Moreover, we show that the spin order of the spin
chain---in particular antiferromagnetic spin order---may be deduced from the
momentum and occupation-number distributions of the system. Finally, we present
efficient numerical methods for the calculation of the single-particle
densities and one-body density matrix elements and of the local exchange
coefficients of the spin chain for large systems containing more than 20
strongly interacting particles in arbitrary confining potentials.Comment: See the ancillary files for the Mathematica notebook used to
calculate the results of this paper, the derivation of the formula for the
one-body density matrix elements, given by Eq. (22), and a table with the
local exchange coefficients of up to 60 harmonically trapped particles. A
less efficient method for calculating the exchange coefficients was given in
the 2nd version of this manuscrip
Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
We study ground state properties of spinless, quasi one-dimensional bosons
which are confined in a harmonic trap and interact via repulsive
delta-potentials. We use the exact diagonalization method to analyze the pair
correlation function, as well as the density, the momentum distribution,
different contributions to the energy and the population of single-particle
orbitals in the whole interaction regime. In particular, we are able to trace
the fascinating transition from bosonic to fermi-like behavior in
characteristic features of the momentum distribution which is accessible to
experiments. Our calculations yield quantitative measures for the interaction
strength limiting the mean-field regime on one side and the Tonks-Girardeau
regime on the other side of an intermediate regime.Comment: 5 pages, 5 figure
Dipolar particles in a double-trap confinement: Response to tilting the dipolar orientation
We analyze the microscopic few-body properties of dipolar particles confined
in two parallel quasi-one-dimensional harmonic traps. In particular, we show
that an adiabatic rotation of the dipole orientation about the trap axes can
drive an initially non-localized few-fermion state into a localized state with
strong inter-trap pairing. For an instant, non-adiabatic rotation, however,
localization is inhibited and a highly excited state is reached. This state may
be interpreted as the few-body analog of a super-Tonks-Girardeau state, known
from one-dimensional systems with contact interactions
Effective multi-body induced tunneling and interactions in the Bose-Hubbard model of the lowest dressed band of an optical lattice
We construct the effective lowest-band Bose-Hubbard model incorporating
interaction-induced on-site correlations. The model is based on ladder
operators for local correlated states, which deviate from the usual Wannier
creation and annihilation, allowing for a systematic construction of the most
appropriate single-band low-energy description in the form of the extended
Bose-Hubbard model. A formulation of this model in terms of ladder operators
not only naturally contains the previously found effective multibody
interactions, but also contains multibody-induced single-particle tunneling,
pair tunneling, and nearest-neighbor interaction processes of higher orders. An
alternative description of the same model can be formulated in terms of
occupation-dependent Bose-Hubbard parameters. These multiparticle effects can
be enhanced using Feshbach resonances, leading to corrections which are well
within experimental reach and of significance to the phase diagram of ultracold
bosonic atoms in an optical lattice. We analyze the energy-reduction mechanism
of interacting atoms on a local lattice site and show that this cannot be
explained only by a spatial broadening of Wannier orbitals on a single-particle
level, which neglects correlations.Comment: 16 pages, 6 figure
Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
We present an exact analytical solution of the fundamental system of
quasi-one-dimensional spin-1 bosons with infinite delta-repulsion. The
eigenfunctions are constructed from the wave functions of non-interacting
spinless fermions, based on Girardeau's Fermi-Bose mapping, and from the wave
functions of distinguishable spins. We show that the spinor bosons behave like
a compound of non-interacting spinless fermions and non-interacting
distinguishable spins. This duality is especially reflected in the spin
densities and the energy spectrum. We find that the momentum distribution of
the eigenstates depends on the symmetry of the spin function. Furthermore, we
discuss the splitting of the ground state multiplet in the regime of large but
finite repulsion.Comment: Revised to discuss large but finite interaction
Influence of the particle number on the spin dynamics of ultracold atoms
We study the dependency of the quantum spin dynamics on the particle number in a system of ultracold spin-1 atoms within the single-spatial-mode approximation. We find, for all strengths of the spin-dependent interaction, convergence toward the mean-field dynamics in the thermodynamic limit. The convergence is, however, particularly slow when the spin-changing collisional energy and the quadratic Zeeman energy are equal; that is, deviations between quantum and mean-field spin dynamics may be extremely large under these conditions. Our estimates show that quantum corrections to the mean-field dynamics may play a relevant role in experiments with spinor Bose-Einstein condensates. This is especially the case in the regime of few atoms, which may be accessible in optical lattices. Here, spin dynamics is modulated by a beat note at large magnetic fields due to the significant influence of correlated many-body spin states. © 2010 The American Physical Society
Self-bound many-body states of quasi-one-dimensional dipolar Fermi gases: Exploiting Bose-Fermi mappings for generalized contact interactions
Using a combination of results from exact mappings and from mean-field theory
we explore the phase diagram of quasi-one-dimensional systems of identical
fermions with attractive dipolar interactions. We demonstrate that at low
density these systems provide a realization of a single-component
one-dimensional Fermi gas with a generalized contact interaction. Using an
exact duality between one-dimensional Fermi and Bose gases, we show that when
the dipole moment is strong enough, bound many-body states exist, and we
calculate the critical coupling strength for the emergence of these states. At
higher densities, the Hartree-Fock approximation is accurate, and by combining
the two approaches we determine the structure of the phase diagram. The
many-body bound states should be accessible in future experiments with
ultracold polar molecules
Two ultracold atoms in a completely anisotropic trap
As a limiting case of ultracold atoms trapped in deep optical lattices, we
consider two interacting atoms trapped in a general anisotropic harmonic
oscillator potential, and obtain exact solutions of the Schrodinger equation
for this system. The energy spectra for different geometries of the trapping
potential are compared.Comment: 4 pages, 2 figure
Heteronuclear molecules in an optical lattice: Theory and experiment
We study properties of two different atoms at a single optical lattice site
at a heteronuclear atomic Feshbach resonance. We calculate the energy spectrum,
the efficiency of rf association and the lifetime as a function of magnetic
field and compare the results with the experimental data obtained for K-40 and
Rb-87 [C. Ospelkaus et al., Phys. Rev. Lett. 97, 120402 (2006)]. We treat the
interaction in terms of a regularized delta function pseudopotential and
consider the general case of particles with different trap frequencies, where
the usual approach of separating center-of-mass and relative motion fails. We
develop an exact diagonalization approach to the coupling between
center-of-mass and relative motion and numerically determine the spectrum of
the system. At the same time, our approach allows us to treat the anharmonicity
of the lattice potential exactly. Within the pseudopotential model, the center
of the Feshbach resonance can be precisely determined from the experimental
data.Comment: 9 pages, 7 figures, revised discussion of transfer efficienc
- …