37 research outputs found

### Born-Oppenheimer study of two-component few-particle systems under one-dimensional confinement

The energy spectrum, atom-dimer scattering length, and atom-trimer scattering
length for systems of three and four ultracold atoms with $\delta$-function
interactions in one dimension are presented as a function of the relative mass
ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat
three-body ("HHL") systems of one light and two heavy atoms, as well as
four-body ("HHHL") systems of one light and three heavy atoms. Zero-range
interactions of arbitrary strength are assumed between different atoms, but the
heavy atoms are assumed to be noninteracting among themselves. Both fermionic
and bosonic heavy atoms are considered.Comment: 22 pages, 6 figures. Includes both positive and negative parity cases
for the four-body secto

### Few-Boson Processes in the Presence of an Attractive Impurity under One-Dimensional Confinement

We consider a few-boson system confined to one dimension with a single
distinguishable particle of lesser mass. All particle interactions are modeled
with $\delta$-functions, but due to the mass imbalance the problem is
nonintegrable. Universal few-body binding energies, atom-dimer and atom-trimer
scattering lengths are all calculated in terms of two parameters, namely the
mass ratio: $m_{\text{L}}/m_{\text{H}}$, and ratio
$g_{\text{HH}}/g_{\text{HL}}$ of the $\delta$-function couplings. We
specifically identify the values of these ratios for which the atom-dimer or
atom-trimer scattering lengths vanish or diverge. We identify regions in this
parameter space in which various few-body inelastic process become
energetically allowed. In the Tonks-Girardeau limit ($g_{\text{HH}}\rightarrow
\infty$), our results are relevant to experiments involving trapped fermions
with an impurity atom

### A Model for Scattering with Proliferating Resonances: Many Coupled Square Wells

We present a multichannel model for elastic interactions, comprised of an
arbitrary number of coupled finite square-well potentials, and derive
semi-analytic solutions for its scattering behavior. Despite the model's
simplicity, it is flexible enough to include many coupled short-ranged
resonances in the vicinity of the collision threshold, as is necessary to
describe ongoing experiments in ultracold molecules and lanthanide atoms. We
also introduce a simple, but physically realistic, statistical ensemble for
parameters in this model. We compute the resulting probability distributions of
nearest-neighbor resonance spacings and analyze them by fitting to the Brody
distribution. We quantify the ability of alternative distribution functions,
for resonance spacing and resonance number variance, to describe the crossover
regime. The analysis demonstrates that the multichannel square-well model with
the chosen ensemble of parameters naturally captures the crossover from
integrable to chaotic scattering as a function of closed channel coupling
strength.Comment: 11 pages, 8 figure

### Homonuclear Ultracold Elastic \u3cem\u3es\u3c/em\u3e-wave Collisions of Alkali-Metal Atoms via Multichannel Quantum Defect Theory

Multichannel quantum-defect theory (MQDT) provides a powerful toolkit for describing and understanding collisions of cold alkali-metal atoms. Various MQDT approximations differ primarily in how they characterize the so-called short-ranged K matrix Ksr, which encapsulates the short-ranged physics into a handful of low-energy parameters that exhibit simple and smooth dependence on energy and field. Here, we compare three different methods for computing Ksr for homonuclear collisions of alkali-metal atoms, from lithium to cesium. The MQDT calculations are benchmarked against numerically converged coupled-channels calculations that use a log-derivative propagator out to the asymptotic region. We study how well these approximations reproduce positions of s-wave magnetic Feshbach resonances, comparing with experiment where possible, and identify the limitations of various approximations

### Scattering of Two Particles in a One-Dimensional Lattice

This study concerns the two-body scattering of particles in a one-dimensional periodic potential. A convenient ansatz allows for the separation of center-of-mass and relative motion, leading to a discrete SchrĂśdinger equation in the relative motion that resembles a tight-binding model. A lattice Green\u27s function is used to develop the Lippmann-Schwinger equation, and ultimately derive a multiband scattering Î matrix which is described in detail in the two-band approximation. Two distinct scattering lengths are defined according to the limits of zero relative quasimomentum at the top and bottom edges of the two-body collision band. Scattering resonances occur in the collision band when the energy is coincident with a bound state attached to another higher or lower band. Notably, repulsive on-site interactions in an energetically closed lower band lead to collision resonances in an excited band

### Microscopic derivation of multi-channel Hubbard models for ultracold nonreactive molecules in an optical lattice

Recent experimental advances in the cooling and manipulation of bialkali
dimer molecules have enabled the production of gases of ultracold molecules
that are not chemically reactive. It has been presumed in the literature that
in the absence of an electric field the low-energy scattering of such
nonreactive molecules (NRMs) will be similar to atoms, in which a single
$s$-wave scattering length governs the collisional physics. However, in Ref.
[1], it was argued that the short-range collisional physics of NRMs is much
more complex than for atoms, and that this leads to a many-body description in
terms of a multi-channel Hubbard model. In this work, we show that this
multi-channel Hubbard model description of NRMs in an optical lattice is robust
against the approximations employed in Ref. [1] to estimate its parameters. We
do so via an exact, albeit formal, derivation of a multi-channel resonance
model for two NRMs from an ab initio description of the molecules in terms of
their constituent atoms. We discuss the regularization of this two-body
multi-channel resonance model in the presence of a harmonic trap, and how its
solutions form the basis for the many-body model of Ref. [1]. We also
generalize the derivation of the effective lattice model to include multiple
internal states (e.g., rotational or hyperfine). We end with an outlook to
future research.Comment: 19 pages, 4 figure

### Model for scattering with proliferating resonances: Many coupled square wells

We present a multichannel model for elastic interactions, composed of an arbitrary number of coupled finite square-well potentials, and derive semianalytic solutions for its scattering behavior. Despite the model\u27s simplicity, it is flexible enough to include many coupled short-ranged resonances in the vicinity of the collision threshold, as is necessary to describe ongoing experiments in ultracold molecules and lanthanide atoms. We also introduce a simple but physically realistic statistical ensemble for parameters in this model. We compute the resulting probability distributions of nearest-neighbor resonance spacings and analyze them by fitting to the Brody distribution. We quantify the ability of alternative distribution functions, for resonance spacing and resonance number variance, to describe the crossover regime. The analysis demonstrates that the multichannel square-well model with the chosen ensemble of parameters naturally captures the crossover from integrable to chaotic scattering as a function of closed-channel coupling strength

### EďŹmov States Embedded in the Three-Body Continuum

We present analytical solutions for the three-body problem with multichannel interactions and identify a class of quasibound Efimov states that can be viewed as three-body Fano-Feshbach resonances. Our method employs a multichannel generalization of the Fermi pseudopotential to model low-energy atom-atom interactions near a magnetically tunable Fano-Feshbach resonance. We discuss the conditions under which quasibound Efimov states may be supported and identify the interaction parameters that limit the lifetimes of these states. We speculate that it may be possible to observe these states using spectroscopic methods, perhaps allowing for the measurement of multiple Efimov resonances