37 research outputs found

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

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    The energy spectrum, atom-dimer scattering length, and atom-trimer scattering length for systems of three and four ultracold atoms with δ\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

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    We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with δ\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: mL/mHm_{\text{L}}/m_{\text{H}}, and ratio gHH/gHLg_{\text{HH}}/g_{\text{HL}} of the δ\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 (gHHg_{\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

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    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

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    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

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    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 Schrödinger 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 Κ 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

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    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 ss-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

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    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

    Efimov States Embedded in the Three-Body Continuum

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    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
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