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arXiv:1703.01147 · Physical Review A

Tetramer bound states in heteronuclear systems

Christiane H. Schmickler, H.‐W. Hammer, Emiko Hiyama

Published May 30, 2017• 9 citations
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Abstract

We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. We focus on the case of one light particle of mass $m$ and two or three heavy bosons of mass $M$ with resonant heavy-light interactions. We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio $M/m$ decreases, the distance between the thresholds for trimer and tetramer states becomes smaller. We also comment on the possibility of observing exotic three-body states consisting of a dimer and two atoms in this region and compare with previous work.

DOI
10.1103/physreva.95.052710

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We calculate the universal spectrum of trimer and tetramer states in heteronuclear mixtures of ultracold atoms with different masses in the vicinity of the heavy-light dimer threshold. To extract the energies, we solve the three- and four-body problem for simple two- and three-body potentials tuned to the universal region using the Gaussian expansion method. We focus on the case of one light particle of mass mmm and two or three heavy bosons of mass MMM with resonant heavy-light interactions. We find that trimer and tetramer cross into the heavy-light dimer threshold at almost the same point and that as the mass ratio M/mM/mM/m decreases, the distance between the thresholds for trimer and tetramer states becomes smaller. We also comment on the possibility of observing exotic three-body states consisting of a dimer and two atoms in this region and compare with previous work.
We study the emergence of universal tetramer and pentamer bound states in the two-dimensional (N+1) system, which consists of N identical heavy fermions interacting with a light atom. We show that the critical heavy-light mass ratio to support a (3+1) tetramer below the trimer threshold is 3.38, and to support a (4+1) pentamer below the tetramer threshold is 5.14. While the ground state tetramer and pentamer are both with zero total angular momentum, they exhibit very different density distributions and correlations in momentum space, due to their distinct angular momentum decompositions in the dimer-fermion frame. These universal bound states can be accessible by a number of Fermi-Fermi mixtures now realized in cold atoms laboratories, which also suggest novel few-body correlations dominant in their corresponding many-body systems.
We consider collisional properties of weakly bound heteronuclear molecules (dimers) formed in a two-species mixture of atoms with a large mass difference. We focus on dimers containing light fermionic atoms as they manifest collisional stability due to an effective dimer-dimer repulsion originating from the exchange of the light atoms. In order to solve the dimer-dimer scattering problem we develop a theoretical approach, which provides a physically transparent and quantitative description of this four-atom system in terms of three- and two-body observables. We calculate the elastic scattering amplitude and the rates of inelastic processes such as the trimer formation and the relaxation of dimers into deeply bound molecular states. Irrespective of whether the heavy atoms are bosons or fermions, the inelastic rate can be significantly lower than the rate of elastic collisions. Moreover, the measurement of the inelastic rate which is a four-body observable, can be an efficient and precise tool for determining three-body observables such as the three-body parameter, positions of Efimov states, and their lifetimes.
We consider weakly bound bosonic and fermionic heteronuclear molecules (dimers) in ultracold atomic gases, where the interspecies interaction is characterized by a large positive scattering length. We develop a new theoretical approach to solve the four-body scattering problem, which is valid when the mass ratio between the constituent atoms is sufficiently large. This approach is then used to study elastic and inelastic dimer- dimer scattering processes in the case that the light constituent atoms are fermions, while the heavy atoms can be either fermions or bosons. Due to the Fermi statistics of the light atoms, the heavy atoms experience a strong repulsion at large intermolecular distances. This leads to suppression of the collisional relaxation to universal trimer (Efimov) states and/or deeply bound molecular states. We present the formation rate of Efimov trimers as a function of the three-body parameter for several experimentally interesting systems. The competition between the formation of trimers and relaxation to deeply bound molecules is analyzed, and prospects for future studies of these systems are discussed.
We study few-body problems in mixed dimensions where two or three heavy atoms are trapped individually in parallel one-dimensional tubes or two-dimensional disks and a single light atom travels freely in three dimensions. Using the Born-Oppenheimer approximation, we find three- and four-body bound states for a broad parameter region. Specifically, the existence of trimer and tetramer states persists to the negative scattering length regime, where no two-body bound state is present. As pointed out by Y. Nishida in an earlier work [Phys. Rev. A 82, 011605(R) (2010)], these few-body bound states are stable against three-body recombination due to geometric separation. In addition, we find that the binding energy of the ground trimer and tetramer state reaches its maximum value when the scattering lengths are comparable to the separation between the low-dimensional traps.
We report the observation of a dimer-dimer inelastic collision resonance for ultracold Feshbach molecules made of bosonic sodium and rubidium atoms. This resonance, which we attribute to the crossing of the dimer-dimer threshold with a heteronuclear tetramer state, manifests itself as a pronounced inelastic loss peak of dimers when the interspecies scattering length between the constituent atoms is tuned. Near this resonance, a strong modification of the temperature dependence of the dimer-dimer scattering is observed. Our result provides insight into the heteronuclear four-body system consisting of heavy and light bosons and offers the possibility of investigating ultracold molecules with tunable interactions.
Universal physics manifests in low-energy phenomena over a large array of different systems from nuclear to atomic physics. Here, two interesting aspects of universality are studied using the Gaussian Expansion Method (GEM). This is a variational method that uses products of Gaussians as basis functions. Gaussian potentials are used as a short-range potential. The first aspect is the behaviour close to the dimer + atom breakup threshold of Efimov states and associated universal tetramers in ultra-cold mixtures of alkali atoms. These can be treated as bosons here. It is shown that trimer and tetramer vanish into the threshold at almost the same point. The predictions of effective Efimov states in the vicinity of the dimer + atom breakup threshold are addressed, but the results are inconclusive. The second aspect is the interplay between universal states of up to four bosons and the Coulomb interaction. This is interesting because it opens up nuclear physics to the investigation. First, the effect of the Coulomb interaction on universal states is studied in natural units. This introduces a scale for the Coulomb potential's strength relative to the strength of the short-range Gaussian potential. A generalised Efimov plot of the binding energies of states of charged bosons versus the Coulomb-modified scattering length is shown. This plot illustrates the impact of different relative strengths of the Coulomb potential on universal states. To complement this analysis, the structure is also calculated via root mean square (rms) radius calculations and contour plots. The results are then applied to the excited state of 17 F, which has a proton halo. The binding energy of this state can be reproduced after fixing the effective range of the potential to the physical value. The N α system proved more problematic. It was found that the ground state of 12 C was too deep to be described within the framework used and the highest excited state of 16 O below the 4α breakup threshold proved difficult to describe. I discuss possible reasons for this. In the last part I studied the zero-range limit in the presence of the Coulomb interaction. I show that my results for the dimer and trimer can be rescaled to coincide with the zero-range result. An extrapolation towards the zero-range limit for the tetramer ground state is also presented.