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arXiv:0907.5523 · Physical Review Letters

Atom-Dimer Scattering and Long-Lived Trimers in Fermionic Mixtures

Jesper Levinsen, T. G. Tiecke, Jook T. M. Walraven, Dmitry S. Petrov

Published Oct 9, 2009• 91 citations
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Abstract

We consider a heteronuclear fermionic mixture on the molecular side of an interspecies Feshbach resonance and discuss atom-dimer scattering properties in uniform space and in the presence of an external confining potential, restricting the system to a quasi-two-dimensional geometry. We find that there is a peculiar atom-dimer p-wave resonance which can be tuned by changing the frequency of the confinement. Our results have implications for the ongoing experiments on lithium-potassium mixtures, where this mechanism allows for switching the p-wave interaction between a K atom and Li-K dimer from attractive to repulsive, and forming a weakly bound trimer with unit angular momentum. We show that such trimers are long lived and the atom-dimer resonance does not enhance inelastic relaxation in the mixture, making it an outstanding candidate for studies of p-wave resonance effects in a many-body system.

DOI
10.1103/physrevlett.103.153202

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We consider a heteronuclear fermionic mixture on the molecular side of an interspecies Feshbach resonance and discuss atom-dimer scattering properties in uniform space and in the presence of an external confining potential, restricting the system to a quasi-two-dimensional geometry. We find that there is a peculiar atom-dimer p-wave resonance which can be tuned by changing the frequency of the confinement. Our results have implications for the ongoing experiments on lithium-potassium mixtures, where this mechanism allows for switching the p-wave interaction between a K atom and Li-K dimer from attractive to repulsive, and forming a weakly bound trimer with unit angular momentum. We show that such trimers are long lived and the atom-dimer resonance does not enhance inelastic relaxation in the mixture, making it an outstanding candidate for studies of p-wave resonance effects in a many-body system.
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 the problem of three distinguishable fermions confined to a quasi-two-dimensional (quasi-2D) geometry, where there is a strong harmonic potential in one direction. We go beyond previous theoretical work and investigate the three-body bound states (trimers) for the case where the two-body short-range interactions between fermions are unequal. Using the scattering parameters from experiments on ultracold 6Li^{6}\mathrm{Li}6Li atoms, we calculate the trimer spectrum throughout the crossover from two to three dimensions. We find that the deepest Efimov trimer in the 6Li^{6}\mathrm{Li}6Li system is unaffected by realistic quasi-2D confinements, while the first excited trimer smoothly evolves from a three-dimensional-like Efimov trimer to an extended 2D-like trimer as the attractive interactions are decreased. We furthermore compute the excited trimer wave function and quantify the stability of the trimer against decay into a dimer and an atom by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry, thus opening the door to realizing long-lived trimers in three-component Fermi gases.
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 solve the three-body problem of a quasi-one-dimensional ultracold Fermi gas with parabolic confinement length a (perpendicular) and 3D scattering length a. On the two-body level, there is a Feshbach-type resonance at a (perpendicular)/a approximately 1.46, and a dimer state for arbitrary a (perpendicular)/a. The three-body problem is shown to be universal, and described by the atom-dimer scattering length a(ad) and a range parameter b(ad). In the dimer limit a (perpendicular)/a>>1, we find a repulsive zero-range atom-dimer interaction. For a (perpendicular)/a<<-1, however, the potential has long range, with a(ad)>0 and b(ad)>>a(ad). There is no trimer state, and despite a(ad)=0 at a( perpendicular)/a approximately 2.6, there is no resonance enhancement of the interaction.
We consider two-dimensional weakly bound heterospecies molecules formed in a Fermi-Bose mixture with attractive Fermi-Bose and repulsive Bose-Bose interactions. Bosonic exchanges lead to an intermolecular attraction, which can be controlled and tuned to a p-wave resonance. Such attractive fermionic molecules can be realized in quasi-two-dimensional ultracold isotopic mixtures. We show that they are stable with respect to the recombination to deeply bound molecular states and with respect to the formation of higher-order clusters (trimers, tetramers, etc.).
We investigate a mixture of ultracold fermionic K40 atoms and weakly bound Li6K40 dimers on the repulsive side of a heteronuclear atomic Feshbach resonance. By radio-frequency spectroscopy we demonstrate that the normally repulsive atom-dimer interaction is turned into a strong attraction. The phenomenon can be understood as a three-body effect in which two heavy K40 fermions exchange the light Li6 atom, leading to attraction in odd partial-wave channels (mainly p wave). Our observations show that mass imbalance in a fermionic system can profoundly change the character of interactions as compared to the well-established mass-balanced case.