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Register a new userCoboson many-body formalism for atom-dimer scattering length
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We use the composite boson (coboson) many-body formalism to tackle scattering lengths for cold fermionic atoms. We show that bound dimers can be taken as elementary entities provided that fermion exchanges between them are treated exactly, as can be done through the coboson formalism. This alternative tool extended to cold atom physics not only makes transparent many-body processes through Shiva diagrams specific to cobosons, but also simplifies calculations. Indeed, the integral equation we derive for the atom-dimer scattering length and solve by restricting the dimer relative motion to the ground state, gives values in remarkable agreement with the exact scattering length values for all fermion mass ratios. This remarkable agreement also holds true for the dimer-dimer scattering length, except for equal fermion masses where our restricted procedure gives a value slightly larger than the accepted one ($0.64a_d$ instead of $0.60a_d$). All this proves that the scattering of a cold-atom dimer with an atom or another dimer is essentially controlled by the dimer relative-motion ground state, a physical result not obvious at first.
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We consider the problem of obtaining the scattering length for a fermion colliding with a dimer, formed from a fermion identical to the incident one and another different fermion. This is done in the universal regime where the range of interactions is short enough so that the scattering length $a$ for non identical fermions is the only relevant quantity. This is the generalization to fermions with different masses of the problem solved long ago by Skorniakov and Ter-Martirosian for particles with equal masses. We solve this problem analytically in the two limiting cases where the mass of the solitary fermion is very large or very small compared to the mass of the two other identical fermions. This is done both for the value of the scattering length and for the function entering the Skorniakov-Ter-Martirosian integral equation, for which simple explicit expressions are obtained.
We study the dimer-dimer scattering length $a_4$ for a two-component Fermi mixture in which the different fermions have different masses $mus$ and $mds$. This is made in the framework of the exact field theoretical method. In the large mass ratio domain the equations are simplified enough to lead to an analytical solution. In particular we link $a_4$ to the fermion-dimer scattering length $a_3$ for the same fermions, and obtain the very simple relation $a_4=a_3/2$. The result $a_4 simeq a_3/2$ is actually valid whatever the mass ratio with quite good precision. As a result we find an analytical expression providing $a_4$ with a fairly good precision for any masses. To dominant orders for large mass ratio it agrees with the literature. We show that, in this large mass ratio domain, the dominant processes are the repeated dimer-dimer Born scatterings, considered earlier by Pieri and Strinati. We conclude that their approximation, of retaining only these processes, is a fairly good one whatever the mass ratio.
Ultracold gases of three distinguishable particles with large scattering lengths are expected to show rich few-body physics related to the Efimov effect. We have created three different mixtures of ultracold 6Li atoms and weakly bound 6Li2 dimers consisting of atoms in three different hyperfine states and studied their inelastic decay via atom-dimer collisions. We have found resonant enhancement of the decay due to the crossing of Efimov-like trimer states with the atom-dimer continuum in one mixture as well as minima of the decay in another mixture, which we interpret as a suppression of exchange reactions of the type |12>+|3> -> |23>+|1>. Such a suppression is caused by interference between different decay paths and demonstrates the possiblity to use Efimov physics to control the rate constants for molecular exchange reactions in the ultracold regime.
We investigate universal behavior in elastic atom-dimer scattering below the dimer breakup threshold calculating the atom-dimer effective-range function $akcotdelta$. Using the He-He system as a reference, we solve the Schrodinger equation for a family of potentials having different values of the two-body scattering length $a$ and we compare our results to the universal zero-range form deduced by Efimov, $akcotdelta=c_1(ka)+c_2(ka)cot[s_0ln(kappa_*a)+phi(ka)]$, for selected values of the three-body parameter $kappa_*$. Using the parametrization of the universal functions $c_1,c_2,phi$ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter $kappa_*$.
We study the collisional properties of an ultracold mixture of cesium atoms and dimers close to a Feshbach resonance near 550G in the regime of positive $s$-wave scattering lengths. We observe an atom-dimer loss resonance that is related to Efimovs scenario of trimer states. The resonance is found at a value of the scattering length that is different from a previous observation at low magnetic fields. This indicates non-universal behavior of the Efimov spectrum for positive scattering lengths. We compare our observations with predictions from effective field theory and with a recent model based on the van der Waals interaction. We present additional measurements on pure atomic samples in order to check for the presence of a resonant loss feature related to an avalanche effect as suggested by observations in other atomic species. We could not confirm the presence of such a feature.
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