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Register a new userUniversal nature and finite-range corrections in elastic atom-dimer scattering below the dimer breakup threshold
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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 $kappa_*$.
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The universal aspects of atom-dimer elastic collisions are investigated within the framework of Faddeev equations. The two-body interactions between the neutral atoms are approximated by the separable potential approach. Our analysis considers a pure van der Waals potential tail as well as soft-core van der Waals interactions permitting us in this manner to address the universally general features of atom-dimer resonant spectra. In particular, we show that the atom-dimer resonances are solely associated with the {it excited} Efimov states. Furthermore, the positions of the corresponding resonances for a soft-core potentials with more than 5 bound states are in good agreement with the corresponding results from an infinitely deep pure van der Waals tail potential.
We show that, near a Feshbach resonance, a strong p-wave resonance is present at low energy in atom-dimer scattering for $^6$Li-$^{40}$K fermionic mixtures. This resonance is due to a virtual bound state, in the atom-dimer system, which is present at this low energy. When the mass ratio between the two fermionic elements is increased, this virtual bound state goes to a known real bound state which appears when the mass ratio reaches 8.17. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the equation of state of balanced mixtures at moderate or high temperature. The frequency and the damping of collective modes should also provide a convenient way to evidence this resonance. Finally it should be possible to modify the effective mass of one the fermionic species by making use of an optical lattice. This would allow to study the strong dependence of the resonance as a function of the mass ratio of the two fermionic elements.
We report on the observation of an elementary exchange process in an optically trapped ultracold sample of atoms and Feshbach molecules. We can magnetically control the energetic nature of the process and tune it from endoergic to exoergic, enabling the observation of a pronounced threshold behavior. In contrast to relaxation to more deeply bound molecular states, the exchange process does not lead to trap loss. We find excellent agreement between our experimental observations and calculations based on the solutions of three-body Schrodinger equation in the adiabatic hyperspherical representation. The high efficiency of the exchange process is explained by the halo character of both the initial and final molecular states.
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 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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