A new method for calculation of Efimov resonances

A. C. Fonseca, Edward F. Redish, Paul E. Shanley

S. Jonsell

The recent experimental results showing the existence of an Efimov state (Kraemer T. et al. , Nature , 440 (2006) 315) are used to fix the three-body parameter for cesium. With the value of this parameter known, several three-body properties can be calculated quantitatively, without any other information about the boson-boson interaction. Finite-temperature results for the rate of formation of dimers are found to agree very well with the experimental results. Properties of bound Efimov states and predissociative Efimov resonances are calculated. The lifetime of the predissociative resonances are calculated using the complex coordinate rotation method. For Efimov states confined by an external harmonic potential there are significant changes to both energies and lifetimes if the oscillator length is comparable to or smaller than the two-body scattering length.

Matteo Zaccanti, Benjamin Deissler, Chiara D’Errico +6 more

Juan Blandón

We are developing theoretical and computational methods to study two related three-body processes in ultracold quantum gases: three-body resonances and three-body recombination. Three-body recombination causes the ultracold gas to heat up and atoms to leave the trap where they are confined. Therefore, it is an undesirable effect in the process of forming ultracold quantum gases. Metastable three-body states (resonances) are formed in the ultracold gas. When decaying they also give additional kinetic energy to the gas, that leads to the heating too. In addition, a reliable method to obtain three-body resonances would be useful in a number of problems in other fields of physics, for example, in models of metastable nuclei or to study dissociative recombination of H3 +. Our project consists of employing computer modeling to develop a method to obtain three-body resonances. The method uses a novel two-step diagonalization approach to solve the three-body Schrödinger equation. The approach employs the SVD method of Tolstikhin et al. coupled with a complex absorbing potential. We tested this method on a model system of three identical bosons with nucleon mass and compared it to the results of a previous study. This model can be employed to understand the 3He nucleus . We found one three-body bound state and four resonances. We are also studying Efimov resonances using a 4He-based model. In a system of identical spinless bosons, Efimov states are a series of loosely bound three-body states which begin to appear as the energy of the two-body bound state approaches zero . Although they were predicted 35 years ago, recent evidence of Efimov states found by Kraemer et al. in a gas of ultracold Cs atoms has sparked great interest by theorists and experimentalists. Efimov resonances are a kind of pre-dissociated Efimov trimer. To search for Efimov resonances we tune the diatom interaction potential, V(r): V(r) → λV(r) as Esry et al. did . We calculated the first two values of λ for which there is a "condensation" (infinite number) of Efimov states. They are λEfimov1 = 0.9765 and λEfimov2 = 6.834. We performed calculations for λ = 2.4, but found no evidence of Efimov resonances. For future work we plan to work with λ ≈ 4 and λ ≈ λEfimov2 where we might see d-wave and higher l-wave Efimov resonances. There is also a many-body project that forms part of this thesis and consists of a direct diagonalization of the Bogolyubov Hamiltonian, which describes elementary excitations of a gas of bosons interacting through a pairwise interaction. We would like to reproduce the corresponding energy spectrum. So far we have performed several convergence tests, but have not observed the desired energy spectrum. We show preliminary results.

Yusuke Nishida

Elena A. Kolganova, Alexander Konstantinovich Motovilov

A mechanism of disappearance and formation of the Efimov levels of the helium ^4He trimer is studied when the force of the interatomic interaction is changed. It is shown that these levels arise from virtual levels which are in turn formed from (quasi)resonances settled on the real axis. The resonances including virtual levels are calculated by the method based on the solution of the boundary value problem, at complex energies, for the Faddeev differential equations describing the scattering processes (2+1\to 2+1; 1+1+1). All the calculations are performed with the known interatomic Aziz He-He potential HFD-B. A very strong repulsive component of this potential at short distances between helium atoms is approximated by a hard core. A special attention is paid to the substantiation of the method used for computing resonances and to the investigation of its applicability range.