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DEVELOPMENT OF THEORETICAL AND COMPUTATIONAL METHODS FOR FEW-BODY PROCESSES IN ULTRACOLD QUANTUM GASES
Title
DEVELOPMENT OF THEORETICAL AND COMPUTATIONAL METHODS FOR FEW-BODY PROCESSES IN ULTRACOLD QUANTUM GASES.
Creator
Blandon, Juan, Kokoouline, Viatcheslav, University of Central Florida
Abstract / Description
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...
Show moreWe 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.
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Date Issued
2006
Identifier
CFE0001320, ucf:47026
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001320
DEVELOPMENT OF THEORETICAL AND COMPUTATIONAL METHODS FOR THREE-BODY PROCESSES
Title
DEVELOPMENT OF THEORETICAL AND COMPUTATIONAL METHODS FOR THREE-BODY PROCESSES.
Creator
Blandon Zapata, Juan, Kokoouline, Viatcheslav, University of Central Florida
Abstract / Description
This thesis discusses the development and application of theoretical and computational methods to study three-body processes. The main focus is on the calculation of three-body resonances and bound states. This broadly includes the study of Efimov states and resonances, three-body shape resonances, three-body Feshbach resonances, three-body pre-dissociated states in systems with a conical intersection, and the calculation of three-body recombination rate coefficients. The method was applied...
Show moreThis thesis discusses the development and application of theoretical and computational methods to study three-body processes. The main focus is on the calculation of three-body resonances and bound states. This broadly includes the study of Efimov states and resonances, three-body shape resonances, three-body Feshbach resonances, three-body pre-dissociated states in systems with a conical intersection, and the calculation of three-body recombination rate coefficients. The method was applied to a number of systems. A chapter of the thesis is dedicated to the related study of deriving correlation diagrams for three-body states before and after a three-body collision. More specifically, the thesis discusses the calculation of the H+H+H three-body recombination rate coefficient using the developed method. Additionally, we discuss a conceptually simple and effective diabatization procedure for the calculation of pre-dissociated vibrational states for a system with a conical intersection. We apply the method to H_3, where the quantum molecular dynamics are notoriously difficult and where non-adiabatic couplings are important, and a correct description of the geometric phase associated with the diabatic representation is crucial for an accurate representation of these couplings. With our approach, we were also able to calculate Efimov-type resonances. The calculations of bound states and resonances were performed by formulating the problem in hyperspherical coordinates, and obtaining three-body eigenstates and eigen-energies by applying the hyperspherical adiabatic separation and the slow variable discretization. We employed the complex absorbing potential to calculate resonance energies and lifetimes, and introduce an uniquely defined diabatization procedure to treat X_3 molecules with a conical intersection. The proposed approach is general enough to be applied to problems in nuclear, atomic, molecular and astrophysics.
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Date Issued
2009
Identifier
CFE0002669, ucf:48225
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0002669